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We need Pi

This is SOD's fault

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John Haine05/07/2020 21:10:15
3181 forum posts
172 photos

An accurate and fast Python program given here **LINK**

duncan webster05/07/2020 21:46:36
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2651 forum posts
36 photos

And here's me thinking the thread title was a typo and the OP hailed from Wigan. If you've got a half decent calculator in the workshop (essential in my view), you don't need to remember pi, there is a dedicated button. Even my mobile phone runs to that

And in case you're wondering why I need a calculator, just try adding 7/16 to 29/64 and converting the answer to decimal in your head

Michael Gilligan05/07/2020 22:27:32
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15886 forum posts
693 photos

For the curious: **LINK**

https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-100

Open Access, 59 page PDF

MichaelG.

John Haine06/07/2020 09:06:10
3181 forum posts
172 photos

Thanks Michael, an interesting read.

John Haine06/07/2020 09:48:31
3181 forum posts
172 photos

You may be interested that I tried the Python code in the link I gave above. I used "Spyder" which is a scientific Python IDE, free to download as part of "Anaconda". All I did was to copy/paste the code and click "run" and it worked.

The program takes a second or two to run and generated this:

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420121

correct to 997 decimal places after 10 iterations. Increasing the number of decimal places to 10,000, it seemed to take hardly any longer and used only 13 iterations. Wow!

ega06/07/2020 11:38:29
1750 forum posts
152 photos

An article in the Scientific American from 1960, "Incidental information about the extra ordinary number pi", mentioned the ENIAC calculating to to 2,000 decimals in 70 hours and opined "Perhaps pi has now been carried accurately to the 10.000 mark."

Most of this article is well above my head but it would no doubt interest the OP and others. It also touches on the computation of pi by hand which can apparently be done by "using any infinite expression that converges on pi".

Two examples of such expressions are given, one discovered by the English mathematician Wallis and the other by Leibnitz; I had thought to post these but, unfortunately, due to water damage they are only partly legible in my copy.

pgk pgk06/07/2020 11:39:35
1851 forum posts
288 photos

..that string of 9's looks like a good place to round up......sorta close enough..

pgk

JA06/07/2020 12:19:29
936 forum posts
51 photos
Posted by John Haine on 06/07/2020 09:48:31:

1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841

2701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520

9209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381

83011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468

44090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830

264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661

1195909216420121

A random number table. I jest not.

JA

Edited By JA on 06/07/2020 12:20:25

SillyOldDuffer06/07/2020 13:41:08
5938 forum posts
1282 photos

The Find your Pi Day website is fun. As pi is believed to be random# and infinite, any sequence of numbers must occur somewhere in it. My youngest's birthday in DDMMYY format pops up in pi after 3,164,548 digits. Start calculating now to make sure presents will arrive on the right day!

Dave

# more pedantically pi is 'normal', rather than random, but hey...

Georgineer07/07/2020 12:55:38
367 forum posts
16 photos
Posted by pgk pgk on 05/07/2020 12:46:38:
Posted by Georgineer on 05/07/2020 12:04:01:
...Hexagons in circles we drew at school to make pretty patterns with our compasses with the simiplicity that using the Radius of the circle to mark points on the circumference effectively gives 6 equailateral triangles with every internal angle being 60deg...

pgk

This worked all right when using a blunt pencil and a pair of school compasses with the dried blood scraped off the point. However, when I borrowed Grandpa's draughting set, I found that, no matter how I tried, I could never get the last circle to coincide with the first. It was only later that I discovered that this is because the value of pi is more than three.

It was when I was studying electrical engineering some years later that I discovered the mnemonic "How I need a drink, alcoholic of course, after the heavy chapters involving quantum mechanics" which by counting the letters gives pi to 15 sig. figs. though I never found a use for it.

Then when I learned computer programming (remember Algol on punched cards, anyone?) I learned that pi equals 4*arctan(1). Much more useful.

These days I just press a button on my calculator.

George B.

I agree that Pi on a calculator is the easy way. I also agree that often my attmepts at drawing interlocking circles failed but that is our/my failure to be neat enough and nothing to do with Pi as Turbocad can easily prove:

circles.jpg

pgk

I never really thought about it in depth until now. I assumed that the gap was because the arc between points is greater than the radius. It is, of course, but I overlooked that what I was stepping off was in fact a chord of the circle, equal in length to the radius. So now I accept that the discrepancy was due to my own youth and inexperience.

I must try it again, now I have my own grown-up drawing set, and see if my technique has improved.

George B.

Nigel Graham 210/07/2020 23:41:43
667 forum posts
15 photos

Michael Gilligan -

Do you mean Mathematical Pie?

It is still going strong!

I recall that from school in the early 1960s, complete with its groups of digits along the top or bottom margin, from some calculation of pi to some absurd length! I don't know if it still publishes the pi values. Try this direct quote resulting from searching just by the title alone:

Mathematical Pie - Mathematical Association

www.m-a.org.uk › mathematical-pie

We hope you enjoy these resources - keep doing some maths! Take a look at this complimentary issue : Mathematical Pie No. 198. Mathematical Pie is published three times a year. It is aimed at pupils from 10 to 14 years of age, but is read by all age groups.

Edition 198 means it's been going now for 66 years - I encountered it first in the First Year at Weymouth Grammar School, nearly 57 years ago. (> 0.5 Century.... oooo-er!)

I do recall three articles. One explained those pi numbers, and gave a potted history of Pi calculations. Another described the geometry of the newly-invented Wankel rotary engine. The third I recall less clearly, something about the principle of a machine for drilling square holes (probably with quadrant corners), but I remember nothing other than it perhaps being somewhat similar to that of the engine.

I believe electricians have available a power-drill accessory for chasing out socket recesses in walls, but I think it is simply a drill-bush on two slides at right-angles to each other.

'

About 30 years ago a work colleague described his shock when, helping his daughter with her homework, he saw the question instructed taking poor little Pi as "3". Not three-and-one-seventh. Not 3.14 - both values well within the level of her maths. Just three.

Mathematics was always among my weakest subjects, but even I could handle 22/7. Just.... Times by 3.142? Errr, slide-rule or log tables unless the other factors are single digits!

There is a neat value worth bearing in mind: 0.7854. Why? Area of a circle = (pi/4)D^2. Which equals 0.7854D^2, near enough for sizing steam-pipes, working out stud strengths, and the like; and sometimes a calculation can be more convenient if all of one operator-type. Now look at a standard calculator keypad!

Michael Gilligan11/07/2020 00:23:05
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15886 forum posts
693 photos
Posted by Nigel Graham 2 on 10/07/2020 23:41:43:

Michael Gilligan -

Do you mean Mathematical Pie?

It is still going strong!

I recall that from school in the early 1960s, complete with its groups of digits along the top or bottom margin, from some calculation of pi to some absurd length! I don't know if it still publishes the pi values. Try this direct quote resulting from searching just by the title alone:

 

Mathematical Pie - Mathematical Association

www.m-a.org.uk › mathematical-pie

 

[…]

.

Thanks, Nigel yes

Yes, I think that must be the one.

MichaelG.

.

http://www.mathematicalpie.com/

..., looks like the list of numbers stopped after issue 51 sad

 

Edited By Michael Gilligan on 11/07/2020 00:39:43

Sam Stones11/07/2020 00:46:00
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762 forum posts
304 photos

In days long gone having just gained an Associate of the Plastics Institute, I found it quaint to discover that their (neck) ties were appropriately strewn with the Greek letter π (PI) stitched into them in gold thread.

Eventually, I stopped wearing mine having realised that my joke [Having Pie on my tie] had also worn too thin.

Sam

SillyOldDuffer11/07/2020 10:34:25
5938 forum posts
1282 photos
Posted by Nigel Graham 2 on 10/07/2020 23:41:43:

About 30 years ago a work colleague described his shock when, helping his daughter with her homework, he saw the question instructed taking poor little Pi as "3". Not three-and-one-seventh. Not 3.14 - both values well within the level of her maths. Just three.

Mathematics was always among my weakest subjects, but even I could handle 22/7. Just.... Times by 3.142? Errr, slide-rule or log tables unless the other factors are single digits!

...

Taking 3 for pi may have been teaching two other important mathematical skills, reading the question! Another database expert and I both got an E in a Mock British Computer Society Exam because the question sought a simple answer rather than the benefit of our extensive practical experience with big data! Computer exams often use gender as a binary example; only a single bit is needed in database to record whether one is one is male or female. In practice humanity is far more diverse; my database experience catered for 21 "genders", his 23. The examiner had no sympathy with me and the other smart ass: we were told to answer the question and stick to the syllabus!

But isn't multiplying by 3.142 easier than multiplying by 22 and then dividing by 7? Division is always harder than multiplication because division involves remainders. For example, the circumference of a 43mm circle is

3142 x 43

giving 9246 + 125680 = 135106

And, the decimal point is easy: 3.142 -> 3 places, 43 -> 0 places, the answer is 3+0 places ie. 135.106

I feel the same sum with 22/7 is distinctly more difficult:

43 x 22 is easy = 946

But dividing 946 by 7 is hard. 7 into 9 goes once remainder 2 etc. etc.

Fractions are wonderful for maths involving simple integers, but otherwise may become clumsy and awkward. Try using 355/113 instead of 22/7. Decimals are much more general purpose, not least because they suit tables, slide-rules, calculators and other mechanical aids.

22/7 is a useful approximation. Despite knowing it's shortcomings I try it first for mental arithmetic because many inputs produce quick easy answers: it's a shortcut if they do. But as soon as the sum gets hard, or more accuracy is needed, I go decimal with a calculator.

Mathematics is one of my weakest subjects too. Curious his struggle with maths led Nigel to prefer 22/7 while mine led to 3.142. Can't take my views too seriously because I used 3.141 for over 50 years rather than 3.142. It was this thread that put me right!!! Ignorance is bliss...

smiley

Dave

pgk pgk11/07/2020 10:59:08
1851 forum posts
288 photos

Early on I was taught to knock out a quick mental arithmatic answer for a rough approximation before doing the sum - a simple way of avoiding gross errors and decimal point mistakes. Pi= 3 and a bit works for that.. times three and add a convenient bit on before the next part of the in-head sum. But then the primary school I went to was heavy in the 3R's.

I do regret not comng across "The Trachtenberg Speed system" as a kiddie.. and too lazy later to adopt it. As I recall kids were able to multiply 15 digit numbers by 15 digit numbers in 75 secs.... and now it's just a calculator.

I tried to get my grand-daughter to visualise numbers as I do.. in playing card layout .. which makes single digit addition and subtration instant. She was pretty poor on her times tables - the fundamental hooks you hang stuff from. I did succeed there by creating adventures on my hobby farm. Each gate we passed only after she answered 2 correct times table q's and one riddle. We have been explorers, on quests, pirates, mountaineers and so forth..

pgk

JA11/07/2020 12:53:01
936 forum posts
51 photos

Pi squared = 10

(Used to be used in electronics)

JA

Georgineer11/07/2020 14:43:16
367 forum posts
16 photos

There was an April Fool's hoax (still believed by some) that one of the American states passed a law which defined the value of π as equal to three. However, there was a genuine attempt in Indiana in 1897 to establish the value of π by law. The bill was apparently so obscure and self-contradictory that it yielded at least three different values, mostly around 3.2, so it was kicked into the long grass.

George B.

robjon4412/07/2020 09:23:01
125 forum posts

Gentlemen, an anectdote if I may, one day I observed my foreman, an inveterate meddler across the gangway so I walked across & held up a box of spent tips so he would give me a requisition for a new box without interrupting his flow, I became aware that he was in the throes of explaining to a giant of a man called Boxer who had the broken nose to prove it & was also one of the highest paid pieceworkers in the shop, how to calculate the circumference of a circle that he might be able to select the precise spindle required for the job in hand, he then proceeded to try to explain the value of Pi & then stumbled at the first hurdle when he couldn't remember if it was 22 over 7 or 7 over 22, at this point I had to run away before I collapsed in hysterical laughter, I use a calculator wiv all them Greek letters on it meself.

BobH

Edited By robjon44 on 12/07/2020 09:25:15

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