Threaded Mode | Linear Mode

Gerson W. Barbosa · 07-13-2014, 08:01 PM

[Image: Pandigitalapproximation_zpse080bdae.png]

Massimo Gnerucci · 07-13-2014, 08:59 PM

(07-13-2014 08:01 PM)Gerson W. Barbosa Wrote:

3.141592652604741850582811832470500214369877171937092730936285...

Bravo!

Massimo Gnerucci · 07-13-2014, 09:01 PM

(07-13-2014 08:01 PM)Gerson W. Barbosa Wrote:

And all of this during the World Championship final Wink

Thomas Klemm · 07-13-2014, 09:03 PM

Very nice!

Gerson W. Barbosa · 07-13-2014, 10:40 PM

(07-13-2014 09:01 PM)Massimo Gnerucci Wrote:
(07-13-2014 08:01 PM)Gerson W. Barbosa Wrote:

And all of this during the World Championship final

It took me about 20 to 25 minutes to find the approximation, put it in pandigital form and post it here. But then I've missed the first half as I thought the final would begin at 1700 local time (it began one hour earlier) Smile

Gerson W. Barbosa · 07-13-2014, 11:04 PM

(07-13-2014 09:03 PM)Thomas Klemm Wrote: Very nice!

Thanks!

On the HP-32S:

2 LN LN pi / --> -1.16664686E-1

--> pi ~ 1/18750 - 60/7*ln(ln(2))

I only tried a pandigital form because I wrongly factored 18750 as 2*3*5^4 (actually 18750 is equal to 2*3*5^5, which made the task a little bit more difficult -- but that's what the properties of logarithms are for :-)

Gerson W. Barbosa · 07-18-2014, 05:19 AM

(07-13-2014 08:59 PM)Massimo Gnerucci Wrote:
(07-13-2014 08:01 PM)Gerson W. Barbosa Wrote:

3.141592652604741850582811832470500214369877171937092730936285...

Ten digits yielding only nine correct digits of pi.
Same with this previous attempt:

[Image: Pandigitalapproximation_2_zpsbe650033.png]

Luckily enough their average gives twelve correct digits :-)

3.141592653588141...

Massimo Gnerucci · (This post was last modified: 07-18-2014 06:00 AM by Massimo Gnerucci.)

(07-18-2014 05:19 AM)Gerson W. Barbosa Wrote:
(07-13-2014 08:59 PM)Massimo Gnerucci Wrote: 3.141592652604741850582811832470500214369877171937092730936285...

Ten digits yielding only nine correct digits of pi.
Same with this previous attempt:

Luckily enough their average gives twelve correct digits :-)

3.141592653588141...

Wow, this is so much nicer! Wink

3.141592654571540303409367866518360732739326280463671619184479...

Gerson W. Barbosa · 07-18-2014, 06:21 AM

(07-18-2014 05:56 AM)Massimo Gnerucci Wrote:
(07-18-2014 05:19 AM)Gerson W. Barbosa Wrote: Ten digits yielding only nine correct digits of pi.
Same with this previous attempt:

Luckily enough their average gives twelve correct digits :-)

3.141592653588141...

Wow, this is so much nicer!
3.141592654571540303409367866518360732739326280463671619184479...

Perhaps (e^-3)^4 would be better than e^(-3*4), but I'm not sure whether the expression would look nicer in the equation editor.

Namir · 09-26-2014, 07:02 PM

Also try:

pi = (8545/4821)^2

is a good approximation (should be to decimal 8 places), and

pi = (119926/67661)^2

To 9 decimals.

Namir

Massimo Gnerucci · 09-27-2014, 09:26 AM

(09-26-2014 07:02 PM)Namir Wrote: Also try:

pi = (8545/4821)^2

is a good approximation (should be to decimal 8 places), and

pi = (119926/67661)^2

To 9 decimals.

Namir

No more pandigital, though...

Namir · (This post was last modified: 09-27-2014 07:11 PM by Namir.)

(09-27-2014 09:26 AM)Massimo Gnerucci Wrote:
(09-26-2014 07:02 PM)Namir Wrote: Also try:

pi = (8545/4821)^2

is a good approximation (should be to decimal 8 places), and

pi = (119926/67661)^2

To 9 decimals.

Namir

No more pandigital, though...

Massimo,

You have to have a special genius mind to see all of the digits!!

(with apologies to The Emperor's New Clothes)

:-)

Namir

Namir · (This post was last modified: 09-27-2014 07:19 PM by Namir.)

I thus define the new term pandigital number of the second kind ... where you use the digits that appear in the number to calculate the missing ones!!! The rule is that you can calculate the missing numbers by using sets of single operations between existing digits. You can reuse an existing digit in different single operations.

For example, the number 123567890 is a pandigital number of the second kind, since we can add 1 and 3 to get 4. The number 12367890 is also a pandigital number of the second kind because the missing digits 4 and 5 are calculated using 4=1+3, and 5=2+3.

However, the number 19 is NOT pandigital number of the second kind, because we cannot use 1 and 9 in a set of single operations to calculate digits other than 8 or 0.

:-)

This is fun and totally absurd at the same time.

"The Heretic" Namir

Joe Horn · (This post was last modified: 09-28-2014 12:53 AM by Joe Horn.)

(09-27-2014 07:17 PM)Namir Wrote: This is fun and totally absurd at the same time.

"A little nonsense, now and then,
Is relished by the wisest men."

Namir · 09-28-2014, 03:16 PM

Joe,

My interest in this thread is really about calculating pi ... regardless of the kinds of digits used. I have two books about calculating pi and then have a ton of short formulas that calculate pi ... as well as the long series that we are familiar with.

Namir

Gerson W. Barbosa · 09-28-2014, 07:15 PM

(09-28-2014 03:16 PM)Namir Wrote: My interest in this thread is really about calculating pi ... regardless of the kinds of digits used. I have two books about calculating pi and then have a ton of short formulas that calculate pi ... as well as the long series that we are familiar with.

What about this palindromic approximation? Is there such a category or is this the first one? Smile

[Image: Palindromic_Approximation_zpsacb447be.png]

Namir · (This post was last modified: 10-01-2014 01:38 AM by Namir.)

(09-28-2014 07:15 PM)Gerson W. Barbosa Wrote:
(09-28-2014 03:16 PM)Namir Wrote: My interest in this thread is really about calculating pi ... regardless of the kinds of digits used. I have two books about calculating pi and then have a ton of short formulas that calculate pi ... as well as the long series that we are familiar with.

What about this palindromic approximation? Is there such a category or is this the first one?

This is a very good palindromic approximation indeed!!

**rprosperi** · 10-01-2014, 02:33 AM

(09-28-2014 07:15 PM)Gerson W. Barbosa Wrote:
(09-28-2014 03:16 PM)Namir Wrote: My interest in this thread is really about calculating pi ... regardless of the kinds of digits used. I have two books about calculating pi and then have a ton of short formulas that calculate pi ... as well as the long series that we are familiar with.

What about this palindromic approximation? Is there such a category or is this the first one?

I don't follow much of the math you guys discuss, so.... why is this expressed in the format shown, since the fraction reduces to 10691 / 462?

Paul Dale · 10-01-2014, 03:50 AM

(10-01-2014 02:33 AM)rprosperi Wrote: I don't follow much of the math you guys discuss, so.... why is this expressed in the format shown, since the fraction reduces to 10691 / 462?

The numbers are palindromic -- i.e. they read the same forwards as they do backwards.

Pauli

Gerson W. Barbosa · 10-01-2014, 03:55 AM

(10-01-2014 02:33 AM)rprosperi Wrote:
(09-28-2014 07:15 PM)Gerson W. Barbosa Wrote: What about this palindromic approximation? Is there such a category or is this the first one?

I don't follow much of the math you guys discuss, so.... why is this expressed in the format shown, since the fraction reduces to 10691 / 462?

The irreducible fraction of course is better, but then neither the numerator nor the denominator are perfect palindromes, like 64146 and 2772.
I wonder if there are more palindromic pi approximation around. Hopefully this is not the beginning of new mania Smile