Rocksolid Light

Welcome to novaBBS (click a section below)

mail  files  register  newsreader  groups  login

Message-ID:  

Nondeterminism means never having to say you are wrong.


tech / sci.math / Is there an equation for this?

SubjectAuthor
* Is there an equation for this?Dan joyce
+* Re: Is there an equation for this?sergio
|`* Re: Is there an equation for this?Dan joyce
| `* Re: Is there an equation for this?sergio
|  `- Re: Is there an equation for this?Dan joyce
`* Re: Is there an equation for this?Barry Schwarz
 `* Re: Is there an equation for this?Dan joyce
  `* Re: Is there an equation for this?Dan joyce
   +- Re: Is there an equation for this?Chris M. Thomasson
   +* Re: Is there an equation for this?Chris M. Thomasson
   |+* Re: Is there an equation for this?FromTheRafters
   ||`- Re: Is there an equation for this?sergio
   |`- Re: Is there an equation for this?Dan joyce
   +* Re: Is there an equation for this?Barry Schwarz
   |`- Re: Is there an equation for this?sergio
   `* Re: Is there an equation for this?Jim Burns
    `* Re: Is there an equation for this?Dan joyce
     `* Re: Is there an equation for this?sergio
      +- Re: Is there an equation for this?Dan joyce
      `* Re: Is there an equation for this?Jim Burns
       +- Re: Is there an equation for this?Dan joyce
       +* Re: Is there an equation for this?Chris M. Thomasson
       |+- Re: Is there an equation for this?Dan joyce
       |+- Re: Is there an equation for this?sergio
       |`* Re: Is there an equation for this?Phil Carmody
       | `* Re: Is there an equation for this?Dan joyce
       |  `- Re: Is there an equation for this?Oscar Yoshinobu
       `* Re: Is there an equation for this?Mike Terry
        `* Re: Is there an equation for this?Dan joyce
         +* Re: Is there an equation for this?Barry Schwarz
         |`- Re: Is there an equation for this?Dan joyce
         `* Re: Is there an equation for this?Mike Terry
          `* Re: Is there an equation for this?Dan joyce
           +* Re: Is there an equation for this?Mike Terry
           |`- Re: Is there an equation for this?Dan joyce
           `* Re: Is there an equation for this?Barry Schwarz
            `- Re: Is there an equation for this?Dan joyce

Pages:12
Is there an equation for this?

<13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99731&group=sci.math#99731

 copy link   Newsgroups: sci.math
X-Received: by 2002:a0c:f482:0:b0:45a:98a0:ddaf with SMTP id i2-20020a0cf482000000b0045a98a0ddafmr23483162qvm.130.1652304015595;
Wed, 11 May 2022 14:20:15 -0700 (PDT)
X-Received: by 2002:a25:7d86:0:b0:64a:5665:fb48 with SMTP id
y128-20020a257d86000000b0064a5665fb48mr25879546ybc.614.1652304015373; Wed, 11
May 2022 14:20:15 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Wed, 11 May 2022 14:20:15 -0700 (PDT)
Injection-Info: google-groups.googlegroups.com; posting-host=32.221.202.28; posting-account=MMV3OwoAAABxhPndZPNv6CW6-fifDabn
NNTP-Posting-Host: 32.221.202.28
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
Subject: Is there an equation for this?
From: danj4...@gmail.com (Dan joyce)
Injection-Date: Wed, 11 May 2022 21:20:15 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 1590
 by: Dan joyce - Wed, 11 May 2022 21:20 UTC

A rectangular box with e length b=e and c= 2.8599384160105..(diagonal opposed e)and side (a)as the width derived from c^2 - e^2
Then pi^2 - c^2 giving the height of the box (a).
Where pi is the inner space diagonal and also the volume of this box.
e*a(width)* a(height) = pi. Giving the volume of this box.

c=2.8599384160105... was found by brute force.
A truly 2 constants rectangular box. Pi and e.
Pi as the space diagonal and with e length and also giving a pi volume for this rectangular box.
Is there an equation for finding the above c value without using brute force?

Just curious.

Dan

Re: Is there an equation for this?

<t5heb9$1c6f$1@gioia.aioe.org>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99739&group=sci.math#99739

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Wed, 11 May 2022 17:46:01 -0500
Organization: Aioe.org NNTP Server
Message-ID: <t5heb9$1c6f$1@gioia.aioe.org>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: gioia.aioe.org; logging-data="45263"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.9.0
X-Notice: Filtered by postfilter v. 0.9.2
Content-Language: en-US
 by: sergio - Wed, 11 May 2022 22:46 UTC

On 5/11/2022 4:20 PM, Dan joyce wrote:
>
> A rectangular box with e length b=e and c= 2.8599384160105..(diagonal opposed e)and side (a)as the width derived from c^2 - e^2
> Then pi^2 - c^2 giving the height of the box (a).
> Where pi is the inner space diagonal and also the volume of this box.
> e*a(width)* a(height) = pi. Giving the volume of this box.
>
> c=2.8599384160105... was found by brute force.
> A truly 2 constants rectangular box. Pi and e.
> Pi as the space diagonal and with e length and also giving a pi volume for this rectangular box.
> Is there an equation for finding the above c value without using brute force?
>
> Just curious.
>
> Dan
>

yes, use equations.

write them in terms of edges, a, b, c for the length depth and height.

do volume, diagonals, in equations in terms of a,b,c

Re: Is there an equation for this?

<0693f3be-28ef-45ab-afa7-8024fc2bb052n@googlegroups.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99745&group=sci.math#99745

 copy link   Newsgroups: sci.math
X-Received: by 2002:a05:622a:1007:b0:2f3:ce52:25cb with SMTP id d7-20020a05622a100700b002f3ce5225cbmr21448849qte.575.1652311713978;
Wed, 11 May 2022 16:28:33 -0700 (PDT)
X-Received: by 2002:a25:8f90:0:b0:648:84d1:1431 with SMTP id
u16-20020a258f90000000b0064884d11431mr23746919ybl.483.1652311713666; Wed, 11
May 2022 16:28:33 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Wed, 11 May 2022 16:28:33 -0700 (PDT)
In-Reply-To: <t5heb9$1c6f$1@gioia.aioe.org>
Injection-Info: google-groups.googlegroups.com; posting-host=32.221.202.28; posting-account=MMV3OwoAAABxhPndZPNv6CW6-fifDabn
NNTP-Posting-Host: 32.221.202.28
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com> <t5heb9$1c6f$1@gioia.aioe.org>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <0693f3be-28ef-45ab-afa7-8024fc2bb052n@googlegroups.com>
Subject: Re: Is there an equation for this?
From: danj4...@gmail.com (Dan joyce)
Injection-Date: Wed, 11 May 2022 23:28:33 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 2196
 by: Dan joyce - Wed, 11 May 2022 23:28 UTC

On Wednesday, May 11, 2022 at 6:46:14 PM UTC-4, sergio wrote:
> On 5/11/2022 4:20 PM, Dan joyce wrote:
> >
> > A rectangular box with e length b=e and c= 2.8599384160105..(diagonal opposed e)and side (a)as the width derived from c^2 - e^2
> > Then pi^2 - c^2 giving the height of the box (a).
> > Where pi is the inner space diagonal and also the volume of this box.
> > e*a(width)* a(height) = pi. Giving the volume of this box.
> >
> > c=2.8599384160105... was found by brute force.
> > A truly 2 constants rectangular box. Pi and e.
> > Pi as the space diagonal and with e length and also giving a pi volume for this rectangular box.
> > Is there an equation for finding the above c value without using brute force?
> >
> > Just curious.
> >
> > Dan
> >
> yes, use equations.
>
> write them in terms of edges, a, b, c for the length depth and height.
>
> do volume, diagonals, in equations in terms of a,b,c

I tried in Wolfram Alpha but could not produce the value for c above which is key
in solving the puzzle. Any hints?

Re: Is there an equation for this?

<t5ho3a$2ij$1@gioia.aioe.org>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99756&group=sci.math#99756

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Wed, 11 May 2022 20:32:25 -0500
Organization: Aioe.org NNTP Server
Message-ID: <t5ho3a$2ij$1@gioia.aioe.org>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<t5heb9$1c6f$1@gioia.aioe.org>
<0693f3be-28ef-45ab-afa7-8024fc2bb052n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: gioia.aioe.org; logging-data="2643"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.9.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2
 by: sergio - Thu, 12 May 2022 01:32 UTC

On 5/11/2022 6:28 PM, Dan joyce wrote:
> On Wednesday, May 11, 2022 at 6:46:14 PM UTC-4, sergio wrote:
>> On 5/11/2022 4:20 PM, Dan joyce wrote:
>>>
>>> A rectangular box with e length b=e and c= 2.8599384160105..(diagonal opposed e)and side (a)as the width derived from c^2 - e^2
>>> Then pi^2 - c^2 giving the height of the box (a).
>>> Where pi is the inner space diagonal and also the volume of this box.
>>> e*a(width)* a(height) = pi. Giving the volume of this box.
>>>
>>> c=2.8599384160105... was found by brute force.
>>> A truly 2 constants rectangular box. Pi and e.
>>> Pi as the space diagonal and with e length and also giving a pi volume for this rectangular box.
>>> Is there an equation for finding the above c value without using brute force?
>>>
>>> Just curious.
>>>
>>> Dan
>>>
>> yes, use equations.
>>
>> write them in terms of edges, a, b, c for the length depth and height.
>>
>> do volume, diagonals, in equations in terms of a,b,c
>
> I tried in Wolfram Alpha but could not produce the value for c above which is key
> in solving the puzzle. Any hints?

well, no need to use real values like pi and e, assign them later.

so the box has length a, width b, height c so volume is abc

inner space diagional... assuming it goes from one corner to the opposite corner...
that is a right triangle with a side that is the diagional on each of the faces, so the length must be (a^2 + b^2 + c^2)^1/2 right ?

but you are setting the volume = length ??

your units dont match, so your problem is ill defined.

so, solve it all using a,b,c for each edge, and assign e and pi later

Re: Is there an equation for this?

<1b67716c-b540-4a76-a9e7-7835cbe23362n@googlegroups.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99768&group=sci.math#99768

 copy link   Newsgroups: sci.math
X-Received: by 2002:a05:6214:262d:b0:45a:9e7d:d16 with SMTP id gv13-20020a056214262d00b0045a9e7d0d16mr25183479qvb.4.1652326829286;
Wed, 11 May 2022 20:40:29 -0700 (PDT)
X-Received: by 2002:a81:25d8:0:b0:2f7:b72f:8a4a with SMTP id
l207-20020a8125d8000000b002f7b72f8a4amr28016447ywl.103.1652326829038; Wed, 11
May 2022 20:40:29 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!proxad.net!feeder1-2.proxad.net!209.85.160.216.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Wed, 11 May 2022 20:40:28 -0700 (PDT)
In-Reply-To: <t5ho3a$2ij$1@gioia.aioe.org>
Injection-Info: google-groups.googlegroups.com; posting-host=32.221.202.28; posting-account=MMV3OwoAAABxhPndZPNv6CW6-fifDabn
NNTP-Posting-Host: 32.221.202.28
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<t5heb9$1c6f$1@gioia.aioe.org> <0693f3be-28ef-45ab-afa7-8024fc2bb052n@googlegroups.com>
<t5ho3a$2ij$1@gioia.aioe.org>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <1b67716c-b540-4a76-a9e7-7835cbe23362n@googlegroups.com>
Subject: Re: Is there an equation for this?
From: danj4...@gmail.com (Dan joyce)
Injection-Date: Thu, 12 May 2022 03:40:29 +0000
Content-Type: text/plain; charset="UTF-8"
 by: Dan joyce - Thu, 12 May 2022 03:40 UTC

On Wednesday, May 11, 2022 at 9:32:37 PM UTC-4, sergio wrote:
> On 5/11/2022 6:28 PM, Dan joyce wrote:
> > On Wednesday, May 11, 2022 at 6:46:14 PM UTC-4, sergio wrote:
> >> On 5/11/2022 4:20 PM, Dan joyce wrote:
> >>>
> >>> A rectangular box with e length b=e and c= 2.8599384160105..(diagonal opposed e)and side (a)as the width derived from c^2 - e^2
> >>> Then pi^2 - c^2 giving the height of the box (a).
> >>> Where pi is the inner space diagonal and also the volume of this box.
> >>> e*a(width)* a(height) = pi. Giving the volume of this box.
> >>>
> >>> c=2.8599384160105... was found by brute force.
> >>> A truly 2 constants rectangular box. Pi and e.
> >>> Pi as the space diagonal and with e length and also giving a pi volume for this rectangular box.
> >>> Is there an equation for finding the above c value without using brute force?
> >>>
> >>> Just curious.
> >>>
> >>> Dan
> >>>
> >> yes, use equations.
> >>
> >> write them in terms of edges, a, b, c for the length depth and height.
> >>
> >> do volume, diagonals, in equations in terms of a,b,c
> >
> > I tried in Wolfram Alpha but could not produce the value for c above which is key
> > in solving the puzzle. Any hints?
> well, no need to use real values like pi and e, assign them later.
>
>
> so the box has length a, width b, height c so volume is abc
>
> inner space diagional... assuming it goes from one corner to the opposite corner...
> that is a right triangle with a side that is the diagional on each of the faces, so the length must be (a^2 + b^2 + c^2)^1/2 right ?

The diagonal of the length (e) is c where c is the key value to find (a) as the width
c^2- e^2= a^2 = sqrt(a^2) =a and then intern pi^2 - c^2 = sqrt (a1^2) =a1 as the height.
Then e*a1*a = pi as the area.
Where pi is also the inner space diagonal of this rectangular box.
I am just looking for a formula to find c where c is changed to b when pi is the new
c when calculating a1.
Just follow the above and the length= e and the volume = pi when a * a1 *e =pi
and the inner space diagonal =pi
c is the key and I can only brute force the value of c=2.8599384160105196176...
to tie the length (e) *a*a1 =pi as the volume and the inner space diagonal as pi.

a =0.88892724361564582759...
a1 = 1.30013716880819873199...
e*a*a1~pi volume
Pi also as the inner space diagonal.
So finding the value for c diagonal in an equation to satisfy the length (e) and inner space diagonal pi is what I am looking for.

> but you are setting the volume = length ??

No, pi as inner space diagonal and volume are the same.
e is the length
> your units dont match, so your problem is ill defined.
Maybe the above will explain iit better
> so, solve it all using a,b,c for each edge, and assign e and pi later

Re: Is there an equation for this?

<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99796&group=sci.math#99796

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: schwa...@delq.com (Barry Schwarz)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Thu, 12 May 2022 02:50:10 -0700
Organization: A noiseless patient Spider
Lines: 56
Message-ID: <4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
Injection-Info: reader02.eternal-september.org; posting-host="94ac9ee14d0c19bb99da620c2cf044cd";
logging-data="12866"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/WHYoIrtUjzgEpJLgikF7toCKVnNVstCM="
Cancel-Lock: sha1:U0LD9fu/vEXWZVcBTJIDovRY+hk=
X-Newsreader: Forte Agent 4.2/32.1118
 by: Barry Schwarz - Thu, 12 May 2022 09:50 UTC

1On Wed, 11 May 2022 14:20:15 -0700 (PDT), Dan joyce
<danj4084@gmail.com> wrote:

>
>A rectangular box with e length b=e and c= 2.8599384160105..(diagonal opposed e)and side (a)as the width derived from c^2 - e^2
>Then pi^2 - c^2 giving the height of the box (a).
>Where pi is the inner space diagonal and also the volume of this box.
>e*a(width)* a(height) = pi. Giving the volume of this box.
>
>c=2.8599384160105... was found by brute force.
>A truly 2 constants rectangular box. Pi and e.
>Pi as the space diagonal and with e length and also giving a pi volume for this rectangular box.
>Is there an equation for finding the above c value without using brute force?

I assume that by inner space diagonal you mean the diagonal between
opposite corners that happens to pass through he center of the box.

The volume of a rectangular box is given by l * w * h.
The diagonal is given by sqrt(l^2 + w^2 + h^2)

You have told us the volume is pi and the length is e so
pi = e * w * h
which leads to
h = pi / (e*w)

Similarly, the diagonal is also pi so
pi = sqrt(e*2 + w*2 + h^2)
which leads to
pi^2 = e^2 + w*2 + h^2
pi^2 = e^2 + w^2 + (pi/(e*w))^2
pi^2 = e^2 + w^2 + pi^2/(e^2*w^2)
Multiply both sides by w^2 to get
pi^2*w^2 = e^2*w^2 + w^4 + pi^2/e^2
and then move the terms to one side to get
w^4 + (e^2-pi^2)*w^2 + pi^2/e^2 = 0

Let x = w^2 to get
x^2 + (e^2-pi^2)*x + pi^2/e^2 = 0
This is a simple quadratic in x and yields
x = 1.690457 and x = 0.790192
which yields
w = 1.300137 and w = 0.888927

These values of w produce
h = 0.888927 and h = 1.300137
which is not a surprise since we can swap w and h by rotating the box
to lie on a different side.

Plugging these values into the formulas for volume and diagonal
produce the desired results. The value c you are so interested in is
not needed for determining the dimensions of the box. However, once
you have w and h you can compute it easy enough if it serves some
other purpose.

--
Remove del for email

Re: Is there an equation for this?

<51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99829&group=sci.math#99829

 copy link   Newsgroups: sci.math
X-Received: by 2002:a05:620a:4488:b0:6a0:2aab:a736 with SMTP id x8-20020a05620a448800b006a02aaba736mr23880349qkp.717.1652364911373;
Thu, 12 May 2022 07:15:11 -0700 (PDT)
X-Received: by 2002:a25:db8f:0:b0:648:a5e3:e254 with SMTP id
g137-20020a25db8f000000b00648a5e3e254mr27598609ybf.465.1652364911176; Thu, 12
May 2022 07:15:11 -0700 (PDT)
Path: i2pn2.org!i2pn.org!aioe.org!news.mixmin.net!proxad.net!feeder1-2.proxad.net!209.85.160.216.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Thu, 12 May 2022 07:15:10 -0700 (PDT)
In-Reply-To: <4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
Injection-Info: google-groups.googlegroups.com; posting-host=32.221.202.28; posting-account=MMV3OwoAAABxhPndZPNv6CW6-fifDabn
NNTP-Posting-Host: 32.221.202.28
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com> <4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
Subject: Re: Is there an equation for this?
From: danj4...@gmail.com (Dan joyce)
Injection-Date: Thu, 12 May 2022 14:15:11 +0000
Content-Type: text/plain; charset="UTF-8"
 by: Dan joyce - Thu, 12 May 2022 14:15 UTC

On Thursday, May 12, 2022 at 5:50:22 AM UTC-4, Barry Schwarz wrote:
> 1On Wed, 11 May 2022 14:20:15 -0700 (PDT), Dan joyce
> <danj...@gmail.com> wrote:
>
> >
> >A rectangular box with e length b=e and c= 2.8599384160105..(diagonal opposed e)and side (a)as the width derived from c^2 - e^2
> >Then pi^2 - c^2 giving the height of the box (a).
> >Where pi is the inner space diagonal and also the volume of this box.
> >e*a(width)* a(height) = pi. Giving the volume of this box.
> >
> >c=2.8599384160105... was found by brute force.
> >A truly 2 constants rectangular box. Pi and e.
> >Pi as the space diagonal and with e length and also giving a pi volume for this rectangular box.
> >Is there an equation for finding the above c value without using brute force?
> I assume that by inner space diagonal you mean the diagonal between
> opposite corners that happens to pass through he center of the box.
>
> The volume of a rectangular box is given by l * w * h.
> The diagonal is given by sqrt(l^2 + w^2 + h^2)
>
> You have told us the volume is pi and the length is e so
> pi = e * w * h
> which leads to
> h = pi / (e*w)
>
> Similarly, the diagonal is also pi so
> pi = sqrt(e*2 + w*2 + h^2)
> which leads to
> pi^2 = e^2 + w*2 + h^2
> pi^2 = e^2 + w^2 + (pi/(e*w))^2
> pi^2 = e^2 + w^2 + pi^2/(e^2*w^2)
> Multiply both sides by w^2 to get
> pi^2*w^2 = e^2*w^2 + w^4 + pi^2/e^2
> and then move the terms to one side to get
> w^4 + (e^2-pi^2)*w^2 + pi^2/e^2 = 0
>
> Let x = w^2 to get
> x^2 + (e^2-pi^2)*x + pi^2/e^2 = 0
> This is a simple quadratic in x and yields
> x = 1.690457 and x = 0.790192
> which yields
> w = 1.300137 and w = 0.888927
>
> These values of w produce
> h = 0.888927 and h = 1.300137
> which is not a surprise since we can swap w and h by rotating the box
> to lie on a different side.
>
> Plugging these values into the formulas for volume and diagonal
> produce the desired results. The value c you are so interested in is
> not needed for determining the dimensions of the box. However, once
> you have w and h you can compute it easy enough if it serves some
> other purpose.
>
> --
> Remove del for email

So my c value that I brute forced calculated is replaced by a different value when
W and H are switched. Which makes h^2 + e^2 giving c^2 a different value and
w^2 +pi^2 that same different value. But the box length and volume is unchanged.

Thanks,
Dan

Re: Is there an equation for this?

<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99869&group=sci.math#99869

 copy link   Newsgroups: sci.math
X-Received: by 2002:a05:622a:6115:b0:2f1:d8fa:84aa with SMTP id hg21-20020a05622a611500b002f1d8fa84aamr1295971qtb.689.1652382978623;
Thu, 12 May 2022 12:16:18 -0700 (PDT)
X-Received: by 2002:a25:d84b:0:b0:649:87d2:5875 with SMTP id
p72-20020a25d84b000000b0064987d25875mr1289404ybg.357.1652382978442; Thu, 12
May 2022 12:16:18 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!proxad.net!feeder1-2.proxad.net!209.85.160.216.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Thu, 12 May 2022 12:16:18 -0700 (PDT)
In-Reply-To: <51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
Injection-Info: google-groups.googlegroups.com; posting-host=32.221.202.28; posting-account=MMV3OwoAAABxhPndZPNv6CW6-fifDabn
NNTP-Posting-Host: 32.221.202.28
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com> <51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
Subject: Re: Is there an equation for this?
From: danj4...@gmail.com (Dan joyce)
Injection-Date: Thu, 12 May 2022 19:16:18 +0000
Content-Type: text/plain; charset="UTF-8"
 by: Dan joyce - Thu, 12 May 2022 19:16 UTC

On Thursday, May 12, 2022 at 10:15:16 AM UTC-4, Dan joyce wrote:
> On Thursday, May 12, 2022 at 5:50:22 AM UTC-4, Barry Schwarz wrote:
> > 1On Wed, 11 May 2022 14:20:15 -0700 (PDT), Dan joyce
> > <danj...@gmail.com> wrote:
> >
> > >
> > >A rectangular box with e length b=e and c= 2.8599384160105..(diagonal opposed e)and side (a)as the width derived from c^2 - e^2
> > >Then pi^2 - c^2 giving the height of the box (a).
> > >Where pi is the inner space diagonal and also the volume of this box.
> > >e*a(width)* a(height) = pi. Giving the volume of this box.
> > >
> > >c=2.8599384160105... was found by brute force.
> > >A truly 2 constants rectangular box. Pi and e.
> > >Pi as the space diagonal and with e length and also giving a pi volume for this rectangular box.
> > >Is there an equation for finding the above c value without using brute force?
> > I assume that by inner space diagonal you mean the diagonal between
> > opposite corners that happens to pass through he center of the box.
> >
> > The volume of a rectangular box is given by l * w * h.
> > The diagonal is given by sqrt(l^2 + w^2 + h^2)
> >
> > You have told us the volume is pi and the length is e so
> > pi = e * w * h
> > which leads to
> > h = pi / (e*w)
> >
> > Similarly, the diagonal is also pi so
> > pi = sqrt(e*2 + w*2 + h^2)
> > which leads to
> > pi^2 = e^2 + w*2 + h^2
> > pi^2 = e^2 + w^2 + (pi/(e*w))^2
> > pi^2 = e^2 + w^2 + pi^2/(e^2*w^2)
> > Multiply both sides by w^2 to get
> > pi^2*w^2 = e^2*w^2 + w^4 + pi^2/e^2
> > and then move the terms to one side to get
> > w^4 + (e^2-pi^2)*w^2 + pi^2/e^2 = 0
> >
> > Let x = w^2 to get
> > x^2 + (e^2-pi^2)*x + pi^2/e^2 = 0
> > This is a simple quadratic in x and yields
> > x = 1.690457 and x = 0.790192
> > which yields
> > w = 1.300137 and w = 0.888927
> >
> > These values of w produce
> > h = 0.888927 and h = 1.300137
> > which is not a surprise since we can swap w and h by rotating the box
> > to lie on a different side.
> >
> > Plugging these values into the formulas for volume and diagonal
> > produce the desired results. The value c you are so interested in is
> > not needed for determining the dimensions of the box. However, once
> > you have w and h you can compute it easy enough if it serves some
> > other purpose.
> >
> > --
> > Remove del for email
> So my c value that I brute forced calculated is replaced by a different value when
> W and H are switched. Which makes h^2 + e^2 giving c^2 a different value and
> w^2 +pi^2 that same different value. But the box length and volume is unchanged.
>
> Thanks,
> Dan

Still trying to plug into Wolfram alpha a formula with two known values Length (e)
and volume (pi) and inner space diagonal (pi).
To get width an height.
Anyone?

Re: Is there an equation for this?

<t5jq32$5mp$1@dont-email.me>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99882&group=sci.math#99882

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Thu, 12 May 2022 13:18:40 -0700
Organization: A noiseless patient Spider
Lines: 73
Message-ID: <t5jq32$5mp$1@dont-email.me>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
<51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Thu, 12 May 2022 20:18:42 -0000 (UTC)
Injection-Info: reader02.eternal-september.org; posting-host="e8f791cec9b20cfa31eabc4fb6298e2f";
logging-data="5849"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/9qBStQcwB4AX1uF5R3e16BS/tq+tijTs="
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.9.0
Cancel-Lock: sha1:zwWJMfTg1E05mL6FL1TwAdPCxj0=
In-Reply-To: <3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
Content-Language: en-US
 by: Chris M. Thomasson - Thu, 12 May 2022 20:18 UTC

On 5/12/2022 12:16 PM, Dan joyce wrote:
> On Thursday, May 12, 2022 at 10:15:16 AM UTC-4, Dan joyce wrote:
>> On Thursday, May 12, 2022 at 5:50:22 AM UTC-4, Barry Schwarz wrote:
>>> 1On Wed, 11 May 2022 14:20:15 -0700 (PDT), Dan joyce
>>> <danj...@gmail.com> wrote:
>>>
>>>>
>>>> A rectangular box with e length b=e and c= 2.8599384160105..(diagonal opposed e)and side (a)as the width derived from c^2 - e^2
>>>> Then pi^2 - c^2 giving the height of the box (a).
>>>> Where pi is the inner space diagonal and also the volume of this box.
>>>> e*a(width)* a(height) = pi. Giving the volume of this box.
>>>>
>>>> c=2.8599384160105... was found by brute force.
>>>> A truly 2 constants rectangular box. Pi and e.
>>>> Pi as the space diagonal and with e length and also giving a pi volume for this rectangular box.
>>>> Is there an equation for finding the above c value without using brute force?
>>> I assume that by inner space diagonal you mean the diagonal between
>>> opposite corners that happens to pass through he center of the box.
>>>
>>> The volume of a rectangular box is given by l * w * h.
>>> The diagonal is given by sqrt(l^2 + w^2 + h^2)
>>>
>>> You have told us the volume is pi and the length is e so
>>> pi = e * w * h
>>> which leads to
>>> h = pi / (e*w)
>>>
>>> Similarly, the diagonal is also pi so
>>> pi = sqrt(e*2 + w*2 + h^2)
>>> which leads to
>>> pi^2 = e^2 + w*2 + h^2
>>> pi^2 = e^2 + w^2 + (pi/(e*w))^2
>>> pi^2 = e^2 + w^2 + pi^2/(e^2*w^2)
>>> Multiply both sides by w^2 to get
>>> pi^2*w^2 = e^2*w^2 + w^4 + pi^2/e^2
>>> and then move the terms to one side to get
>>> w^4 + (e^2-pi^2)*w^2 + pi^2/e^2 = 0
>>>
>>> Let x = w^2 to get
>>> x^2 + (e^2-pi^2)*x + pi^2/e^2 = 0
>>> This is a simple quadratic in x and yields
>>> x = 1.690457 and x = 0.790192
>>> which yields
>>> w = 1.300137 and w = 0.888927
>>>
>>> These values of w produce
>>> h = 0.888927 and h = 1.300137
>>> which is not a surprise since we can swap w and h by rotating the box
>>> to lie on a different side.
>>>
>>> Plugging these values into the formulas for volume and diagonal
>>> produce the desired results. The value c you are so interested in is
>>> not needed for determining the dimensions of the box. However, once
>>> you have w and h you can compute it easy enough if it serves some
>>> other purpose.
>>>
>>> --
>>> Remove del for email
>> So my c value that I brute forced calculated is replaced by a different value when
>> W and H are switched. Which makes h^2 + e^2 giving c^2 a different value and
>> w^2 +pi^2 that same different value. But the box length and volume is unchanged.
>>
>> Thanks,
>> Dan
>
> Still trying to plug into Wolfram alpha a formula with two known values Length (e)
> and volume (pi) and inner space diagonal (pi).
> To get width an height.
> Anyone?

Trying to clarify myself here... The height should be the tip (say,
positive y axis) of the right triangle in the diagonal of the box,
right? It needs its hypotenuse to be pi, right?

Re: Is there an equation for this?

<t5jqqm$b0g$1@dont-email.me>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99888&group=sci.math#99888

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Thu, 12 May 2022 13:31:17 -0700
Organization: A noiseless patient Spider
Lines: 15
Message-ID: <t5jqqm$b0g$1@dont-email.me>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
<51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Thu, 12 May 2022 20:31:19 -0000 (UTC)
Injection-Info: reader02.eternal-september.org; posting-host="e8f791cec9b20cfa31eabc4fb6298e2f";
logging-data="11280"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX192u8WCjXABqJRT8TY212K3oH8Swi0RcuE="
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.9.0
Cancel-Lock: sha1:yw2t5tLRB9IGarWwUDFk9tmZfQk=
In-Reply-To: <3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
Content-Language: en-US
 by: Chris M. Thomasson - Thu, 12 May 2022 20:31 UTC

On 5/12/2022 12:16 PM, Dan joyce wrote:
> On Thursday, May 12, 2022 at 10:15:16 AM UTC-4, Dan joyce wrote:
>> On Thursday, May 12, 2022 at 5:50:22 AM UTC-4, Barry Schwarz wrote:
>>> 1On Wed, 11 May 2022 14:20:15 -0700 (PDT), Dan joyce
>>> <danj...@gmail.com> wrote:
[...]
> Still trying to plug into Wolfram alpha a formula with two known values Length (e)
> and volume (pi) and inner space diagonal (pi).
> To get width an height.
> Anyone?

Just a sketch, the dimensions are arbitrary for now. However, you are
talking about the diagonal in the purple line, right? Just to clarify.

https://i.ibb.co/ct8GgZb/ct-pov-music.png

Re: Is there an equation for this?

<t5jrh0$g0o$1@dont-email.me>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99891&group=sci.math#99891

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Thu, 12 May 2022 13:43:06 -0700
Organization: Peripheral Visions
Lines: 21
Message-ID: <t5jrh0$g0o$1@dont-email.me>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com> <4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com> <51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com> <3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com> <t5jqqm$b0g$1@dont-email.me>
Reply-To: erratic.howard@gmail.com
MIME-Version: 1.0
Content-Type: text/plain; charset="iso-8859-15"; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Thu, 12 May 2022 20:43:12 -0000 (UTC)
Injection-Info: reader02.eternal-september.org; posting-host="a5647e66ebad9eeefe61735784510abc";
logging-data="16408"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+K/k2fwvA6VxQ64LcrE7IEXzQ1CR2hUFg="
Cancel-Lock: sha1:ZSFFT21Ac9KyBQpdyEUf9FmXycA=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376
 by: FromTheRafters - Thu, 12 May 2022 20:43 UTC

Chris M. Thomasson explained on 5/12/2022 :
> On 5/12/2022 12:16 PM, Dan joyce wrote:
>> On Thursday, May 12, 2022 at 10:15:16 AM UTC-4, Dan joyce wrote:
>>> On Thursday, May 12, 2022 at 5:50:22 AM UTC-4, Barry Schwarz wrote:
>>>> 1On Wed, 11 May 2022 14:20:15 -0700 (PDT), Dan joyce
>>>> <danj...@gmail.com> wrote:
> [...]
>> Still trying to plug into Wolfram alpha a formula with two known values
>> Length (e)
>> and volume (pi) and inner space diagonal (pi).
>> To get width an height.
>> Anyone?
>
> Just a sketch, the dimensions are arbitrary for now. However, you are talking
> about the diagonal in the purple line, right? Just to clarify.
>
> https://i.ibb.co/ct8GgZb/ct-pov-music.png

I think he is saying the volume of the right rectangular prism is fixed
at pi as is the length of that purple diagonal, and e is the prism's
length.

Re: Is there an equation for this?

<t5jrt2$5cg$1@gioia.aioe.org>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99894&group=sci.math#99894

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Thu, 12 May 2022 15:49:37 -0500
Organization: Aioe.org NNTP Server
Message-ID: <t5jrt2$5cg$1@gioia.aioe.org>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
<51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
<t5jqqm$b0g$1@dont-email.me> <t5jrh0$g0o$1@dont-email.me>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: gioia.aioe.org; logging-data="5520"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.9.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2
 by: sergio - Thu, 12 May 2022 20:49 UTC

On 5/12/2022 3:43 PM, FromTheRafters wrote:
> Chris M. Thomasson explained on 5/12/2022 :
>> On 5/12/2022 12:16 PM, Dan joyce wrote:
>>> On Thursday, May 12, 2022 at 10:15:16 AM UTC-4, Dan joyce wrote:
>>>> On Thursday, May 12, 2022 at 5:50:22 AM UTC-4, Barry Schwarz wrote:
>>>>> 1On Wed, 11 May 2022 14:20:15 -0700 (PDT), Dan joyce
>>>>> <danj...@gmail.com> wrote:
>> [...]
>>> Still trying to plug into Wolfram alpha a formula with two known values Length (e)
>>> and volume (pi) and inner space diagonal (pi).
>>> To get width an height.
>>> Anyone?
>>
>> Just a sketch, the dimensions are arbitrary for now. However, you are talking about the diagonal in the purple line, right? Just to clarify.
>>
>> https://i.ibb.co/ct8GgZb/ct-pov-music.png
>
> I think he is saying the volume of the right rectangular prism is fixed at pi as is the length of that purple diagonal, and e is the prism's length.

e is one outside edge.
the problem could be over specified, via pi as volume and purble diagonal
but its all simple equations

Re: Is there an equation for this?

<gj1r7h1qk82pqih8ggmakl3ol0qcoaii74@4ax.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99901&group=sci.math#99901

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: schwa...@delq.com (Barry Schwarz)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Thu, 12 May 2022 15:27:51 -0700
Organization: A noiseless patient Spider
Lines: 46
Message-ID: <gj1r7h1qk82pqih8ggmakl3ol0qcoaii74@4ax.com>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com> <4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com> <51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com> <3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
Injection-Info: reader02.eternal-september.org; posting-host="d37b511df869245e0173c590fecba82b";
logging-data="28198"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19kkaoMe00CjeNPAVqNphSiKlK3/dQyVtM="
Cancel-Lock: sha1:49aPiRsunTTuy8H4uHkkOLhaCnQ=
X-Newsreader: Forte Agent 4.2/32.1118
 by: Barry Schwarz - Thu, 12 May 2022 22:27 UTC

On Thu, 12 May 2022 12:16:18 -0700 (PDT), Dan joyce
<danj4084@gmail.com> wrote:

>On Thursday, May 12, 2022 at 10:15:16 AM UTC-4, Dan joyce wrote:
>> On Thursday, May 12, 2022 at 5:50:22 AM UTC-4, Barry Schwarz wrote:
>> > 1On Wed, 11 May 2022 14:20:15 -0700 (PDT), Dan joyce
>> > <danj...@gmail.com> wrote:
>> >
>> > >
>> > >A rectangular box with e length b=e and c= 2.8599384160105..(diagonal opposed e)and side (a)as the width derived from c^2 - e^2
>> > >Then pi^2 - c^2 giving the height of the box (a).
>> > >Where pi is the inner space diagonal and also the volume of this box.
>> > >e*a(width)* a(height) = pi. Giving the volume of this box.
>> > >
>> > >c=2.8599384160105... was found by brute force.
>> > >A truly 2 constants rectangular box. Pi and e.
>> > >Pi as the space diagonal and with e length and also giving a pi volume for this rectangular box.
>> > >Is there an equation for finding the above c value without using brute force?

snip algebraic solution

>Still trying to plug into Wolfram alpha a formula with two known values Length (e)
>and volume (pi) and inner space diagonal (pi).
>To get width an height.
>Anyone?

It's actually three known quantities: length, volume, and diagonal.
Two of the quantities happen to have the same value but that is just a
nit.

You have a set of two simultaneous equations in two unknowns, w and h:
pi = ewh
pi^2 = e^2+w^2+h^2

I don't know anything about Wolfram but I would expect it to have some
facility for dealing with simultaneous equations.

By the way, you computed your value c, a face diagonal, to 13 decimal
places. If your unit of measurement were light years, that would give
you precision to .01 mm. If your unit of measurement were more
common, like meters or feet, that would give you precision within the
radius of a hydrogen atom. In either case, what is the point of such
precision? Are you really working with subatomic particles?

--
Remove del for email

Re: Is there an equation for this?

<7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99902&group=sci.math#99902

 copy link   Newsgroups: sci.math
Path: i2pn2.org!rocksolid2!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Thu, 12 May 2022 18:50:04 -0400
Organization: A noiseless patient Spider
Lines: 15
Message-ID: <7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
<51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: reader02.eternal-september.org; posting-host="ff7946ee3d6469b99453d0b84d690b67";
logging-data="3906"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19xyBamgAwKsv2FlVg2p6VMkt200Kd9edo="
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.8.1
Cancel-Lock: sha1:hvv/M0b7i6Z5RDEfX8Y3F7UG68Q=
In-Reply-To: <3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
Content-Language: en-US
 by: Jim Burns - Thu, 12 May 2022 22:50 UTC

On 5/12/2022 3:16 PM, Dan joyce wrote:

> Still trying to plug into Wolfram alpha
> a formula with two known values Length (e)
> and volume (pi) and inner space diagonal (pi).
> To get width an height.
> Anyone?

pi = e*w*h, pi^2 = e^2+w^2+h^2

One line, comma separated.

I tried it, it works.
There's an "exact form" button, if you'd like that.

Re: Is there an equation for this?

<t5k8fj$59i$1@gioia.aioe.org>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99903&group=sci.math#99903

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Thu, 12 May 2022 19:24:17 -0500
Organization: Aioe.org NNTP Server
Message-ID: <t5k8fj$59i$1@gioia.aioe.org>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
<51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
<gj1r7h1qk82pqih8ggmakl3ol0qcoaii74@4ax.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: gioia.aioe.org; logging-data="5426"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.9.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2
 by: sergio - Fri, 13 May 2022 00:24 UTC

On 5/12/2022 5:27 PM, Barry Schwarz wrote:
> On Thu, 12 May 2022 12:16:18 -0700 (PDT), Dan joyce
> <danj4084@gmail.com> wrote:
>
>> On Thursday, May 12, 2022 at 10:15:16 AM UTC-4, Dan joyce wrote:
>>> On Thursday, May 12, 2022 at 5:50:22 AM UTC-4, Barry Schwarz wrote:
>>>> 1On Wed, 11 May 2022 14:20:15 -0700 (PDT), Dan joyce
>>>> <danj...@gmail.com> wrote:
>>>>
>>>>>
>>>>> A rectangular box with e length b=e and c= 2.8599384160105..(diagonal opposed e)and side (a)as the width derived from c^2 - e^2
>>>>> Then pi^2 - c^2 giving the height of the box (a).
>>>>> Where pi is the inner space diagonal and also the volume of this box.
>>>>> e*a(width)* a(height) = pi. Giving the volume of this box.
>>>>>
>>>>> c=2.8599384160105... was found by brute force.
>>>>> A truly 2 constants rectangular box. Pi and e.
>>>>> Pi as the space diagonal and with e length and also giving a pi volume for this rectangular box.
>>>>> Is there an equation for finding the above c value without using brute force?
>
> snip algebraic solution
>
>> Still trying to plug into Wolfram alpha a formula with two known values Length (e)
>> and volume (pi) and inner space diagonal (pi).
>> To get width an height.
>> Anyone?
>
> It's actually three known quantities: length, volume, and diagonal.
> Two of the quantities happen to have the same value but that is just a
> nit.
>
> You have a set of two simultaneous equations in two unknowns, w and h:
> pi = ewh
> pi^2 = e^2+w^2+h^2

so

e^2+w^2+h^2 = e^2*w^2*h^2

or

w^2 - e^2*w^2*h^2 + e^2 + h^2 = 0

w^2(1-e^2*h^2) = -e^2 - h^2

w^2 = -(e^2 + h^2)/(1-e^2*h^2)

Extra Credit problem;

1 h cannot be this value: _______________

2. what does - sign mean in above equation ?

>
> I don't know anything about Wolfram but I would expect it to have some
> facility for dealing with simultaneous equations.
>
> By the way, you computed your value c, a face diagonal, to 13 decimal
> places. If your unit of measurement were light years, that would give
> you precision to .01 mm. If your unit of measurement were more
> common, like meters or feet, that would give you precision within the
> radius of a hydrogen atom. In either case, what is the point of such
> precision? Are you really working with subatomic particles?
>

agree, one can measure to 3 places, perhaps thousandths, but not 10 thousands that is tiny light scrap on metal, your fingerprint will disrupt it

Re: Is there an equation for this?

<01280444-4e33-413a-beec-2b4ec3941563n@googlegroups.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99940&group=sci.math#99940

 copy link   Newsgroups: sci.math
X-Received: by 2002:a37:b4d:0:b0:69f:7742:9778 with SMTP id 74-20020a370b4d000000b0069f77429778mr4083394qkl.109.1652454549160;
Fri, 13 May 2022 08:09:09 -0700 (PDT)
X-Received: by 2002:a81:2185:0:b0:2f1:de50:5ecb with SMTP id
h127-20020a812185000000b002f1de505ecbmr6379792ywh.40.1652454548948; Fri, 13
May 2022 08:09:08 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer02.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Fri, 13 May 2022 08:09:08 -0700 (PDT)
In-Reply-To: <7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>
Injection-Info: google-groups.googlegroups.com; posting-host=32.221.202.28; posting-account=MMV3OwoAAABxhPndZPNv6CW6-fifDabn
NNTP-Posting-Host: 32.221.202.28
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com> <51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com> <7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <01280444-4e33-413a-beec-2b4ec3941563n@googlegroups.com>
Subject: Re: Is there an equation for this?
From: danj4...@gmail.com (Dan joyce)
Injection-Date: Fri, 13 May 2022 15:09:09 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 1801
 by: Dan joyce - Fri, 13 May 2022 15:09 UTC

On Thursday, May 12, 2022 at 6:50:16 PM UTC-4, Jim Burns wrote:
> On 5/12/2022 3:16 PM, Dan joyce wrote:
>
> > Still trying to plug into Wolfram alpha
> > a formula with two known values Length (e)
> > and volume (pi) and inner space diagonal (pi).
> > To get width an height.
> > Anyone?
> pi = e*w*h, pi^2 = e^2+w^2+h^2
>
> One line, comma separated.
>
> I tried it, it works.
> There's an "exact form" button, if you'd like that.

That is neat.
Thanks

Dan

Re: Is there an equation for this?

<t5ltrr$98g$1@gioia.aioe.org>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99941&group=sci.math#99941

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Fri, 13 May 2022 10:35:21 -0500
Organization: Aioe.org NNTP Server
Message-ID: <t5ltrr$98g$1@gioia.aioe.org>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
<51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
<7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>
<01280444-4e33-413a-beec-2b4ec3941563n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: gioia.aioe.org; logging-data="9488"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.9.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2
 by: sergio - Fri, 13 May 2022 15:35 UTC

On 5/13/2022 10:09 AM, Dan joyce wrote:
> On Thursday, May 12, 2022 at 6:50:16 PM UTC-4, Jim Burns wrote:
>> On 5/12/2022 3:16 PM, Dan joyce wrote:
>>
>>> Still trying to plug into Wolfram alpha
>>> a formula with two known values Length (e)
>>> and volume (pi) and inner space diagonal (pi).
>>> To get width an height.
>>> Anyone?
>> pi = e*w*h, pi^2 = e^2+w^2+h^2
>>
>> One line, comma separated.
>>
>> I tried it, it works.
>> There's an "exact form" button, if you'd like that.
>
> That is neat.
> Thanks
>
> Dan

wow! that is neat!! has 4 roots

and exact solutions are very complex,

Re: Is there an equation for this?

<69e017c2-2864-4ef9-bfaf-2f49330816edn@googlegroups.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99942&group=sci.math#99942

 copy link   Newsgroups: sci.math
X-Received: by 2002:a05:6214:b94:b0:456:38b2:2d76 with SMTP id fe20-20020a0562140b9400b0045638b22d76mr4795130qvb.70.1652456302117;
Fri, 13 May 2022 08:38:22 -0700 (PDT)
X-Received: by 2002:a25:4244:0:b0:64b:3af3:45a9 with SMTP id
p65-20020a254244000000b0064b3af345a9mr5768742yba.536.1652456301869; Fri, 13
May 2022 08:38:21 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Fri, 13 May 2022 08:38:21 -0700 (PDT)
In-Reply-To: <t5jqqm$b0g$1@dont-email.me>
Injection-Info: google-groups.googlegroups.com; posting-host=32.221.202.28; posting-account=MMV3OwoAAABxhPndZPNv6CW6-fifDabn
NNTP-Posting-Host: 32.221.202.28
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com> <51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com> <t5jqqm$b0g$1@dont-email.me>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <69e017c2-2864-4ef9-bfaf-2f49330816edn@googlegroups.com>
Subject: Re: Is there an equation for this?
From: danj4...@gmail.com (Dan joyce)
Injection-Date: Fri, 13 May 2022 15:38:22 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 2539
 by: Dan joyce - Fri, 13 May 2022 15:38 UTC

On Thursday, May 12, 2022 at 4:31:29 PM UTC-4, Chris M. Thomasson wrote:
> On 5/12/2022 12:16 PM, Dan joyce wrote:
> > On Thursday, May 12, 2022 at 10:15:16 AM UTC-4, Dan joyce wrote:
> >> On Thursday, May 12, 2022 at 5:50:22 AM UTC-4, Barry Schwarz wrote:
> >>> 1On Wed, 11 May 2022 14:20:15 -0700 (PDT), Dan joyce
> >>> <danj...@gmail.com> wrote:
> [...]
> > Still trying to plug into Wolfram alpha a formula with two known values Length (e)
> > and volume (pi) and inner space diagonal (pi).
> > To get width an height.
> > Anyone?
> Just a sketch, the dimensions are arbitrary for now. However, you are
> talking about the diagonal in the purple line, right? Just to clarify.
>
> https://i.ibb.co/ct8GgZb/ct-pov-music.png

Yes, I refer to that as the inner space diagonal as being pi and also the volume
being pi if the length is e
Jim and Barry set me straight on finding width and height.
Jim entered this equation into Wolfram --- pi = e*w*h, pi^2 = e^2+w^2+h^2
Solved the problem.
I went after it in a different way.
Finding the diagonal of the side for e in a brute force method.
Barry also pointed out that diagonal can have two different values with the same
results depending if the box is flipped over once.

Re: Is there an equation for this?

<5bcec9e8-8721-473e-bf11-87690fde844an@googlegroups.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99943&group=sci.math#99943

 copy link   Newsgroups: sci.math
X-Received: by 2002:a05:620a:102c:b0:69f:c056:43a1 with SMTP id a12-20020a05620a102c00b0069fc05643a1mr4069721qkk.526.1652457053471;
Fri, 13 May 2022 08:50:53 -0700 (PDT)
X-Received: by 2002:a0d:d844:0:b0:2fe:c4e2:cfb1 with SMTP id
a65-20020a0dd844000000b002fec4e2cfb1mr1703678ywe.368.1652457053295; Fri, 13
May 2022 08:50:53 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Fri, 13 May 2022 08:50:53 -0700 (PDT)
In-Reply-To: <t5ltrr$98g$1@gioia.aioe.org>
Injection-Info: google-groups.googlegroups.com; posting-host=32.221.202.28; posting-account=MMV3OwoAAABxhPndZPNv6CW6-fifDabn
NNTP-Posting-Host: 32.221.202.28
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com> <51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com> <7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>
<01280444-4e33-413a-beec-2b4ec3941563n@googlegroups.com> <t5ltrr$98g$1@gioia.aioe.org>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <5bcec9e8-8721-473e-bf11-87690fde844an@googlegroups.com>
Subject: Re: Is there an equation for this?
From: danj4...@gmail.com (Dan joyce)
Injection-Date: Fri, 13 May 2022 15:50:53 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 2173
 by: Dan joyce - Fri, 13 May 2022 15:50 UTC

On Friday, May 13, 2022 at 11:35:37 AM UTC-4, sergio wrote:
> On 5/13/2022 10:09 AM, Dan joyce wrote:
> > On Thursday, May 12, 2022 at 6:50:16 PM UTC-4, Jim Burns wrote:
> >> On 5/12/2022 3:16 PM, Dan joyce wrote:
> >>
> >>> Still trying to plug into Wolfram alpha
> >>> a formula with two known values Length (e)
> >>> and volume (pi) and inner space diagonal (pi).
> >>> To get width an height.
> >>> Anyone?
> >> pi = e*w*h, pi^2 = e^2+w^2+h^2
> >>
> >> One line, comma separated.
> >>
> >> I tried it, it works.
> >> There's an "exact form" button, if you'd like that.
> >
> > That is neat.
> > Thanks
> >
> > Dan
> wow! that is neat!! has 4 roots
>
> and exact solutions are very complex,

You can say that again.
Way over my head.

Re: Is there an equation for this?

<57394eae-4a88-671e-95a5-20792f1383fd@att.net>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99955&group=sci.math#99955

 copy link   Newsgroups: sci.math
Path: i2pn2.org!rocksolid2!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Fri, 13 May 2022 14:03:23 -0400
Organization: A noiseless patient Spider
Lines: 71
Message-ID: <57394eae-4a88-671e-95a5-20792f1383fd@att.net>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
<51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
<7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>
<01280444-4e33-413a-beec-2b4ec3941563n@googlegroups.com>
<t5ltrr$98g$1@gioia.aioe.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: reader02.eternal-september.org; posting-host="43ac8678e817fa63ae37d7e77430b28a";
logging-data="7296"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/k5mZVahvH8o46j9W+riRq3XgaBeXiEoM="
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.8.1
Cancel-Lock: sha1:LtELpTMJenndEbSDKx5ZIKuNiu4=
In-Reply-To: <t5ltrr$98g$1@gioia.aioe.org>
Content-Language: en-US
 by: Jim Burns - Fri, 13 May 2022 18:03 UTC

On 5/13/2022 11:35 AM, sergio wrote:
> On 5/13/2022 10:09 AM, Dan joyce wrote:
>> On Thursday, May 12, 2022 at 6:50:16 PM UTC-4,
>> Jim Burns wrote:
>>> On 5/12/2022 3:16 PM, Dan joyce wrote:

>>>> Still trying to plug into Wolfram alpha
>>>> a formula with two known values Length (e)
>>>> and volume (pi) and inner space diagonal (pi).
>>>> To get width an height.
>>>> Anyone?
>>>
>>> pi = e*w*h, pi^2 = e^2+w^2+h^2
>>>
>>> One line, comma separated.
>>>
>>> I tried it, it works.
>>> There's an "exact form" button, if you'd like that.
>>
>> That is neat.
>> Thanks

> wow! that is neat!!   has 4 roots

Agreed, very neat,
not that I helped build Wolfram Alpha or anything.

The 4 roots are trivial variations of each other.
h₀=0.888927..., w₀=1.30014...

h=h₀, w=w₀
h=-h₀, w=-w₀
h=w₀, w=h₀
h=-w₀, w=-h₀

> and exact solutions are very complex,

The good news is that Wolfram Alpha doesn't care
about "complex".

The bad news is that Wolfram Alpha doesn't care
about "complex".

We mere humans can do better than that, though.

pi = e*w*h, pi^2 = e^2+w^2+h^2

pi^2 = e^2*w^2*h^2

W = w^2, H = h^2

pi^2/e^2 = W*H, pi^2 - e^2 = W + H

(pi^2-e^2)*H = W*H + H^2

(pi^2-e^2)*H = (pi^2/e^2) + H^2

H/(pi^2-e^2) = (pi^2/e^2)/(pi^2-e^2)^2 + (H/(pi^2-e^2))^2

η = H/(pi^2-e^2)

β = (pi^2/e^2)/(pi^2-e^2)^2

η = β + η^2

η = (1 - sqrt(1 - 4*β))/2
η = (1 + sqrt(1 - 4*β))/2

h₀ = sqrt((pi^2-e^2)*(1 - sqrt(1 - 4*β))/2)
w₀ = sqrt((pi^2-e^2)*(1 + sqrt(1 - 4*β))/2)

Re: Is there an equation for this?

<6215eb33-2e6e-427f-bbd7-d009695e14acn@googlegroups.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99984&group=sci.math#99984

 copy link   Newsgroups: sci.math
X-Received: by 2002:a05:620a:248c:b0:6a0:54f8:9077 with SMTP id i12-20020a05620a248c00b006a054f89077mr5011302qkn.500.1652474932972;
Fri, 13 May 2022 13:48:52 -0700 (PDT)
X-Received: by 2002:a81:70c3:0:b0:2fe:c68c:aa1d with SMTP id
l186-20020a8170c3000000b002fec68caa1dmr2612893ywc.431.1652474932775; Fri, 13
May 2022 13:48:52 -0700 (PDT)
Path: i2pn2.org!i2pn.org!aioe.org!pasdenom.info!usenet-fr.net!fdn.fr!proxad.net!feeder1-2.proxad.net!209.85.160.216.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Fri, 13 May 2022 13:48:52 -0700 (PDT)
In-Reply-To: <57394eae-4a88-671e-95a5-20792f1383fd@att.net>
Injection-Info: google-groups.googlegroups.com; posting-host=32.221.202.28; posting-account=MMV3OwoAAABxhPndZPNv6CW6-fifDabn
NNTP-Posting-Host: 32.221.202.28
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com> <51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com> <7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>
<01280444-4e33-413a-beec-2b4ec3941563n@googlegroups.com> <t5ltrr$98g$1@gioia.aioe.org>
<57394eae-4a88-671e-95a5-20792f1383fd@att.net>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <6215eb33-2e6e-427f-bbd7-d009695e14acn@googlegroups.com>
Subject: Re: Is there an equation for this?
From: danj4...@gmail.com (Dan joyce)
Injection-Date: Fri, 13 May 2022 20:48:52 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
 by: Dan joyce - Fri, 13 May 2022 20:48 UTC

On Friday, May 13, 2022 at 2:03:36 PM UTC-4, Jim Burns wrote:
> On 5/13/2022 11:35 AM, sergio wrote:
> > On 5/13/2022 10:09 AM, Dan joyce wrote:
> >> On Thursday, May 12, 2022 at 6:50:16 PM UTC-4,
> >> Jim Burns wrote:
> >>> On 5/12/2022 3:16 PM, Dan joyce wrote:
>
> >>>> Still trying to plug into Wolfram alpha
> >>>> a formula with two known values Length (e)
> >>>> and volume (pi) and inner space diagonal (pi).
> >>>> To get width an height.
> >>>> Anyone?
> >>>
> >>> pi = e*w*h, pi^2 = e^2+w^2+h^2
> >>>
> >>> One line, comma separated.
> >>>
> >>> I tried it, it works.
> >>> There's an "exact form" button, if you'd like that.
> >>
> >> That is neat.
> >> Thanks
> > wow! that is neat!! has 4 roots
> Agreed, very neat,
> not that I helped build Wolfram Alpha or anything.
>
> The 4 roots are trivial variations of each other.
> h₀=0.888927..., w₀=1.30014...
>
> h=h₀, w=w₀
> h=-h₀, w=-w₀
> h=w₀, w=h₀
> h=-w₀, w=-h₀
> > and exact solutions are very complex,
> The good news is that Wolfram Alpha doesn't care
> about "complex".
>
> The bad news is that Wolfram Alpha doesn't care
> about "complex".
>
> We mere humans can do better than that, though.
> pi = e*w*h, pi^2 = e^2+w^2+h^2
> pi^2 = e^2*w^2*h^2
>
> W = w^2, H = h^2
>
> pi^2/e^2 = W*H, pi^2 - e^2 = W + H
>
> (pi^2-e^2)*H = W*H + H^2
>
> (pi^2-e^2)*H = (pi^2/e^2) + H^2
>
> H/(pi^2-e^2) = (pi^2/e^2)/(pi^2-e^2)^2 + (H/(pi^2-e^2))^2
>
> η = H/(pi^2-e^2)
>
> β = (pi^2/e^2)/(pi^2-e^2)^2
>
> η = β + η^2
>
> η = (1 - sqrt(1 - 4*β))/2
> η = (1 + sqrt(1 - 4*β))/2
>
> h₀ = sqrt((pi^2-e^2)*(1 - sqrt(1 - 4*β))/2)
> w₀ = sqrt((pi^2-e^2)*(1 + sqrt(1 - 4*β))/2)

Nice.
Here is another interesting one where e has length and width or height and the inner space
diagonal is the same as the volume.
3.879925 = e*w*h,3.879925^2 = e^2+w^2+h^2

Re: Is there an equation for this?

<t5mkhr$8nq$4@dont-email.me>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99992&group=sci.math#99992

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Fri, 13 May 2022 15:02:36 -0700
Organization: A noiseless patient Spider
Lines: 80
Message-ID: <t5mkhr$8nq$4@dont-email.me>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
<51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
<7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>
<01280444-4e33-413a-beec-2b4ec3941563n@googlegroups.com>
<t5ltrr$98g$1@gioia.aioe.org> <57394eae-4a88-671e-95a5-20792f1383fd@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Fri, 13 May 2022 22:02:35 -0000 (UTC)
Injection-Info: reader02.eternal-september.org; posting-host="c63447f04d0ac8f29a607d8609e872a0";
logging-data="8954"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19az5NEWiNnVo7V2sH7BbzJVtDu5rOp9g8="
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.9.0
Cancel-Lock: sha1:8qmqZGev74zsk9UDH3ZMBoKO5G8=
In-Reply-To: <57394eae-4a88-671e-95a5-20792f1383fd@att.net>
Content-Language: en-US
 by: Chris M. Thomasson - Fri, 13 May 2022 22:02 UTC

On 5/13/2022 11:03 AM, Jim Burns wrote:
> On 5/13/2022 11:35 AM, sergio wrote:
>> On 5/13/2022 10:09 AM, Dan joyce wrote:
>>> On Thursday, May 12, 2022 at 6:50:16 PM UTC-4,
>>> Jim Burns wrote:
>>>> On 5/12/2022 3:16 PM, Dan joyce wrote:
>
>>>>> Still trying to plug into Wolfram alpha
>>>>> a formula with two known values Length (e)
>>>>> and volume (pi) and inner space diagonal (pi).
>>>>> To get width an height.
>>>>> Anyone?
>>>>
>>>> pi = e*w*h, pi^2 = e^2+w^2+h^2
>>>>
>>>> One line, comma separated.
>>>>
>>>> I tried it, it works.
>>>> There's an "exact form" button, if you'd like that.
>>>
>>> That is neat.
>>> Thanks
>
>> wow! that is neat!!   has 4 roots
>
> Agreed, very neat,
> not that I helped build Wolfram Alpha or anything.
>
> The 4 roots are trivial variations of each other.
> h₀=0.888927..., w₀=1.30014...
>
> h=h₀, w=w₀
> h=-h₀, w=-w₀
> h=w₀, w=h₀
> h=-w₀, w=-h₀
>
>> and exact solutions are very complex,
>
> The good news is that Wolfram Alpha doesn't care
> about "complex".
>
> The bad news is that Wolfram Alpha doesn't care
> about "complex".
>
> We mere humans can do better than that, though.
>
> pi = e*w*h, pi^2 = e^2+w^2+h^2
>
> pi^2 = e^2*w^2*h^2
>
> W = w^2, H = h^2
>
> pi^2/e^2 = W*H, pi^2 - e^2 = W + H
>
> (pi^2-e^2)*H = W*H + H^2
>
> (pi^2-e^2)*H = (pi^2/e^2) + H^2
>
> H/(pi^2-e^2) = (pi^2/e^2)/(pi^2-e^2)^2 + (H/(pi^2-e^2))^2
>
> η = H/(pi^2-e^2)
>
> β = (pi^2/e^2)/(pi^2-e^2)^2
>
> η = β + η^2
>
> η = (1 - sqrt(1 - 4*β))/2
> η = (1 + sqrt(1 - 4*β))/2
>
> h₀ = sqrt((pi^2-e^2)*(1 - sqrt(1 - 4*β))/2)
> w₀ = sqrt((pi^2-e^2)*(1 + sqrt(1 - 4*β))/2)
>

The two square roots definitely remind me of choosing roots in a reverse
iteration Julia set. Check this out, the main equations are from me:

http://paulbourke.net/fractals/multijulia

Paul was nice enough to experiment with it, and dedicate server space to
show it.

Re: Is there an equation for this?

<4d71f6ae-f483-4bd2-aba6-3ba853ca1080n@googlegroups.com>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99996&group=sci.math#99996

 copy link   Newsgroups: sci.math
X-Received: by 2002:a05:620a:248c:b0:6a0:54f8:9077 with SMTP id i12-20020a05620a248c00b006a054f89077mr5244550qkn.500.1652480665491;
Fri, 13 May 2022 15:24:25 -0700 (PDT)
X-Received: by 2002:a81:4782:0:b0:2eb:1cb1:5441 with SMTP id
u124-20020a814782000000b002eb1cb15441mr7977003ywa.479.1652480665329; Fri, 13
May 2022 15:24:25 -0700 (PDT)
Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Fri, 13 May 2022 15:24:25 -0700 (PDT)
In-Reply-To: <t5mkhr$8nq$4@dont-email.me>
Injection-Info: google-groups.googlegroups.com; posting-host=32.221.202.28; posting-account=MMV3OwoAAABxhPndZPNv6CW6-fifDabn
NNTP-Posting-Host: 32.221.202.28
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com> <51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com> <7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>
<01280444-4e33-413a-beec-2b4ec3941563n@googlegroups.com> <t5ltrr$98g$1@gioia.aioe.org>
<57394eae-4a88-671e-95a5-20792f1383fd@att.net> <t5mkhr$8nq$4@dont-email.me>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <4d71f6ae-f483-4bd2-aba6-3ba853ca1080n@googlegroups.com>
Subject: Re: Is there an equation for this?
From: danj4...@gmail.com (Dan joyce)
Injection-Date: Fri, 13 May 2022 22:24:25 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
X-Received-Bytes: 4153
 by: Dan joyce - Fri, 13 May 2022 22:24 UTC

On Friday, May 13, 2022 at 6:02:45 PM UTC-4, Chris M. Thomasson wrote:
> On 5/13/2022 11:03 AM, Jim Burns wrote:
> > On 5/13/2022 11:35 AM, sergio wrote:
> >> On 5/13/2022 10:09 AM, Dan joyce wrote:
> >>> On Thursday, May 12, 2022 at 6:50:16 PM UTC-4,
> >>> Jim Burns wrote:
> >>>> On 5/12/2022 3:16 PM, Dan joyce wrote:
> >
> >>>>> Still trying to plug into Wolfram alpha
> >>>>> a formula with two known values Length (e)
> >>>>> and volume (pi) and inner space diagonal (pi).
> >>>>> To get width an height.
> >>>>> Anyone?
> >>>>
> >>>> pi = e*w*h, pi^2 = e^2+w^2+h^2
> >>>>
> >>>> One line, comma separated.
> >>>>
> >>>> I tried it, it works.
> >>>> There's an "exact form" button, if you'd like that.
> >>>
> >>> That is neat.
> >>> Thanks
> >
> >> wow! that is neat!! has 4 roots
> >
> > Agreed, very neat,
> > not that I helped build Wolfram Alpha or anything.
> >
> > The 4 roots are trivial variations of each other.
> > h₀=0.888927..., w₀=1.30014...
> >
> > h=h₀, w=w₀
> > h=-h₀, w=-w₀
> > h=w₀, w=h₀
> > h=-w₀, w=-h₀
> >
> >> and exact solutions are very complex,
> >
> > The good news is that Wolfram Alpha doesn't care
> > about "complex".
> >
> > The bad news is that Wolfram Alpha doesn't care
> > about "complex".
> >
> > We mere humans can do better than that, though.
> >
> > pi = e*w*h, pi^2 = e^2+w^2+h^2
> >
> > pi^2 = e^2*w^2*h^2
> >
> > W = w^2, H = h^2
> >
> > pi^2/e^2 = W*H, pi^2 - e^2 = W + H
> >
> > (pi^2-e^2)*H = W*H + H^2
> >
> > (pi^2-e^2)*H = (pi^2/e^2) + H^2
> >
> > H/(pi^2-e^2) = (pi^2/e^2)/(pi^2-e^2)^2 + (H/(pi^2-e^2))^2
> >
> > η = H/(pi^2-e^2)
> >
> > β = (pi^2/e^2)/(pi^2-e^2)^2
> >
> > η = β + η^2
> >
> > η = (1 - sqrt(1 - 4*β))/2
> > η = (1 + sqrt(1 - 4*β))/2
> >
> > h₀ = sqrt((pi^2-e^2)*(1 - sqrt(1 - 4*β))/2)
> > w₀ = sqrt((pi^2-e^2)*(1 + sqrt(1 - 4*β))/2)
> >
> The two square roots definitely remind me of choosing roots in a reverse
> iteration Julia set. Check this out, the main equations are from me:
>
> http://paulbourke.net/fractals/multijulia
>
> Paul was nice enough to experiment with it, and dedicate server space to
> show it.

Nice complex shapes.

Re: Is there an equation for this?

<t5mmm2$1126$1@gioia.aioe.org>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=99997&group=sci.math#99997

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!aioe.org!CC3uK9WYEoa7s1kzH7komw.user.46.165.242.75.POSTED!not-for-mail
From: news.dea...@darjeeling.plus.com (Mike Terry)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Fri, 13 May 2022 23:38:59 +0100
Organization: Aioe.org NNTP Server
Message-ID: <t5mmm2$1126$1@gioia.aioe.org>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
<51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
<7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>
<01280444-4e33-413a-beec-2b4ec3941563n@googlegroups.com>
<t5ltrr$98g$1@gioia.aioe.org> <57394eae-4a88-671e-95a5-20792f1383fd@att.net>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="33862"; posting-host="CC3uK9WYEoa7s1kzH7komw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:60.0) Gecko/20100101
Firefox/60.0 SeaMonkey/2.53.7.1
X-Notice: Filtered by postfilter v. 0.9.2
 by: Mike Terry - Fri, 13 May 2022 22:38 UTC

On 13/05/2022 19:03, Jim Burns wrote:
> On 5/13/2022 11:35 AM, sergio wrote:
>> On 5/13/2022 10:09 AM, Dan joyce wrote:
>>> On Thursday, May 12, 2022 at 6:50:16 PM UTC-4,
>>> Jim Burns wrote:
>>>> On 5/12/2022 3:16 PM, Dan joyce wrote:
>
>>>>> Still trying to plug into Wolfram alpha
>>>>> a formula with two known values Length (e)
>>>>> and volume (pi) and inner space diagonal (pi).
>>>>> To get width an height.
>>>>> Anyone?
>>>>
>>>> pi = e*w*h, pi^2 = e^2+w^2+h^2
>>>>
>>>> One line, comma separated.
>>>>
>>>> I tried it, it works.
>>>> There's an "exact form" button, if you'd like that.
>>>
>>> That is neat.
>>> Thanks
>
>> wow! that is neat!!   has 4 roots
>
> Agreed, very neat,
> not that I helped build Wolfram Alpha or anything.
>
> The 4 roots are trivial variations of each other.
> h₀=0.888927..., w₀=1.30014...
>
> h=h₀, w=w₀
> h=-h₀, w=-w₀
> h=w₀, w=h₀
> h=-w₀, w=-h₀
>
>> and exact solutions are very complex,
>
> The good news is that Wolfram Alpha doesn't care
> about "complex".
>
> The bad news is that Wolfram Alpha doesn't care
> about "complex".
>
> We mere humans can do better than that, though.
>
> pi = e*w*h, pi^2 = e^2+w^2+h^2
>
> pi^2 = e^2*w^2*h^2
>
> W = w^2, H = h^2
>
> pi^2/e^2 = W*H, pi^2 - e^2 = W + H

alternatively.. we have the WH and W+H (constant) values, so straight away W and H are the two roots
of the quadratic

x^2 - (W+H)x + (WH) = 0

i.e. x^2 - (pi^2 - e^2)x + pi^2/e^2 = 0

and we can use our favourite quadratic formula! (This way it's implicit that w,h can be swapped -
they are the two roots, but either way round...)

(Or we could find constants for wh, w+h directly from the start equations and get their quadratic
directly, without introducing W,H)

Mike.

>
> (pi^2-e^2)*H = W*H + H^2
>
> (pi^2-e^2)*H = (pi^2/e^2) + H^2
>
> H/(pi^2-e^2) = (pi^2/e^2)/(pi^2-e^2)^2 + (H/(pi^2-e^2))^2
>
> η = H/(pi^2-e^2)
>
> β = (pi^2/e^2)/(pi^2-e^2)^2
>
> η = β + η^2
>
> η = (1 - sqrt(1 - 4*β))/2
> η = (1 + sqrt(1 - 4*β))/2
>
> h₀ = sqrt((pi^2-e^2)*(1 - sqrt(1 - 4*β))/2)
> w₀ = sqrt((pi^2-e^2)*(1 + sqrt(1 - 4*β))/2)
>

Re: Is there an equation for this?

<t5n1g4$1tnt$1@gioia.aioe.org>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=100005&group=sci.math#100005

 copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Is there an equation for this?
Date: Fri, 13 May 2022 20:43:31 -0500
Organization: Aioe.org NNTP Server
Message-ID: <t5n1g4$1tnt$1@gioia.aioe.org>
References: <13878638-902d-42c7-a651-dea6aa7278a4n@googlegroups.com>
<4qkp7h1bgob8smthqjibfrgd1btburkd9v@4ax.com>
<51476a00-bbe4-45e3-a1eb-1d76074c53ebn@googlegroups.com>
<3dc86887-a1a1-49e0-941b-fc348ea0cdefn@googlegroups.com>
<7fe091a7-d98a-bdc4-3b9b-2a7ad501fb29@att.net>
<01280444-4e33-413a-beec-2b4ec3941563n@googlegroups.com>
<t5ltrr$98g$1@gioia.aioe.org> <57394eae-4a88-671e-95a5-20792f1383fd@att.net>
<t5mkhr$8nq$4@dont-email.me>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: gioia.aioe.org; logging-data="63229"; posting-host="jq9Zon5wYWPEc6MdU7JpBw.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.9.0
X-Notice: Filtered by postfilter v. 0.9.2
Content-Language: en-US
 by: sergio - Sat, 14 May 2022 01:43 UTC

On 5/13/2022 5:02 PM, Chris M. Thomasson wrote:
> On 5/13/2022 11:03 AM, Jim Burns wrote:
>> On 5/13/2022 11:35 AM, sergio wrote:
>>> On 5/13/2022 10:09 AM, Dan joyce wrote:
>>>> On Thursday, May 12, 2022 at 6:50:16 PM UTC-4,
>>>> Jim Burns wrote:
>>>>> On 5/12/2022 3:16 PM, Dan joyce wrote:
>>
>>>>>> Still trying to plug into Wolfram alpha
>>>>>> a formula with two known values Length (e)
>>>>>> and volume (pi) and inner space diagonal (pi).
>>>>>> To get width an height.
>>>>>> Anyone?
>>>>>
>>>>> pi = e*w*h, pi^2 = e^2+w^2+h^2
>>>>>
>>>>> One line, comma separated.
>>>>>
>>>>> I tried it, it works.
>>>>> There's an "exact form" button, if you'd like that.
>>>>
>>>> That is neat.
>>>> Thanks
>>
>>> wow! that is neat!!   has 4 roots
>>
>> Agreed, very neat,
>> not that I helped build Wolfram Alpha or anything.
>>
>> The 4 roots are trivial variations of each other.
>> h₀=0.888927..., w₀=1.30014...
>>
>> h=h₀, w=w₀
>> h=-h₀, w=-w₀
>> h=w₀, w=h₀
>> h=-w₀, w=-h₀
>>
>>> and exact solutions are very complex,
>>
>> The good news is that Wolfram Alpha doesn't care
>> about "complex".
>>
>> The bad news is that Wolfram Alpha doesn't care
>> about "complex".
>>
>> We mere humans can do better than that, though.
>>
>> pi = e*w*h, pi^2 = e^2+w^2+h^2
>>
>> pi^2 = e^2*w^2*h^2
>>
>> W = w^2, H = h^2
>>
>> pi^2/e^2 = W*H, pi^2 - e^2 = W + H
>>
>> (pi^2-e^2)*H = W*H + H^2
>>
>> (pi^2-e^2)*H = (pi^2/e^2) + H^2
>>
>> H/(pi^2-e^2) = (pi^2/e^2)/(pi^2-e^2)^2 + (H/(pi^2-e^2))^2
>>
>> η = H/(pi^2-e^2)
>>
>> β = (pi^2/e^2)/(pi^2-e^2)^2
>>
>> η = β + η^2
>>
>> η = (1 - sqrt(1 - 4*β))/2
>> η = (1 + sqrt(1 - 4*β))/2
>>
>> h₀ = sqrt((pi^2-e^2)*(1 - sqrt(1 - 4*β))/2)
>> w₀ = sqrt((pi^2-e^2)*(1 + sqrt(1 - 4*β))/2)
>>
>
> The two square roots definitely remind me of choosing roots in a reverse iteration Julia set. Check this out, the main equations are from me:
>
> http://paulbourke.net/fractals/multijulia
>
> Paul was nice enough to experiment with it, and dedicate server space to show it.

excellent drawings, how do you do the 3D effect ? lighting, or is it some parts shadowing others ?

Pages:12
server_pubkey.txt

rocksolid light 0.9.7
clearnet tor