Talk:Pi/Archive 17

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Archive 17

Semi-protected edit request on 6 August 2023

Request to add to "In popular culture":

In the TV show "Person of Interest", Season 2, Episode 11 "2 Pi R", one of the main characters gives a quote about Pi and its significance as an infinite and non-repeating number. When asked by a student what math is good for, and why would we ever use it, Harold Finch replies:

"Pi, the ratio of the circumference of a circle to its diameter, and this is just the beginning; it keeps on going, forever, without ever repeating. Which means that contained within this string of decimals, is every single other number. Your birth date, combination to your locker, your social security number, it's all in there, somewhere. And if you convert these decimals into letters, you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, everything we ever say or do; all of the world's infinite possibilities rest within this one simple circle. Now what you do with that information; what it's good for, well that would be up to you." Byow888 (talk) 19:39, 6 August 2023 (UTC)

Thanks for your contribution.

This quotation states an unproven claim as fact (see normal number and Pi § Irrationality and normality). This character's answer does not address the other character's question, and uses a technical claim as a launching point for a pseudoscientific shower thought / daydream. The philosophical subject here is much better addressed in other places, e.g. "The Library of Babel", and in my opinion really doesn't have that much to do with π or even mathematics, except in the narrowest sense. But see the previous links and also Infinite monkey theorem for more about both technical and philosophical aspects.

I don't think including it would benefit readers of this article. This TV episode is not especially culturally or mathematically significant. There have been thousands (perhaps millions) of cultural references to π, dating even to before the use of the π symbol, among which Wikipedians have no obvious way to choose, and even if we did it wouldn't much help our readers. Note that Wikipedia is not an indiscriminate collection of information. –jacobolus (t) 21:24, 6 August 2023 (UTC)

Thank you for your consideration and explanation, appreciate the time and effort! Byow888 (talk) 19:51, 7 August 2023 (UTC)

Id like to point out that pi is an ESTIMATE of the ratio im pretty sure its been calculated and proven to less than 20 decimal places and estimated the rest of the way and the ratio may not even be an irrational number 2407:7000:9055:2323:BC70:109B:D62E:B6E4 (talk) 22:51, 17 August 2023 (UTC)

Well not estimate but average of limits that cant possibly be correct to the decimal places touted 2407:7000:9055:2323:BC70:109B:D62E:B6E4 (talk) 22:57, 17 August 2023 (UTC)

Ancient Pi approximations

In the history section it says:

"The earliest written approximations of π are found in Babylon and Egypt, both within one percent of the true value. In Babylon, a clay tablet dated 1900–1600 BC has a geometrical statement that, by implication, treats π as 25/8

25/8 = 3.125. In Egypt, the Rhind Papyrus, dated around 1650 BC but copied from a document dated to 1850 BC, has a formula for the area of a circle that treats π as 256/81."

I know they say "by implication" and "treats pi as" rather than say they had values for pi, but this should be more clear that neither of those cultures had yet a concept of pi as either circumference/diameter or as area/(radius^2).

For the babylonians, they have a tablet that basically says that the circumference of a circle is 25/24 multiplied by the perimeter of the inscribed regular hexagon. So if the circle has diameter=1, the side of the hexagon is 0.5 and the perimeter of the hexagon is 3 so the circumference of the circle would be 25/24*3=25/8=3 1/8. So this is a formula for circumference of a circle, basically 25/8 * diameter, so it is not totally wrong to say 'by implication treats pi as 25/8".

But for Egypt, this is much more of a stretch. They have a formula for the area of a circle which is A=(D-D/9)^2. It is a great formula, but to say "treats pi as 256/81" is really not accurate. While it is true that this formula could be written as A=(2r-2r/9)^2=(16r/9)^2=256/81*r^2 it is not accurate to say that it treated pi as 256/81.

I think it would be better to just say that these cultures had formulas for circumference and area which are equivalent to the formulas C=(25/8)D and A=(256/81)r^2 so it is like they had values for pi, but it wasn't like they were using the formulas C=pi*D and A=pi*r^2 and they were trying to use the best approximation of pi they could think of.

Might there be a simple way to edit this so that it is more accurate and does not claim that these cultures were aware there there was this constant pi, but not to make it too complicated to explain?

Nymathteacher (talk) 20:52, 22 August 2023 (UTC)

A Begged Question?

The definition of pi assumes that the diameter/circumference ratio is the same for all circles. Is this something that has ever been proved? It seems a self-evident truth, but are there such things in mathematics? Esedowns (talk) 12:35, 2 September 2023 (UTC)

It's not self-evident, relevant or even true. What is true is that in a Euclidean space the ratio is invariant. I updated the lead to reflect this. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:08, 3 September 2023 (UTC)

If not explicitly specified otherwise, circles are those of Euclidean geometry. D.Lazard (talk) 17:04, 3 September 2023 (UTC)

That's certainly the common case, but in an article about Mathematics there should be no such assumption. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:34, 5 September 2023 (UTC)

In an article aimed at a general audience, unqualified "circle" means a flat Euclidean circle, unless something else is obvious from context. If there's some ambiguity because e.g. Euclidean vs. spherical circles are being directly compared, then it can be directly specified for clarity.

@Esedowns to answer your question plainly: yes it has been proved that the ratio of the circumference to diameter of a circle is the same for all circles. But as @Chatul points out, if you generalize the concept of "circle" to apply in contexts other than Euclidean geometry, then π can take another value, can vary from circle to circle, can be infinite, or can be undefined. –jacobolus (t) 12:52, 5 September 2023 (UTC)

Many thanks for your reply. I wonder where the proof is. Something I read years ago, by Russell I think, said there are begged questions in Euclid.

Esedowns (talk) 15:08, 5 September 2023 (UTC)

Euclid proves that the ratio of area of a circle to a square on its diameter is constant in Elements 12.2 (c. 300 BC). Archimedes' Measurement of a Circle (c. 250 BC) shows that area of a circle is half the area of the rectangle of sides radius · circumference. The combination of these two results may be what you are looking for. Modern mathematicians might disagree about whether the methods used were sufficiently rigorous. Nowadays concepts like arc length are formalized using calculus. –jacobolus (t) 17:55, 5 September 2023 (UTC)

Many thanks again. It is all above me really! Esedowns (talk) 18:33, 5 September 2023 (UTC)

A literature search turns up:

Richeson, David (2015). "Circular Reasoning: Who First Proved That C Divided by d Is a Constant?". The College Mathematics Journal. 46 (3): 162–171.

Lima, Fábio M. S.; Jordão, Pedro G. F. (2022). "Why is it that the Ratio of Any Circle's Circumference to its Diameter is a Constant?". The College Mathematics Journal. 53 (3): 171–182.

–jacobolus (t) 18:31, 5 September 2023 (UTC)

Flinders Petrie

Why is the father of Egyptology, Flinders Petrie, labelled a "pyramidologist"? Surely that is a serious insult? 165.73.112.52 (talk) 05:49, 6 September 2023 (UTC)

What I gleaned in a quick skim through the source (Roger Herz-Fischler's The Shape of the Great Pyramid), is that Flinders Petrie was an adherent of the "π theory" about the proportions of the Egyptian pyramids starting at age 21, which his father had been promoting for years beforehand. He never explicitly recanted such claims, but it seems like later in his career he stopped talking about it. I don't think this is a priori insulting, but perhaps there's a more concrete way of describing this, still linking to pyramidology without calling anyone specifically out with a term that might lead readers to conclude they were a pseudoscientific crank (aside: there were plenty of other prominent, serious people who were "pyramidologists" in the 19th century). –jacobolus (t) 06:06, 6 September 2023 (UTC)

The context in which we mention Flinders Petrie is that of theories that the dimensions of the great pyramid are based on π. Those theories are indeed pyramidology, and we should say so. It is accurate labeling, not insult for the sake of being pejorative. Flinders Petrie is notable for other things (including debunking some other branches of pyramidology) but it is not those other things that we are discussing here. —David Eppstein (talk) 07:30, 6 September 2023 (UTC)

The dimensions of the great pyramid do indeed supply an approximation of π (twice base over height is 880/280 = 22/7). That much is agreed by scholars. The question is, was it designed with that in mind, or is it merely a consequence of the chosen slope angle?

The question is actually more subtle than that. Khufu is based on a whole-cubit Kepler triangle, while Khafre is based on the Pythagorean 3:4:5 triangle. Thus they form a matching pair of the two unique right-angled triangles (arithmetic sequence 3:4:5 and geometric sequence 1:√φ:φ). Egyptologists dismiss this as "co-incidence" because they don't want to answer questions about Pythagorean triangles and the golden ratio. (Can't see the wood for the trees!)

The π ratio is a side effect of the Kepler design, since 4/π ≈ √φ. Both the φ and π values are within 0.1% of true. So good approximations for a stone building.

I think WP's definition of "pyramidologist" is too wide ... it effectively shuts down much discussion about all the mathematics on display at Giza (and elsewhere)... the motivation being because such analysis effectively challenges the accepted time line. This is the "settled science" argument which is anathema to any sort of progress in understanding the past.

Calling people names is not the way to deal with bad arguments. Play the ball, not the man.

As for Petrie, he went to Egypt to disprove assorted theories, and devotes a whole chapter to debunking, as well as in various other places in the text. But Petrie was very smart, he could see that there were things about Giza that did not mesh with the known history. He hints at these carefully. 165.73.112.52 (talk) 15:47, 10 September 2023 (UTC)

"The context in which we mention Flinders Petrie is that of theories that the dimensions of the great pyramid are based on π. "

Can you prove that they are not? 165.73.112.52 (talk) 15:58, 10 September 2023 (UTC)

@David Eppstein, inre "we should say so" – the problem with our current presentation is that this is a single throwaway line. The article here doesn't do any kind of deep analysis of pyramidology or even the "π theory", explaining full context about the characters involved or their specific claims. Instead we gratuitously call out Petrie specifically, attach a label that could plausibly lead readers to conclude he was a crank, and then leave the subject aside. Personally I don't think it would materially affect our presentation to say "some 19th century pyramidologists ..." without specifically naming anyone. But if you think we need an example name to make the claim more concrete, we should pick whoever originated or most forcefully propounded the π theory. –jacobolus (t) 16:30, 10 September 2023 (UTC)

I'd be ok with omitting Petrie's name here. —David Eppstein (talk) 17:07, 10 September 2023 (UTC)

Ridiculous. Petrie is the father of Egyptology. To call him a pyramidologist is a total insult. He is the one who fought the pyramidologists, headlined by Scottish astronomer C Piazzi Smyth. This battle is famous and Petrie is credited with debunking the pyramidologists and putting Egyptology onto forensic footings. Remove his name and replace it with a real pyramidologist. John Taylor in his 1859 book started the Pi theory and Piazzi Smyth and the others went with that. Get Petrie's name off. It's simple or you are remaining willfully ignorant of the facts and of Petrie's high esteem among Egyptologists today. He is the patriarch. EulerConstant (talk) 15:20, 10 September 2023 (UTC)

General and cited ources

"s" missing. KDAM71 (talk) 20:24, 8 October 2023 (UTC)

Fixed. Thanks for alerting us. HiLo48 (talk) 05:40, 9 October 2023 (UTC)

Semi-protected edit request on 10 October 2023

change

"It is a transcendental number, meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers"

to

"It is a transcendental number, meaning that it cannot be a solution of an equation involving only finite sums, products, powers, and integers"

the word finite is necessary here, because pi *can*, in fact, as is described in the sections below, be expressed as an infinite sum. 188.167.159.122 (talk) 17:42, 10 October 2023 (UTC)

 Done Tito Omburo (talk) 18:30, 10 October 2023 (UTC)

more digits

I have looked ad more digits: 3.1415926535927 66.58.219.246 (talk) 17:38, 21 October 2023 (UTC)

Pi § Approximate value and digits lists 50 digits and links to OEIS where you can see many more (here are the first 20,000 digits). There are also many places on the internet where you can find as many digits as you care to read (here are the first 1,000,000 digits and here are the first 100,000,000,000,000 digits), as well as computer code to generate arbitrarily many on your own computer. –jacobolus (t) 18:05, 21 October 2023 (UTC)