Hi,

includes the easy ways and the harder, precise ways.

https://www.youtube.com/watch?v=gMlf1ELvRzc

For math freaks, engineers happy to just look it up.

...... Phil

On 10/07/2021 12:16, Phil Allison wrote:
> Hi,
>
> includes the easy ways and the harder, precise ways.
>
> https://www.youtube.com/watch?v=gMlf1ELvRzc
>
> For math freaks, engineers happy to just look it up.
>
>
> ..... Phil
>

Fun, thanks. As a common or garden workaday engineer I often need to
calculate with 2pi and most of time for back of the envelope work using
6 is good enough to 5% and 6.3 is better than 1%. Anything more precise
I turn on the computer :)

piglet

On 7/10/2021 7:43 AM, Piglet wrote:
> On 10/07/2021 12:16, Phil Allison wrote:
>> Hi,
>>
>> includes the easy ways and the harder, precise ways.
>>
>> https://www.youtube.com/watch?v=gMlf1ELvRzc
>>
>> For math freaks, engineers happy to just look it up.
>>
>>
>> .....   Phil
>>
>
> Fun, thanks. As a common or garden workaday engineer I often need to
> calculate with 2pi and most of time for back of the envelope work using
> 6 is good enough to 5% and 6.3 is better than 1%. Anything more precise
> I turn on the computer :)
>
> piglet
>

Limits of human knowledge in the 21st century, we know that the numbers
e.g. e and pi are irrational and transcendental and have for about 200
years I think, but what do we know for sure about the numbers pi + e, pi
- e, (pi + e)^2, etc? Big lot of nothing, AFAIK it hasn't been proved if
numbers like that involving those constant are even irrational, much
less transcendental. It's suspected they are but it's difficult to prove.

Piglet wrote:
> On 10/07/2021 12:16, Phil Allison wrote:
>> Hi,
>>
>> includes the easy ways and the harder, precise ways.
>>
>> https://www.youtube.com/watch?v=gMlf1ELvRzc
>>
>> For math freaks, engineers happy to just look it up.
>>
>>
>> .....   Phil
>>
>
> Fun, thanks. As a common or garden workaday engineer I often need to
> calculate with 2pi and most of time for back of the envelope work using
> 6 is good enough to 5% and 6.3 is better than 1%. Anything more precise
> I turn on the computer :)
>
> piglet
>

There aren't that many analogue things that need pi to more than two places.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

bitrex wrote:
>
> Limits of human knowledge in the 21st century, we know that the
> numbers e.g. e and pi are irrational and transcendental and have for
> about 200 years I think, but what do we know for sure about the
> numbers pi + e, pi - e, (pi + e)^2, etc? Big lot of nothing, AFAIK it
> hasn't been proved if numbers like that involving those constant are
> even irrational, much less transcendental. It's suspected they are
> but it's difficult to prove.

There is a recent youtube video that makes the case that a number like
pi^pi (or something like that) could be an integer for all we know.

--
Defund the Thought Police

Tom Del Rosso wrote:
> bitrex wrote:
>>
>> Limits of human knowledge in the 21st century, we know that the
>> numbers e.g. e and pi are irrational and transcendental and have for
>> about 200 years I think, but what do we know for sure about the
>> numbers pi + e, pi - e, (pi + e)^2, etc? Big lot of nothing, AFAIK it
>> hasn't been proved if numbers like that involving those constant are
>> even irrational, much less transcendental. It's suspected they are
>> but it's difficult to prove.
>
> There is a recent youtube video that makes the case that a number like
> pi^pi (or something like that) could be an integer for all we know.

Not pi^pi I realize. Then it wouldn't be transcendental because the
square root would equal pi.

It was some other function. Maybe it had two transcendentals so there
couldn't be a function to derive either one from it.

--
Defund the Thought Police

On Sat, 10 Jul 2021 15:01:27 -0400, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

>Piglet wrote:
>> On 10/07/2021 12:16, Phil Allison wrote:
>>> Hi,
>>>
>>> includes the easy ways and the harder, precise ways.
>>>
>>> https://www.youtube.com/watch?v=gMlf1ELvRzc
>>>
>>> For math freaks, engineers happy to just look it up.
>>>
>>>
>>> .....   Phil
>>>
>>
>> Fun, thanks. As a common or garden workaday engineer I often need to
>> calculate with 2pi and most of time for back of the envelope work using
>> 6 is good enough to 5% and 6.3 is better than 1%. Anything more precise
>> I turn on the computer :)
>>
>> piglet
>>
>
>There aren't that many analogue things that need pi to more than two places.
>
>Cheers
>
>Phil Hobbs

I used to know pi to 100 places. I'm down to 20 now.

We're doing a timing project now and sometimes switch between cycles
and radians, to about 1 PPB resolution.

--

John Larkin Highland Technology, Inc

The best designs are necessarily accidental.

Tom Del Rosso wrote:
>
> Not pi^pi I realize. Then it wouldn't be transcendental because the
> square root would equal pi.

Not square root. Meant to write pi-root.

Not sure if that would rule out being transcendental, if it could be
expressed as a function of a transcendental.

--
Defund the Thought Police

jlarkin@highlandsniptechnology.com wrote:
> On Sat, 10 Jul 2021 15:01:27 -0400, Phil Hobbs
> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>
>> Piglet wrote:
>>> On 10/07/2021 12:16, Phil Allison wrote:
>>>> Hi,
>>>>
>>>> includes the easy ways and the harder, precise ways.
>>>>
>>>> https://www.youtube.com/watch?v=gMlf1ELvRzc
>>>>
>>>> For math freaks, engineers happy to just look it up.
>>>>
>>>>
>>>> .....   Phil
>>>>
>>>
>>> Fun, thanks. As a common or garden workaday engineer I often need to
>>> calculate with 2pi and most of time for back of the envelope work using
>>> 6 is good enough to 5% and 6.3 is better than 1%. Anything more precise
>>> I turn on the computer :)
>>>
>>> piglet
>>>
>>
>> There aren't that many analogue things that need pi to more than two places.

>
> I used to know pi to 100 places. I'm down to 20 now.
>
> We're doing a timing project now and sometimes switch between cycles
> and radians, to about 1 PPB resolution.

Sure, plus frequency synthesis and all sorts of DSP things. (I only
ever memorized pi to REAL*8 accuracy---for higher precision it's
4*ridiculous_precision_atan(1.).) ;)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

jlarkin@highlandsniptechnology.com wrote:
>
> I used to know pi to 100 places. I'm down to 20 now.

I know more than 100 digits of pi, e and sqrt(2) combined.

I like to mix it up. pi alone is monotonous.

--
Defund the Thought Police

On 10/07/2021 21:39, Tom Del Rosso wrote:
> jlarkin@highlandsniptechnology.com wrote:
>>
>> I used to know pi to 100 places. I'm down to 20 now.
>
> I know more than 100 digits of pi, e and sqrt(2) combined.
>
> I like to mix it up. pi alone is monotonous.
>

I know all the digits of pi.

But not necessarily in the right order.

--
Cheers
Eric Morecambe

On 7/10/2021 4:24 PM, Tom Del Rosso wrote:
> Tom Del Rosso wrote:
>> bitrex wrote:
>>>
>>> Limits of human knowledge in the 21st century, we know that the
>>> numbers e.g. e and pi are irrational and transcendental and have for
>>> about 200 years I think, but what do we know for sure about the
>>> numbers pi + e, pi - e, (pi + e)^2, etc? Big lot of nothing, AFAIK it
>>> hasn't been proved if numbers like that involving those constant are
>>> even irrational, much less transcendental. It's suspected they are
>>> but it's difficult to prove.
>>
>> There is a recent youtube video that makes the case that a number like
>> pi^pi (or something like that) could be an integer for all we know.
>
> Not pi^pi I realize. Then it wouldn't be transcendental because the
> square root would equal pi.
>
> It was some other function. Maybe it had two transcendentals so there
> couldn't be a function to derive either one from it.
>
>

I think numbers like pi^pi fall into the same case as pi + e, not even
known if they're irrational, so yeah it could be an integer for all we
know. That'd be weird. See e.g. the English translation of:

<https://ru.wikipedia.org/wiki/%D0%9E%D1%82%D0%BA%D1%80%D1%8B%D1%82%D1%8B%D0%B5_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B5_%D0%BF%D1%80%D0%BE%D0%B1%D0%BB%D0%B5%D0%BC%D1%8B#%D0%92%D0%BE%D0%BF%D1%80%D0%BE%D1%81%D1%8B_%D0%B8%D1%80%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D0%B8>

I think it's believed pi^pi is irrational but it's based on the unproven

<https://en.wikipedia.org/wiki/Schanuel%27s_conjecture>

which would also settle the issue of e + pi and e - pi.

On 7/10/2021 6:02 PM, Clive Arthur wrote:
> On 10/07/2021 21:39, Tom Del Rosso wrote:
>> jlarkin@highlandsniptechnology.com wrote:
>>>
>>> I used to know pi to 100 places. I'm down to 20 now.
>>
>> I know more than 100 digits of pi, e and sqrt(2) combined.
>>
>> I like to mix it up. pi alone is monotonous.
>>
>
> I know all the digits of pi.
>
> But not necessarily in the right order.
>

Everything about the history of your life is written in the digits of
pi! And all the alternate histories too. And every other irrational
number. And a library that contains everything, contains nothing :(

On 10/07/2021 21:38, Phil Hobbs wrote:
> jlarkin@highlandsniptechnology.com wrote:
>> On Sat, 10 Jul 2021 15:01:27 -0400, Phil Hobbs
>> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>>
>>> Piglet wrote:
>>>> On 10/07/2021 12:16, Phil Allison wrote:
>>>>> Hi,
>>>>>
>>>>> includes the easy ways and the harder, precise ways.
>>>>>
>>>>> https://www.youtube.com/watch?v=gMlf1ELvRzc
>>>>>
>>>>> For math freaks, engineers happy to just look it up.
>>>>>
>>>>>
>>>>> .....   Phil
>>>>>
>>>>
>>>> Fun, thanks. As a common or garden workaday engineer I often need to
>>>> calculate with 2pi and most of time for back of the envelope work using
>>>> 6 is good enough to 5% and 6.3 is better than 1%. Anything more precise
>>>> I turn on the computer :)

We were allowed pi^2 = g in physics calculations at university. But not
in crystallography classes where answers were required to 6 sig fig -
forcing me to actually buy a calculator for the first time.

I recently had to do battle with REAL*16 to check something that was
intended to be better than REAL*10 in normal use. Finding a friendly
compiler that supported it was interesting. I tried the Intel one but it
insisted on Win10 and then declared that my graphic card was inadequate!
I also tried their online system but that proved rather unfriendly too.

Salford FORTRAN (now SilverFrost) was OK comes with a reasonable set of
development tools and is free for hobby use £250 to license for research
or commercial use. Alas it has no support for quad precision reals.

GFORTRAN as a part of the GCC compiler suite is surprisingly capable and
handles quad precision without any difficulty. Best if the code is error
free though - its error messages are terse and to the point. It doesn't
insist on having a state of the art graphics card either.

>>> There aren't that many analogue things that need pi to more than two
>>> places.
>>
>> I used to know pi to 100 places. I'm down to 20 now.

It featured (or rather its square root did) in a new series Dr Who
episode when someone was taken over by a malevolent entity and copies
everything the Dr says in a very claustrophobic space tourism flight.

https://youtu.be/QWboRfYGhpI

longer version with more tension in the build up
https://youtu.be/-uZHlvCA1j8

>> We're doing a timing project now and sometimes switch between cycles
>> and radians, to about 1 PPB resolution.
>
> Sure, plus frequency synthesis and all sorts of DSP things.  (I only
> ever memorized pi to REAL*8 accuracy---for higher precision it's
> 4*ridiculous_precision_atan(1.).) ;)

6*ridiculous_precision_asin(0.5) converges a lot faster.

These days it isn't such a problem since hardware support for floating
point is much better. Some older implementations struggled with atan(1).

My supervisor used to use 4*atan(1) until someone pointed out to him
that was the most difficult to converge point of the atan function.
Some older FORTRAN compilers did not get it right to full precision!

--
Regards,
Martin Brown

On 2021-07-11 09:56, Martin Brown wrote:
> On 10/07/2021 21:38, Phil Hobbs wrote:
>> jlarkin@highlandsniptechnology.com wrote:
>>> On Sat, 10 Jul 2021 15:01:27 -0400, Phil Hobbs
>>> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>>>
>>>> Piglet wrote:
>>>>> On 10/07/2021 12:16, Phil Allison wrote:
>>>>>> Hi,
>>>>>>
>>>>>> includes the easy ways and the harder, precise ways.
>>>>>>
>>>>>> https://www.youtube.com/watch?v=gMlf1ELvRzc
>>>>>>
>>>>>> For math freaks, engineers happy to just look it up.
>>>>>>
>>>>>>
>>>>>> ..... Phil
>>>>>>
>>>>>
>>>>> Fun, thanks. As a common or garden workaday engineer I often need to
>>>>> calculate with 2pi and most of time for back of the envelope work using
>>>>> 6 is good enough to 5% and 6.3 is better than 1%. Anything more precise
>>>>> I turn on the computer :)
>
> We were allowed pi^2 = g in physics calculations at university.

The trouble with that is that it makes no physical sense. It's
a coincidence, and not even a very accurate one. It's numerology.

<https://xkcd.com/1047/>

Jeroen Belleman

On Saturday, July 10, 2021 at 7:16:09 AM UTC-4, palli...@gmail.com wrote:
> Hi,
>
> includes the easy ways and the harder, precise ways.
>
> https://www.youtube.com/watch?v=gMlf1ELvRzc
>
> For math freaks, engineers happy to just look it up.

He doesn't establish that PI is a constant. Sloppy thinking from start to finish.

>
>
> ..... Phil

On Sunday, July 11, 2021 at 11:24:03 PM UTC+10, Fred Bloggs wrote:
> On Saturday, July 10, 2021 at 7:16:09 AM UTC-4, palli...@gmail.com wrote:
> > Hi,
> >
> > includes the easy ways and the harder, precise ways.
> >
> > https://www.youtube.com/watch?v=gMlf1ELvRzc
> >
> > For math freaks, engineers happy to just look it up.
>
> He doesn't establish that PI is a constant. Sloppy thinking from start to finish.

It isn't - where space isn't flat. And Einstein established that it isn't flat anywhere where we feel comfortable.

--
Bill Sloman, Sydney

Fred Bloggs wrote:
================
>
> > includes the easy ways and the harder, precise ways.
> >
> > https://www.youtube.com/watch?v=gMlf1ELvRzc
> >
> > For math freaks, engineers happy to just look it up.
>
> He doesn't establish that PI is a constant.
>
-------------------------------------------------------------------

** With the aid of a number of tasty looking pizzas - he demonstrates that the area of a circle with radius 1 is pi.

That will do me.

> Sloppy thinking from start to finish.

** Who's ?

On Sun, 11 Jul 2021 06:24:00 -0700 (PDT), Fred Bloggs
<bloggs.fredbloggs.fred@gmail.com> wrote:

>On Saturday, July 10, 2021 at 7:16:09 AM UTC-4, palli...@gmail.com wrote:
>> Hi,
>>
>> includes the easy ways and the harder, precise ways.
>>
>> https://www.youtube.com/watch?v=gMlf1ELvRzc
>>
>> For math freaks, engineers happy to just look it up.
>
>He doesn't establish that PI is a constant. Sloppy thinking from start to finish.
>
>>
>>
>> ..... Phil

Pi=6 is usually good enough.

--

John Larkin Highland Technology, Inc

The best designs are necessarily accidental.

On Sunday, July 11, 2021 at 10:46:19 AM UTC-4, jla...@highlandsniptechnology.com wrote:
> On Sun, 11 Jul 2021 06:24:00 -0700 (PDT), Fred Bloggs
> <bloggs.fred...@gmail.com> wrote:
>
> >On Saturday, July 10, 2021 at 7:16:09 AM UTC-4, palli...@gmail.com wrote:
> >> Hi,
> >>
> >> includes the easy ways and the harder, precise ways.
> >>
> >> https://www.youtube.com/watch?v=gMlf1ELvRzc
> >>
> >> For math freaks, engineers happy to just look it up.
> >
> >He doesn't establish that PI is a constant. Sloppy thinking from start to finish.
> >
> >>
> >>
> >> ..... Phil
> Pi=6 is usually good enough.

Just remember PI Day is March 14th, good enuf.

> --
>
> John Larkin Highland Technology, Inc
>
> The best designs are necessarily accidental.

On Sunday, July 11, 2021 at 9:58:48 AM UTC-4, palli...@gmail.com wrote:
> Fred Bloggs wrote:
> ================
> >
> > > includes the easy ways and the harder, precise ways.
> > >
> > > https://www.youtube.com/watch?v=gMlf1ELvRzc
> > >
> > > For math freaks, engineers happy to just look it up.
> >
> > He doesn't establish that PI is a constant.
> >
> -------------------------------------------------------------------
>
> ** With the aid of a number of tasty looking pizzas - he demonstrates that the area of a circle with radius 1 is pi.
>
> That will do me.
> > Sloppy thinking from start to finish.
> ** Who's ?

This looks like a lot of hand waving to me, their argument starts out being "circular." Everyone knows circular arguments are logically invalid.
https://math.wikia.org/wiki/Proof:_Pi_is_Constant

On 11/07/2021 15:56, Fred Bloggs wrote:
> On Sunday, July 11, 2021 at 10:46:19 AM UTC-4, jla...@highlandsniptechnology.com wrote:
>> On Sun, 11 Jul 2021 06:24:00 -0700 (PDT), Fred Bloggs
>> <bloggs.fred...@gmail.com> wrote:
>>
>>> On Saturday, July 10, 2021 at 7:16:09 AM UTC-4, palli...@gmail.com wrote:
>>>> Hi,
>>>>
>>>> includes the easy ways and the harder, precise ways.
>>>>
>>>> https://www.youtube.com/watch?v=gMlf1ELvRzc
>>>>
>>>> For math freaks, engineers happy to just look it up.
>>>
>>> He doesn't establish that PI is a constant. Sloppy thinking from start to finish.
>>>
>>>>
>>>>
>>>> ..... Phil
>> Pi=6 is usually good enough.
>
> Just remember PI Day is March 14th, good enuf.

22nd July in UK speak is better = 22/7 = 3.1428...

--
Regards,
Martin Brown

On Sun, 11 Jul 2021 08:56:05 +0100, Martin Brown
<'''newspam'''@nonad.co.uk> wrote:

>On 10/07/2021 21:38, Phil Hobbs wrote:
>> jlarkin@highlandsniptechnology.com wrote:
>>> On Sat, 10 Jul 2021 15:01:27 -0400, Phil Hobbs
>>> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>>>
>>>> Piglet wrote:
>>>>> On 10/07/2021 12:16, Phil Allison wrote:
>>>>>> Hi,
>>>>>>
>>>>>> includes the easy ways and the harder, precise ways.
>>>>>>
>>>>>> https://www.youtube.com/watch?v=gMlf1ELvRzc
>>>>>>
>>>>>> For math freaks, engineers happy to just look it up.
>>>>>>
>>>>>>
>>>>>> .....   Phil
>>>>>>
>>>>>
>>>>> Fun, thanks. As a common or garden workaday engineer I often need to
>>>>> calculate with 2pi and most of time for back of the envelope work using
>>>>> 6 is good enough to 5% and 6.3 is better than 1%. Anything more precise
>>>>> I turn on the computer :)
>
>We were allowed pi^2 = g in physics calculations at university. But not
>in crystallography classes where answers were required to 6 sig fig -
>forcing me to actually buy a calculator for the first time.
>
>I recently had to do battle with REAL*16 to check something that was
>intended to be better than REAL*10 in normal use. Finding a friendly
>compiler that supported it was interesting. I tried the Intel one but it
>insisted on Win10 and then declared that my graphic card was inadequate!
>I also tried their online system but that proved rather unfriendly too.
>
>Salford FORTRAN (now SilverFrost) was OK comes with a reasonable set of
>development tools and is free for hobby use £250 to license for research
>or commercial use. Alas it has no support for quad precision reals.
>
>GFORTRAN as a part of the GCC compiler suite is surprisingly capable and
>handles quad precision without any difficulty. Best if the code is error
>free though - its error messages are terse and to the point. It doesn't
>insist on having a state of the art graphics card either.
>
>>>> There aren't that many analogue things that need pi to more than two
>>>> places.
>>>
>>> I used to know pi to 100 places. I'm down to 20 now.
>
>It featured (or rather its square root did) in a new series Dr Who
>episode when someone was taken over by a malevolent entity and copies
>everything the Dr says in a very claustrophobic space tourism flight.
>
>https://youtu.be/QWboRfYGhpI
>
>longer version with more tension in the build up
>https://youtu.be/-uZHlvCA1j8
>
>>> We're doing a timing project now and sometimes switch between cycles
>>> and radians, to about 1 PPB resolution.
>>
>> Sure, plus frequency synthesis and all sorts of DSP things.  (I only
>> ever memorized pi to REAL*8 accuracy---for higher precision it's
>> 4*ridiculous_precision_atan(1.).) ;)
>
>6*ridiculous_precision_asin(0.5) converges a lot faster.
>
>These days it isn't such a problem since hardware support for floating
>point is much better. Some older implementations struggled with atan(1).
>
>My supervisor used to use 4*atan(1) until someone pointed out to him
>that was the most difficult to converge point of the atan function.
>Some older FORTRAN compilers did not get it right to full precision!

Later DEC VAX hardware implemented 128-bit floats in hardware.

Mathematica handles arbitrary precision quite well. See the N[]
operator.

Joe Gwinn

On Sun, 11 Jul 2021 07:56:43 -0700 (PDT), Fred Bloggs
<bloggs.fredbloggs.fred@gmail.com> wrote:

>On Sunday, July 11, 2021 at 10:46:19 AM UTC-4, jla...@highlandsniptechnology.com wrote:
>> On Sun, 11 Jul 2021 06:24:00 -0700 (PDT), Fred Bloggs
>> <bloggs.fred...@gmail.com> wrote:
>>
>> >On Saturday, July 10, 2021 at 7:16:09 AM UTC-4, palli...@gmail.com wrote:
>> >> Hi,
>> >>
>> >> includes the easy ways and the harder, precise ways.
>> >>
>> >> https://www.youtube.com/watch?v=gMlf1ELvRzc
>> >>
>> >> For math freaks, engineers happy to just look it up.
>> >
>> >He doesn't establish that PI is a constant. Sloppy thinking from start to finish.
>> >
>> >>
>> >>
>> >> ..... Phil
>> Pi=6 is usually good enough.
>
>Just remember PI Day is March 14th, good enuf.

There's always a long line at Mission Pie on that day.

I'm baking a pi right now. I promised the neighbors some of the last
one, but Certain Parties ate all of it. So I have a moral obligation
to do another one.

--

John Larkin Highland Technology, Inc

The best designs are necessarily accidental.

On Sun, 11 Jul 2021 16:44:16 +0100, Martin Brown
<'''newspam'''@nonad.co.uk> wrote:

>On 11/07/2021 15:56, Fred Bloggs wrote:
>> On Sunday, July 11, 2021 at 10:46:19 AM UTC-4, jla...@highlandsniptechnology.com wrote:
>>> On Sun, 11 Jul 2021 06:24:00 -0700 (PDT), Fred Bloggs
>>> <bloggs.fred...@gmail.com> wrote:
>>>
>>>> On Saturday, July 10, 2021 at 7:16:09 AM UTC-4, palli...@gmail.com wrote:
>>>>> Hi,
>>>>>
>>>>> includes the easy ways and the harder, precise ways.
>>>>>
>>>>> https://www.youtube.com/watch?v=gMlf1ELvRzc
>>>>>
>>>>> For math freaks, engineers happy to just look it up.
>>>>
>>>> He doesn't establish that PI is a constant. Sloppy thinking from start to finish.
>>>>
>>>>>
>>>>>
>>>>> ..... Phil
>>> Pi=6 is usually good enough.
>>
>> Just remember PI Day is March 14th, good enuf.
>
>22nd July in UK speak is better = 22/7 = 3.1428...

Do you still say "four and twenty" ?

How about "fortnight" ?

--

John Larkin Highland Technology, Inc

The best designs are necessarily accidental.