Pi Approximation Day

07222019, 03:41 AM
(This post was last modified: 07222019 03:45 AM by Gerson W. Barbosa.)
Post: #1




Pi Approximation Day
Today is Pi Approximation Day. Well, at least in countries that use DD/MM date format, like mine.
As a small celebration, here’s a \(\pi\) approximation good to 16 significant digits. That’s just about the same number of digits required to write it. No big deal, except perhaps for the mnemonic part. \[\frac{22}{7}\frac{1}{790+\frac{55567}{66697}}\] 

07222019, 10:01 AM
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RE: Pi Approximation Day
Hi Gerson,
Very good ! Have a good day. Gérard. 

07222019, 01:02 PM
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RE: Pi Approximation Day
Have an approximately good day!
≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ ! 

07222019, 01:05 PM
Post: #4




RE: Pi Approximation Day
Very nice numbers in there Gerson. You must be quite satisfied to find numbers with repeating digits and ending in both 67 and 97 as components of the approximation. It may not actually be Pi, but most of my calculators can't tell the difference.
Bob Prosperi 

07222019, 03:14 PM
(This post was last modified: 07222019 03:26 PM by Gerson W. Barbosa.)
Post: #5




RE: Pi Approximation Day
Thank you all for your comments!
Yes, I am having an approximately good day (I wish the numbers on the callendar weren't a reminder I am getting older  58 and counting :) Now, time for a little riddle. The following appears to be a pretty bad approximation. It really is, depending on how we look at it. However, when I change only one digit or, equivalently, when I remove one of its parts, it returns a perfect 10digit result on my HP41C, which I am using to evaluate it. BTW, I have used the HP41C for this one because of its 10digit display and a seldom used useful builtin function which most of my Voyagers lack. Too many tips, but it doesn't matter :) Have fun! \(\frac{\frac{26}{7}\frac{6}{11211}}{\left (\frac{4141}{3313}\right ) ^{\frac{3}{4}}}\) Edited to include a pair of parentheses in order to avoid ambiguity 

07222019, 05:19 PM
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RE: Pi Approximation Day  
07222019, 07:48 PM
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RE: Pi Approximation Day
I got the simplest formula:
3 Sorry, I'm an engineer, that's enough precision most of the time... 

07222019, 09:40 PM
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RE: Pi Approximation Day
Perfect! Just for fun I put it on my HP38C simulator on iPhone:
01  2 2 02  2 2 03  31 ENTER 04  7 7 05  71 ÷ 06  5 5 07  5 5 08  5 5 09  6 6 10  7 7 11  31 ENTER 12  6 6 13  6 6 14  6 6 15  9 9 16  7 7 17  71 ÷ 18  7 7 19  9 9 20  0 0 21  51 + 22  24 71 1/x 23  41 − 24  25 7 00 GTO 00 Regards, Bob 

07222019, 10:49 PM
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RE: Pi Approximation Day
Hi, all: Happy Pi Approximation Day (i.e.: 22/7) Use your CAS (or your math ingenuity) to compute the exact symbolic value (not numeric) of: Integral between 0 and 1 of: x^{4}(1x^{4})/(1+x^{2}) . dx and there you are, your Pi Approximation present. Regards to all. V. All My Articles & other Materials here: Valentin Albillo's HP Collection 

07232019, 03:15 PM
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RE: Pi Approximation Day  
07232019, 05:07 PM
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RE: Pi Approximation Day  
07232019, 05:09 PM
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RE: Pi Approximation Day
(07222019 10:49 PM)Valentin Albillo Wrote: I got 2/35 from an (emulated) HP 50g. — Ian Abbott 

07232019, 05:18 PM
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RE: Pi Approximation Day
(07232019 05:07 PM)Dave Shaffer Wrote:(07222019 07:48 PM)Claudio L. Wrote: I got the simplest formula: Or a molten sea (1 Kings 7:23). — Ian Abbott 

07232019, 05:31 PM
(This post was last modified: 07232019 05:41 PM by BartDB.)
Post: #14




RE: Pi Approximation Day
(07232019 03:15 PM)Gerson W. Barbosa Wrote:(07222019 10:49 PM)Valentin Albillo Wrote: On the 50G: (noting Gerson's slight modification) EVAL FDIST 

07232019, 06:18 PM
(This post was last modified: 07232019 06:20 PM by Gerson W. Barbosa.)
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RE: Pi Approximation Day  
07232019, 08:26 PM
(This post was last modified: 07232019 08:37 PM by Erwin.)
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RE: Pi Approximation Day
(07232019 05:09 PM)ijabbott Wrote:(07222019 10:49 PM)Valentin Albillo Wrote: Hi Valentin, wondering that you didn't put the "old" HP71b code in your post So I'll do that. Code: PI = 22/7INTEGRAL(0,1,1E11,(IVAR^4*(1IVAR)^4/(1+IVAR^2))) best regards Erwin 

07242019, 12:35 AM
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RE: Pi Approximation Day
(07222019 07:48 PM)Claudio L. Wrote: I got the simplest formula: “Pi is about 22/7”, says the engineer in this math jokes page. Roman engineers would say it was close to 25/8. The builders of King Solomon’s Temple knew it was a bit great than 3, I think, but apparently the reporters believed it was exactly 3. I’ve read 3.1416 is good enough in Mechanical Engineering. Other types of engineering might use other aproximate values for pi, though. I remember 377 was commonly used as an approximation for 2\(\pi\times\)60 in EE texbooks, for convenience. 

07242019, 06:03 AM
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RE: Pi Approximation Day
(07242019 12:35 AM)Gerson W. Barbosa Wrote: I remember 377 was commonly used as an approximation for 2\(\pi\times\)60 in EE texbooks, for convenience. Indeed... The good old 2πf we used in EE formulas... In Mozambique we used 2*3,14*50 though. Jose Mesquita RadioMuseum.org member 

07242019, 10:30 AM
(This post was last modified: 07242019 11:04 AM by BartDB.)
Post: #19




RE: Pi Approximation Day
(07232019 06:18 PM)Gerson W. Barbosa Wrote: That is, I entered this into my Sharp Writeview ELW506T and got the result of 'π' Admittedly I expected the numerical value of π EDIT: when I enter the numerical value of pi to more than 10 digits (correctly rounded) it will convert to the symbol 'π' 

07242019, 12:37 PM
(This post was last modified: 07242019 12:41 PM by Gerson W. Barbosa.)
Post: #20




RE: Pi Approximation Day
(07242019 10:30 AM)BartDB Wrote:(07232019 06:18 PM)Gerson W. Barbosa Wrote: That is, Same on the CASIO fx991 LA X CLASSWIZ. There’s a setting for numerical values: SHIFT SETUP 1: Input/Output 2: MathI/DecimalO Regardless the setting, the S<=>D key cycles between both formats. On the ELW506T you can try the >CHANGE< key. 

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