On Friday, June 4, 2021 at 6:05:34 AM UTC+2, djoyce099 wrote:
> On Thursday, June 3, 2021 at 11:21:47 AM UTC-4, Peter wrote:
> > djoyce099 wrote:
> > > On Wednesday, June 2, 2021 at 2:13:03 PM UTC-4, Peter wrote:
> > >> djoyce099 wrote:
> > >>> On Wednesday, June 2, 2021 at 10:33:33 AM UTC-4, Peter wrote:
> > >>>> djoyce099 wrote:
> > >>>>> [...]
> > >>>>> Here is the description of the digital calculator I use. Not sure if there is a download available.
> > >>>>>
> > >>>>> b calc for windows
> > >>>> Betcha you are being misled by a sans serif font. Or you _were_ misled,
> > >>>> but why go on being misled?
> > >>>> version 2.05 copyright @1999,2010 GF Cornwell
> > >>>
> > >>> This is a powerful scientific calculator where I have not used all its features.
> > >>> The log(e) key (In) is right next to the (e^x) key.
> > >>> It is easy to use and has up to 10,000 digit accuracy so shame on me for using it.
> > >>> As long as it continues to produce correct results, then I am going to continue to use it.
> > >>> I am not being misled at all.
> > >> And yet you just wrote "The log(e) key (In) is..." when "The log(e) key
> > >> (ln) is..." is correct.
> > >>
> > >> My comments were not about your use of BCalc, they were about what you
> > >> type here.
> > >
> > > MY bad-- so to the original problem, is there a closer relationship to pi and e than what I show?
> > > Except for the imaginary version, it is just a coincidence I know but still interesting.
> > There are some positive integers called Heegner numbers. These are
> > they: 1, 2, 3, 7, 11, 19, 43, 67, and 163. They arise in algebra in
> > ways that needn't concern us. If h is a Heenger number then
> >
> > e^{pi sqrt h}
> >
> > is close to an integer, and the bigger h the closer. For example with h
> > = 163 the difference is about 0.00000000000075.
> Interesting that 163 is probably the largest known Heenger number and why e and pi
> are involved.

Probably? You think the proof there are just 9 Heegner numbers might be flawed?

https://en.wikipedia.org/wiki/Heegner_number

> Is it just another coincidence?
>
> > You may know that
> Yes.
> > n^2 - n + 41
> >
> > is prime for n = 1, 2, ..., 40. And this is connected to max h = 4*41 - 1.
> > Just as 'beautiful' points the way for aesthetics and 'good' for ethics,
> > so do words like 'true' for logic. All sciences have truth as their
> > goal; but logic is also concerned with it in a quite different way:
> > logic has much the same relation to truth as physics has to weight or
> > heat. Frege in 'Thoughts' (Der Gedanke)

On Sunday, May 30, 2021 at 4:14:01 PM UTC-4, djoyce099 wrote:
> On Sunday, May 30, 2021 at 3:32:16 PM UTC-4, djoyce099 wrote:
> > On Sunday, May 30, 2021 at 2:40:00 PM UTC-4, mitchr...@gmail.com wrote:
> > > On Sunday, May 30, 2021 at 8:54:35 AM UTC-7, djoyce099 wrote:
> > > > On Saturday, May 29, 2021 at 8:52:52 PM UTC-4, djoyce099 wrote:
> > > > > On Saturday, May 29, 2021 at 8:44:31 PM UTC-4, djoyce099 wrote:
> > > > > > On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
> > > > > > > sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
> > > > > > >
> > > > > > > 3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382706863183574...
> > > > > > > 3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267326022276173...
> > > > > > >
> > > > > > > The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> > > > > > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > > > > > A much closer approximation to pi (12 correct digits of pi).
> > > > > > > Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> > > > > > > from above the results are the same---
> > > > > > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > > > > >
> > > > > > > Dan
> > > > > > Correction To the above--
> > > > > > (e^6-pi^5)/(pi^3)= 3.1415932235b (no sqrt.)
> > > > > Enter this in Wolfram Alpha --- (e^6 - pi^5)/pi^3 =>pi
> > > > Who can come up with a closer relationship of the above of pi and e outside of the imaginary e^pi*i = -1
> > > >
> > > > Dan
> > > PI is a round closed curve... e is not...
> > >
> > >
> > > Mitchell Raemsch
> > Yeah, I know the difference, but that is not the question!
> > I am just looking for a closer relationship of what I found with ---
> > (e^6 - pi^5)/pi^3 =>pi (5.699592e-7 a > pi difference)
> > Using any or all of the 4 operators, +,-,/,^ and any integers along with pi and e in the equation to accomplish the challenge
> > above.
> >
> > Dan
> 1/(((e^6)/(pi^5))-1) =<pi (5.6999581e-7 a < pi difference) so (e^6 - pi^5)/pi^3 =>pi is the best so far.

This is somewhat disingenuous, but
e^5 pi^5 / e (pi e )^ 4
gets a perfect pi, but no, I don't accuse you of a bad construction. Still, it does carry this low-brow problem.

djoyce099 wrote:
> On Thursday, June 3, 2021 at 11:21:47 AM UTC-4, Peter wrote:
>> djoyce099 wrote:
>>> On Wednesday, June 2, 2021 at 2:13:03 PM UTC-4, Peter wrote:
>>>> djoyce099 wrote:
>>>>> On Wednesday, June 2, 2021 at 10:33:33 AM UTC-4, Peter wrote:
>>>>>> djoyce099 wrote:
>>>>>>> [...]
>>>>>>> Here is the description of the digital calculator I use. Not sure if there is a download available.
>>>>>>>
>>>>>>> b calc for windows
>>>>>> Betcha you are being misled by a sans serif font. Or you _were_ misled,
>>>>>> but why go on being misled?
>>>>>> version 2.05 copyright @1999,2010 GF Cornwell
>>>>>
>>>>> This is a powerful scientific calculator where I have not used all its features.
>>>>> The log(e) key (In) is right next to the (e^x) key.
>>>>> It is easy to use and has up to 10,000 digit accuracy so shame on me for using it.
>>>>> As long as it continues to produce correct results, then I am going to continue to use it.
>>>>> I am not being misled at all.
>>>> And yet you just wrote "The log(e) key (In) is..." when "The log(e) key
>>>> (ln) is..." is correct.
>>>>
>>>> My comments were not about your use of BCalc, they were about what you
>>>> type here.
>>>
>>> MY bad-- so to the original problem, is there a closer relationship to pi and e than what I show?
>>> Except for the imaginary version, it is just a coincidence I know but still interesting.
>> There are some positive integers called Heegner numbers. These are
>> they: 1, 2, 3, 7, 11, 19, 43, 67, and 163. They arise in algebra in
>> ways that needn't concern us. If h is a Heenger number then
>>
>> e^{pi sqrt h}
>>
>> is close to an integer, and the bigger h the closer. For example with h
>> = 163 the difference is about 0.00000000000075.
>
> Interesting that 163 is probably the largest known Heenger number and why e and pi

_The_ largest.

> are involved.
> Is it just another coincidence?

No, but it's a complicated matter to do with elliptic functions.

--
Just as 'beautiful' points the way for aesthetics and 'good' for ethics,
so do words like 'true' for logic. All sciences have truth as their
goal; but logic is also concerned with it in a quite different way:
logic has much the same relation to truth as physics has to weight or
heat. Frege in 'Thoughts' (Der Gedanke)

djoyce099 wrote on 6/4/2021 :
> On Thursday, June 3, 2021 at 11:21:47 AM UTC-4, Peter wrote:
>> djoyce099 wrote:
>>> On Wednesday, June 2, 2021 at 2:13:03 PM UTC-4, Peter wrote:
>>>> djoyce099 wrote:
>>>>> On Wednesday, June 2, 2021 at 10:33:33 AM UTC-4, Peter wrote:
>>>>>> djoyce099 wrote:
>>>>>>> [...]
>>>>>>> Here is the description of the digital calculator I use. Not sure if
>>>>>>> there is a download available.
>>>>>>>
>>>>>>> b calc for windows
>>>>>> Betcha you are being misled by a sans serif font. Or you _were_ misled,
>>>>>> but why go on being misled?
>>>>>> version 2.05 copyright @1999,2010 GF Cornwell
>>>>>
>>>>> This is a powerful scientific calculator where I have not used all its
>>>>> features. The log(e) key (In) is right next to the (e^x) key.
>>>>> It is easy to use and has up to 10,000 digit accuracy so shame on me for
>>>>> using it. As long as it continues to produce correct results, then I am
>>>>> going to continue to use it. I am not being misled at all.
>>>> And yet you just wrote "The log(e) key (In) is..." when "The log(e) key
>>>> (ln) is..." is correct.
>>>>
>>>> My comments were not about your use of BCalc, they were about what you
>>>> type here.
>>>
>>> MY bad-- so to the original problem, is there a closer relationship to pi
>>> and e than what I show? Except for the imaginary version, it is just a
>>> coincidence I know but still interesting.
>> There are some positive integers called Heegner numbers. These are
>> they: 1, 2, 3, 7, 11, 19, 43, 67, and 163. They arise in algebra in
>> ways that needn't concern us. If h is a Heenger number then
>>
>> e^{pi sqrt h}
>>
>> is close to an integer, and the bigger h the closer. For example with h
>> = 163 the difference is about 0.00000000000075.
>
> Interesting that 163 is probably the largest known Heenger number and why e
> and pi are involved.
> Is it just another coincidence?

I'm used to e and pi popping up in seemingly unrelated contexts, this
doesn't surprise me much as the i in e to the pi i is pure phase in
this context and so could sqrt of h simply be an angular thing in C.

Funny to me is the apparent connection to primes and probably the prime
counting function and the RH too.

On Friday, June 4, 2021 at 7:44:24 AM UTC-4, timba...@gmail.com wrote:
> On Sunday, May 30, 2021 at 4:14:01 PM UTC-4, djoyce099 wrote:
> > On Sunday, May 30, 2021 at 3:32:16 PM UTC-4, djoyce099 wrote:
> > > On Sunday, May 30, 2021 at 2:40:00 PM UTC-4, mitchr...@gmail.com wrote:
> > > > On Sunday, May 30, 2021 at 8:54:35 AM UTC-7, djoyce099 wrote:
> > > > > On Saturday, May 29, 2021 at 8:52:52 PM UTC-4, djoyce099 wrote:
> > > > > > On Saturday, May 29, 2021 at 8:44:31 PM UTC-4, djoyce099 wrote:
> > > > > > > On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
> > > > > > > > sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
> > > > > > > >
> > > > > > > > 3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382706863183574...
> > > > > > > > 3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267326022276173...
> > > > > > > >
> > > > > > > > The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> > > > > > > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > > > > > > A much closer approximation to pi (12 correct digits of pi).
> > > > > > > > Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> > > > > > > > from above the results are the same---
> > > > > > > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > > > > > >
> > > > > > > > Dan
> > > > > > > Correction To the above--
> > > > > > > (e^6-pi^5)/(pi^3)= 3.1415932235b (no sqrt.)
> > > > > > Enter this in Wolfram Alpha --- (e^6 - pi^5)/pi^3 =>pi
> > > > > Who can come up with a closer relationship of the above of pi and e outside of the imaginary e^pi*i = -1
> > > > >
> > > > > Dan
> > > > PI is a round closed curve... e is not...
> > > >
> > > >
> > > > Mitchell Raemsch
> > > Yeah, I know the difference, but that is not the question!
> > > I am just looking for a closer relationship of what I found with ---
> > > (e^6 - pi^5)/pi^3 =>pi (5.699592e-7 a > pi difference)
> > > Using any or all of the 4 operators, +,-,/,^ and any integers along with pi and e in the equation to accomplish the challenge
> > > above.
> > >
> > > Dan
> > 1/(((e^6)/(pi^5))-1) =<pi (5.6999581e-7 a < pi difference) so (e^6 - pi^5)/pi^3 =>pi is the best so far.
> This is somewhat disingenuous, but
> e^5 pi^5 / e (pi e )^ 4
> gets a perfect pi, but no, I don't accuse you of a bad construction. Still, it does carry this low-brow problem.

Come on, both sides of your equation will work with any numbers.
(7^5*8^5) /( 7 ((8*7 )^ 4)) =8
By just replacing e with 7 and pi with 8.
Cute play on numbers.

On Friday, June 4, 2021 at 7:53:51 AM UTC-4, Peter wrote:
> djoyce099 wrote:
> > On Thursday, June 3, 2021 at 11:21:47 AM UTC-4, Peter wrote:
> >> djoyce099 wrote:
> >>> On Wednesday, June 2, 2021 at 2:13:03 PM UTC-4, Peter wrote:
> >>>> djoyce099 wrote:
> >>>>> On Wednesday, June 2, 2021 at 10:33:33 AM UTC-4, Peter wrote:
> >>>>>> djoyce099 wrote:
> >>>>>>> [...]
> >>>>>>> Here is the description of the digital calculator I use. Not sure if there is a download available.
> >>>>>>>
> >>>>>>> b calc for windows
> >>>>>> Betcha you are being misled by a sans serif font. Or you _were_ misled,
> >>>>>> but why go on being misled?
> >>>>>> version 2.05 copyright @1999,2010 GF Cornwell
> >>>>>
> >>>>> This is a powerful scientific calculator where I have not used all its features.
> >>>>> The log(e) key (In) is right next to the (e^x) key.
> >>>>> It is easy to use and has up to 10,000 digit accuracy so shame on me for using it.
> >>>>> As long as it continues to produce correct results, then I am going to continue to use it.
> >>>>> I am not being misled at all.
> >>>> And yet you just wrote "The log(e) key (In) is..." when "The log(e) key
> >>>> (ln) is..." is correct.
> >>>>
> >>>> My comments were not about your use of BCalc, they were about what you
> >>>> type here.
> >>>
> >>> MY bad-- so to the original problem, is there a closer relationship to pi and e than what I show?
> >>> Except for the imaginary version, it is just a coincidence I know but still interesting.
> >> There are some positive integers called Heegner numbers. These are
> >> they: 1, 2, 3, 7, 11, 19, 43, 67, and 163. They arise in algebra in
> >> ways that needn't concern us. If h is a Heenger number then
> >>
> >> e^{pi sqrt h}
> >>
> >> is close to an integer, and the bigger h the closer. For example with h
> >> = 163 the difference is about 0.00000000000075.
> >
> > Interesting that 163 is probably the largest known Heenger number and why e and pi
> _The_ largest.
> > are involved.
> > Is it just another coincidence?
> No, but it's a complicated matter to do with elliptic functions.

and maybe the fact that e^(pi)i + 1 =0 which is surely complicated,
at least for me.
Is it possible that the square root of a prime > 163 but not a Heenger number
have a closer result than the sqrt(163)
> --
> Just as 'beautiful' points the way for aesthetics and 'good' for ethics,
> so do words like 'true' for logic. All sciences have truth as their
> goal; but logic is also concerned with it in a quite different way:
> logic has much the same relation to truth as physics has to weight or
> heat. Frege in 'Thoughts' (Der Gedanke)

On 5/29/2021 2:54 PM, djoyce099 wrote:
>
> sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
>
> 3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382706863183574...
> 3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267326022276173...
>
> The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> A much closer approximation to pi (12 correct digits of pi).
> Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> from above the results are the same---
> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>
> Dan
>

atan(1) * 4 ?

On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
> sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
Expanding this outward --

((e^24)/(pi^15))/((pi+1)^4) => pi

3.141593204098745805252355494447...
A little closer to pi than the original above--
3.141593223585714204304623374489...

>3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
> >3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
>
> The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> A much closer approximation to pi (12 correct digits of pi).
> Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> from above the results are the same---
> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>
> Dan

On Saturday, June 5, 2021 at 12:41:46 PM UTC-4, djoyce099 wrote:
> On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
> > sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
> Expanding this outward --
>
>
> ((e^24)/(pi^15))/((pi+1)^4) => pi
>
> 3.141593204098745805252355494447...
> A little closer to pi than the original above--
> 3.141593223585714204304623374489...
>
>
> >3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
> > >3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
> >
> > The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > A much closer approximation to pi (12 correct digits of pi).
> > Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> > from above the results are the same---
> > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> >
> > Dan

Does this explain, e^pi(i) +1 = 0 in a simplified manner?

n= (NL(pi))/(NL((pi)-1)) =
7.909422985661426544687605808867791752718052124496231483161724...
Then--
(pi^n)/(e^n)=pi

(Using the Laplace transform)??

Dan

On Sunday, June 6, 2021 at 9:47:44 AM UTC-4, djoyce099 wrote:
> On Saturday, June 5, 2021 at 12:41:46 PM UTC-4, djoyce099 wrote:
> > On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
> > > sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
> > Expanding this outward --
> >
> >
> > ((e^24)/(pi^15))/((pi+1)^4) => pi
> >
> > 3.141593204098745805252355494447...
> > A little closer to pi than the original above--
> > 3.141593223585714204304623374489...
> >
> >
> > >3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
> > > >3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
> > >
> > > The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > A much closer approximation to pi (12 correct digits of pi).
> > > Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> > > from above the results are the same---
> > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > >
> > > Dan
> Does this explain, e^pi(i) +1 = 0 in a simplified manner?
>
> n= (NL(pi))/(NL((pi)-1)) =
> 7.909422985661426544687605808867791752718052124496231483161724...
> Then--
> (pi^n)/(e^n)=pi
>
> (Using the Laplace transform)??
>
> Dan
Sorry my screw-up-
Should be -- n= (NL(pi))/(NL((e)-1))

On Sunday, June 6, 2021 at 10:03:10 AM UTC-4, djoyce099 wrote:
> On Sunday, June 6, 2021 at 9:47:44 AM UTC-4, djoyce099 wrote:
> > On Saturday, June 5, 2021 at 12:41:46 PM UTC-4, djoyce099 wrote:
> > > On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
> > > > sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
> > > Expanding this outward --
> > >
> > >
> > > ((e^24)/(pi^15))/((pi+1)^4) => pi
> > >
> > > 3.141593204098745805252355494447...
> > > A little closer to pi than the original above--
> > > 3.141593223585714204304623374489...
> > >
> > >
> > > >3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
> > > > >3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
> > > >
> > > > The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> > > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > > A much closer approximation to pi (12 correct digits of pi).
> > > > Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> > > > from above the results are the same---
> > > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > >
> > > > Dan
> > Does this explain, e^pi(i) +1 = 0 in a simplified manner?
> >
> > n= (NL(pi))/(NL((pi)-1)) =
> > 7.909422985661426544687605808867791752718052124496231483161724...
> > Then--
> > (pi^n)/(e^n)=pi
> >
> > (Using the Laplace transform)??
> >
> > Dan
> Sorry my screw-up-
> Should be -- n= (NL(pi))/(NL((e)-1))
Or is it Wolfram-- here is what I entered --- n= (NL(pi))/(NL((pi)-1)) then (pi^n)/(e^n)=pi

On Sunday, June 6, 2021 at 10:07:14 AM UTC-4, djoyce099 wrote:
> On Sunday, June 6, 2021 at 10:03:10 AM UTC-4, djoyce099 wrote:
> > On Sunday, June 6, 2021 at 9:47:44 AM UTC-4, djoyce099 wrote:
> > > On Saturday, June 5, 2021 at 12:41:46 PM UTC-4, djoyce099 wrote:
> > > > On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
> > > > > sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
> > > > Expanding this outward --
> > > >
> > > >
> > > > ((e^24)/(pi^15))/((pi+1)^4) => pi
> > > >
> > > > 3.141593204098745805252355494447...
> > > > A little closer to pi than the original above--
> > > > 3.141593223585714204304623374489...
> > > >
> > > >
> > > > >3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
> > > > > >3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
> > > > >
> > > > > The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> > > > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > > > A much closer approximation to pi (12 correct digits of pi).
> > > > > Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> > > > > from above the results are the same---
> > > > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > > >
> > > > > Dan
> > > Does this explain, e^pi(i) +1 = 0 in a simplified manner?
> > >
> > > n= (NL(pi))/(NL((pi)-1)) =
> > > 7.909422985661426544687605808867791752718052124496231483161724...
> > > Then--
> > > (pi^n)/(e^n)=pi
> > >
> > > (Using the Laplace transform)??
> > >
> > > Dan
> > Sorry my screw-up-
> > Should be -- n= (NL(pi))/(NL((e)-1))
> Or is it Wolfram-- here is what I entered --- n= (NL(pi))/(NL((pi)-1)) then (pi^n)/(e^n)=pi
My bad-- it is just the Laplace transform which works with any number.

djoyce099 wrote:
> On Saturday, June 5, 2021 at 12:41:46 PM UTC-4, djoyce099 wrote:
>> On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
>>> sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
>> Expanding this outward --
>>
>>
>> ((e^24)/(pi^15))/((pi+1)^4) => pi
>>
>> 3.141593204098745805252355494447...
>> A little closer to pi than the original above--
>> 3.141593223585714204304623374489...
>>
>>
>>> 3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
>>>> 3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
>>>
>>> The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
>>> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>>> A much closer approximation to pi (12 correct digits of pi).
>>> Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
>>> from above the results are the same---
>>> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>>>
>>> Dan
>
> Does this explain, e^pi(i) +1 = 0 in a simplified manner?
>
> n= (NL(pi))/(NL((pi)-1)) =
> 7.909422985661426544687605808867791752718052124496231483161724...
> Then--
> (pi^n)/(e^n)=pi
>
> (Using the Laplace transform)??
>
> Dan
>

What's N?

--
The world will little note, nor long remember what we say here
Abraham Lincoln at Gettysburg

djoyce099 presented the following explanation :
> On Saturday, June 5, 2021 at 12:41:46 PM UTC-4, djoyce099 wrote:
>> On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
>>> sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) =
>>> 3.1415920835...
>> Expanding this outward --
>>
>>
>> ((e^24)/(pi^15))/((pi+1)^4) => pi
>>
>> 3.141593204098745805252355494447...
>> A little closer to pi than the original above--
>> 3.141593223585714204304623374489...
>>
>>
>>> 3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
>>>> 3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
>>>
>>> The difference between the two then divide by 2 and add to the second entry
>>> above of <pi and this will =
>>> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>>> A much closer approximation to pi (12 correct digits of pi). Also curious
>>> if you divide the difference by 2, as above but subtract it from the first
>>> larger entry from above the results are the same---
>>> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>>>
>>> Dan
>
> Does this explain, e^pi(i) +1 = 0 in a simplified manner?

It's actually pretty simple, it is the variety of explanations that
make it difficult. It's basically just a description of the unit circle
in the complex plane intersecting with the real line.

> n= (NL(pi))/(NL((pi)-1)) =
> 7.909422985661426544687605808867791752718052124496231483161724...
> Then--
> (pi^n)/(e^n)=pi
>
> (Using the Laplace transform)??

I don't know, but it wouldn't surprise me to find other ways of stating
this same relation between e and pi.

On Sun, 6 Jun 2021 06:47:37 -0700 (PDT), djoyce099
<hlauk.h.bogart@gmail.com> wrote:

>On Saturday, June 5, 2021 at 12:41:46 PM UTC-4, djoyce099 wrote:
>> On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
>> > sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
>> Expanding this outward --
>>
>>
>> ((e^24)/(pi^15))/((pi+1)^4) => pi
>>
>> 3.141593204098745805252355494447...
>> A little closer to pi than the original above--
>> 3.141593223585714204304623374489...
>>
>>
>> >3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
>> > >3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
>> >
>> > The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
>> > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>> > A much closer approximation to pi (12 correct digits of pi).
>> > Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
>> > from above the results are the same---
>> > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>> >
>> > Dan
>
>Does this explain, e^pi(i) +1 = 0 in a simplified manner?
>
>n= (NL(pi))/(NL((pi)-1)) =
>7.909422985661426544687605808867791752718052124496231483161724...
>Then--
>(pi^n)/(e^n)=pi
>
>(Using the Laplace transform)??

Ignoring the fact that the first statement is nothing more than a
computational result and the second is obviously false -

What is the LOGIC that led you from the first to the second?

--
Remove del for email

On Sun, 6 Jun 2021 06:47:37 -0700 (PDT), djoyce099
<hlauk.h.bogart@gmail.com> wrote:

>On Saturday, June 5, 2021 at 12:41:46 PM UTC-4, djoyce099 wrote:
>> On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
>> > sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
>> Expanding this outward --
>>
>>
>> ((e^24)/(pi^15))/((pi+1)^4) => pi
>>
>> 3.141593204098745805252355494447...
>> A little closer to pi than the original above--
>> 3.141593223585714204304623374489...
>>
>>
>> >3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
>> > >3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
>> >
>> > The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
>> > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>> > A much closer approximation to pi (12 correct digits of pi).
>> > Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
>> > from above the results are the same---
>> > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>> >
>> > Dan
>
>Does this explain, e^pi(i) +1 = 0 in a simplified manner?
>
>n= (NL(pi))/(NL((pi)-1)) =
>7.909422985661426544687605808867791752718052124496231483161724...
>Then--
>(pi^n)/(e^n)=pi
>
>(Using the Laplace transform)??

My previous response was a incorrect.

Observe that NL(pi) =q such that e^q = pi
and
NL(pi)-1 = q-1 but also
NL(pi)-1 = NL(pi) - NL(e) = NL(pi/e) = r such that e^r = pi/e
and also r = q-1

Then n = q/r, pi^n = pi^(q/r), and e^n = e^(q/r)

Let Q denote pi^n/e^n.
Q = (pi/e)^n = (pi/e)^(q/r)
Q^r = (pi/e)^q = pi^q / e^q
Since e^q = pi then Q^r = = pi^q / pi = pi^(q-1)

Since r = q-1
Q^(q-1) = pi^(q-1) and Q = pi.

No Laplace transform needed.

--
Remove del for email

On Sun, 6 Jun 2021 07:03:02 -0700 (PDT), djoyce099
<hlauk.h.bogart@gmail.com> wrote:

>On Sunday, June 6, 2021 at 9:47:44 AM UTC-4, djoyce099 wrote:
>> On Saturday, June 5, 2021 at 12:41:46 PM UTC-4, djoyce099 wrote:
>> > On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
>> > > sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
>> > Expanding this outward --
>> >
>> >
>> > ((e^24)/(pi^15))/((pi+1)^4) => pi
>> >
>> > 3.141593204098745805252355494447...
>> > A little closer to pi than the original above--
>> > 3.141593223585714204304623374489...
>> >
>> >
>> > >3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
>> > > >3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
>> > >
>> > > The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
>> > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>> > > A much closer approximation to pi (12 correct digits of pi).
>> > > Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
>> > > from above the results are the same---
>> > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>> > >
>> > > Dan
>> Does this explain, e^pi(i) +1 = 0 in a simplified manner?
>>
>> n= (NL(pi))/(NL((pi)-1)) =
>> 7.909422985661426544687605808867791752718052124496231483161724...
>> Then--
>> (pi^n)/(e^n)=pi
>>
>> (Using the Laplace transform)??
>>
>> Dan
>Sorry my screw-up-
>Should be -- n= (NL(pi))/(NL((e)-1))

You had it right the first time. NL(e) is obviously 1. NL(e)-1 is 0
and that is not a suitable denominator.

--
Remove del for email

On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
> sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
>
> 3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382706863183574...
> 3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267326022276173...
>
> The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> A much closer approximation to pi (12 correct digits of pi).
> Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> from above the results are the same---
> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>
> Dan

In this case ---When n is >7 and <8 then (pi^n)/(e^n)= pi

(pi^n)/(e^n)= pi then the smallest and only power number is--- n = log(pi)/log(pi)-1

Is (n) listed as a constant?

There used to be a constants lookup where it either hit on a constant or showed how close
the number you entered was to that constant.
If still out there, what is the link?

On Mon, 7 Jun 2021 08:47:43 -0700 (PDT), djoyce099
<hlauk.h.bogart@gmail.com> wrote:

>On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
>> sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
>>
>> 3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382706863183574...
>> 3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267326022276173...
>>
>> The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
>> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>> A much closer approximation to pi (12 correct digits of pi).
>> Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
>> from above the results are the same---
>> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
>>
>> Dan
>
>In this case ---When n is >7 and <8 then (pi^n)/(e^n)= pi
>
>(pi^n)/(e^n)= pi then the smallest and only power number is--- n = log(pi)/log(pi)-1
>

Since log(pi)/log(pi) = 1, you obviously meant log(pi)/[log(pi)-1]. We
have discussed this before.

Why did you decide to use new terminology? log(pi) is very different
than ln(pi). You started this thread using NL instead on ln but at
least that was understandable.

n = log(pi)/[log(pi)-1] = -0.988664108 which when substituted into
your equation produces 0.86667672 which is nowhere near pi.

n = ln(pi)/[ln(pi)-1] = 7.909422986 as you previously noted and this
does produce the result you want. I showed in a previous message why
this must be true.

>Is (n) listed as a constant?
>
>There used to be a constants lookup where it either hit on a constant or showed how close
>the number you entered was to that constant.
>If still out there, what is the link?

For n to be on a list of useful constants, it would have to be useful.
While pi is a fascinating number, you should be aware that for any
real number R =/=e, if you compute
n = ln(R)/[ln(R)-1]
then (R^n)/(e^n) will always equal R. So what makes your n for R = pi
any more useful than the one for R = phi or the one for R = omega?

Furthermore, there is nothing special about e in the above. If you
use log instead on ln, then you only need to replace e^n with 10^n. In
point of fact, for base b and R =/= b:
when n = log_b(R)/[log_b(R)-1]
then (R^n)/(b^n) will always equal R

Rather than try to bedazzle us with useless arithmetic carried out to
an excessive number of decimal places, when you find a relationship
like this that catches your fancy, you ought to try to understand why
it is true.

--
Remove del for email

On Monday, June 7, 2021 at 12:42:26 PM UTC-4, Barry Schwarz wrote:
> On Mon, 7 Jun 2021 08:47:43 -0700 (PDT), djoyce099
> <hlauk.h...@gmail.com> wrote:
>
> >On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
> >> sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
> >>
> >> 3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382706863183574...
> >> 3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267326022276173...
> >>
> >> The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> >> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> >> A much closer approximation to pi (12 correct digits of pi).
> >> Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> >> from above the results are the same---
> >> 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> >>
> >> Dan
> >
> >In this case ---When n is >7 and <8 then (pi^n)/(e^n)= pi
> >
> >(pi^n)/(e^n)= pi then the smallest and only power number is--- n = log(pi)/log(pi)-1
> >
> Since log(pi)/log(pi) = 1, you obviously meant log(pi)/[log(pi)-1]. We
> have discussed this before.
>
> Why did you decide to use new terminology? log(pi) is very different
> than ln(pi). You started this thread using NL instead on ln but at
> least that was understandable.
>
> n = log(pi)/[log(pi)-1] = -0.988664108 which when substituted into
> your equation produces 0.86667672 which is nowhere near pi.
>
> n = ln(pi)/[ln(pi)-1] = 7.909422986 as you previously noted and this
> does produce the result you want. I showed in a previous message why
> this must be true.
> >Is (n) listed as a constant?
> >
> >There used to be a constants lookup where it either hit on a constant or showed how close
> >the number you entered was to that constant.
> >If still out there, what is the link?
> For n to be on a list of useful constants, it would have to be useful.
> While pi is a fascinating number, you should be aware that for any
> real number R =/=e, if you compute
> n = ln(R)/[ln(R)-1]
> then (R^n)/(e^n) will always equal R. So what makes your n for R = pi
> any more useful than the one for R = phi or the one for R = omega?
>
> Furthermore, there is nothing special about e in the above. If you
> use log instead on ln, then you only need to replace e^n with 10^n. In
> point of fact, for base b and R =/= b:
> when n = log_b(R)/[log_b(R)-1]
> then (R^n)/(b^n) will always equal R
>
> Rather than try to bedazzle us with useless arithmetic carried out to
> an excessive number of decimal places, when you find a relationship
> like this that catches your fancy, you ought to try to understand why
> it is true.
> --
> Remove del for email

No bedazzled, just curious.
So not significant enough for a constant.
Do you know the website lookup for constants?
I lost that info and it was very informative on all known constants
or numbers entered that was close to a constant.

Thanks,
Dan

On Sunday, June 6, 2021 at 3:47:44 PM UTC+2, djoyce099 wrote:
> On Saturday, June 5, 2021 at 12:41:46 PM UTC-4, djoyce099 wrote:
> > On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
> > > sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
> > Expanding this outward --
> >
> >
> > ((e^24)/(pi^15))/((pi+1)^4) => pi
> >
> > 3.141593204098745805252355494447...
> > A little closer to pi than the original above--
> > 3.141593223585714204304623374489...
> >
> >
> > >3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
> > > >3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
> > >
> > > The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > A much closer approximation to pi (12 correct digits of pi).
> > > Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> > > from above the results are the same---
> > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > >
> > > Dan
> Does this explain, e^pi(i) +1 = 0 in a simplified manner?
>

This seems to be one of the best explanations on youtube
(or at least one of the more popular ones with over a million views):

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

On Monday, June 7, 2021 at 1:46:22 PM UTC-4, sobriquet wrote:
> On Sunday, June 6, 2021 at 3:47:44 PM UTC+2, djoyce099 wrote:
> > On Saturday, June 5, 2021 at 12:41:46 PM UTC-4, djoyce099 wrote:
> > > On Saturday, May 29, 2021 at 5:54:39 PM UTC-4, djoyce099 wrote:
> > > > sqrt((e^6-pi^5)/(pi^3))= 3.1415932235... or ---- 1/(((e^6)/(pi^5))-1) = 3.1415920835...
> > > Expanding this outward --
> > >
> > >
> > > ((e^24)/(pi^15))/((pi+1)^4) => pi
> > >
> > > 3.141593204098745805252355494447...
> > > A little closer to pi than the original above--
> > > 3.141593223585714204304623374489...
> > >
> > >
> > > >3.1415932235857142043046233744896247010613124302570133810522481987395535359444161389937382>706863183574...
> > > > >3.1415920835939756900037537697591231827972490365729352503570427152871946951610718594628267>326022276173...
> > > >
> > > > The difference between the two then divide by 2 and add to the second entry above of <pi and this will =
> > > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > > A much closer approximation to pi (12 correct digits of pi).
> > > > Also curious if you divide the difference by 2, as above but subtract it from the first larger entry
> > > > from above the results are the same---
> > > > 3.14159265358984494715418857212437394192928073341497431570464545701337411555274399922828250164427298735...
> > > >
> > > > Dan
> > Does this explain, e^pi(i) +1 = 0 in a simplified manner?
> >
> This seems to be one of the best explanations on youtube
> (or at least one of the more popular ones with over a million views):
>
> https://www.youtube.com/watch?v=mvmuCPvRoWQ

Thanks, It gives a good explanation on (i)

On Tue, 1 Jun 2021 17:57:07 -0700 (PDT), djoyce099
<hlauk.h.bogart@gmail.com> wrote:

>On Tuesday, June 1, 2021 at 1:41:08 PM UTC-4, Barry Schwarz wrote:
>> On Tue, 1 Jun 2021 08:59:41 -0700 (PDT), djoyce099
>> <hlauk.h...@gmail.com> wrote:
>>
>> >We had this discussion before and that is the symbol used on the button of the 10,000 digit calculator that I use. In(n)
>> And during that discussion, we asked you to identify the calculator so
>> anyone sufficiently interested could see what other non-standard
>> nomenclature it used. It would help us understand when you use terms
>> we are not familiar with or use them in an unusual way.
>> >Next time I will use what Wolfram excepts--- natural log(e)(n).
>> I'm not familiar with what Wolfram accepts but there is no other base
>> of natural logarithms than e. So if you formula includes the text
>> "natural log" then the (e) is superfluous.
>>
>> The common terminology uses ln (ell-en) for natural log (log base e)
>> and log for log base 10. Logarithms for a particular base b usually
>> specify the base as a subscript after the word "log." Since Usenet
>> doesn't support subscripts, it is usually written as log_b to
>> differentiate it from base 10. 2 is the most common base other than
>> 10.
>> >example-- n =403.4287934927 then log(e)(n) =<6
>> >Is that acceptable?
>> As long as what you write can be understood by someone who doesn't
>> know where your non-standard notations come from, then yes.
>>
>> --
>> Remove del for email
>Here is the description of the digital calculator I use. Not sure if there is a download available.
>
>b calc for windows version 2.05 copyright @1999,2010 GF Cornwell

I have downloaded the 2.06 version of that application at
https://www.softpedia.com/get/Science-CAD/Cornwell-BCalc.shtml

If you are going to claim that the natural log button is labeled In
(with an uppercase eye) then you must also believe that the common log
button is labeled Iog (ditto). Why do you find it so hard to accept
that the common usage is ln (with an ell) and log?

Yes, the integer button is labeled Int (with an uppercase eye) and due
to the font used for the button labels it is indistinguishable from an
ell. I expect the author assumed that users of his application would
recognize common terms.

--
Remove del for email