## Sunday, December 17, 2023

### Archimedes, Pi, and Pickelball

I typed

3,1,4,1,5,9

into OEIS and,  as expected, I found that these are the first few digits of $$\pi$$. See here.

I then read on the page:

$$\pi$$ is sometimes refereed to a Archimedes constant, because the Greek mathematician computed lower and upper bounds of $$\pi$$ by drawing regular polygons inside and outside a circle.

In my 40 or so years being involved with math, I have never heard $$\pi$$ called Archimedes constant. Whats going on here?

(a) The term is STILL in use I just happened to never hear it. I noted in a blog here that I didn't have a single book on trig in my house, so this is plausible.

(b) The term is NOT in use but the person who wrote that entry either is rather old or THOUGHT it was in use or heard it once when he was 10 years old or...

(c) Some weighted sum of (a) and (b)

I suspect the term is NOT in use anymore. So when was it in use, and when did it fall out of favor?

More random thoughts

1) I googled why is it called pi but it was auto filled to ask why is it called pickleball. I'll report on both:

pi: It was first called pi  in 1706 by [The Welsh Mathematician] William Jones because pi is the first letter in the Greek word perimitros which means perimeter. (ADDED LATER- the comments say that the question-and-answer are not as simple as this quote would imply. I am sure they are right.)

Pickleball: This website here says the following. Joel Pritchard invented the game (the story is more complicated than that). With that in mind here is a direct quote:

Okay, now you know how it all started but the question we’re all thinking still remains: why do they call pickleball, well, pickleball? According the to U.S.A. Pickleball Association, the origins of the name differs between different accounts.

Joel Pritchard’s wife, Joan, started to call their game pickleball because “the combination of different sports reminded me of the pickle boat in crew where oarsmen were chosen from the leftovers of other boats.” But according to Barney McCallum, they named the game after Pritchard’s dog, who was (as you might’ve guessed) named Pickles! Despite the sour taste of actual pickles, their dog was sweet and known to run off with the ball while it was still being played!

Depending on who you ask, both accounts of the game’s name may actually be true. At the start, there wasn’t any name for pickleball until an official one was needed when the game started to gain traction. With the laid-back nature of pickleball, it’s only appropriate that it was named in a similar fashion.

1. Evangelos Georgiadis2:26 AM, December 18, 2023

While there might be a unanimous vote of confidence amongst
mathematicians that Archimedes represents a great constant
in the history of geometry (i.e., one of our revered friends christened a yacht after him), the history behind the origin of the letter or symbol $\pi$ and its correct attribution with respect to the ratio of circumference to diameter, remains a bit less unanimously clear -- perhaps even a bit nebulous.

We know that there were other people, such as William Oughtred
and Isaac Barrow, who associated the letter $\pi$ as a
variable relating to the circle -- predating our Welsh friend William Jones.
Further, while we do know William Jones. While we do know William Jones used $\pi$ to denote our constant', he used it to describe work by "The Truly Ingenious John Machin."
This organically leads to the question:
should it be attributed to the man whose work he actually endorsed or cited?

A probably more interesting (not necessarily better) question would
be: whose stamp of approval was necessary to popularize $\pi$ and
standardize it? Some might argue that it wasn't until Euler adopted it,
and used it as early as 1736 in "Mechanica, sive, Motus scientia analytice exposita" in
Volume I, on page 123 under "Proposito 38, Theorema 304.":
".... et $\pi$ : 1 rationem peripheriae ad diametrum." -- translating from Latin to English as "and $\pi$ : 1 ratio of the periphery to the diameter."

In Volume II, on page 70: "et ratio perifpheriae ad diametrum = \pi" which translates from Latin to English
as "and the ratio of the periphery to the diameter = \pi."
(NB: perifpheriae' should have been peripheriae' or periferiae', but here we witness a typographical mistake in Latin.)

Interestingly, before Euler adopted using $\pi,$ he kept using symbols, p and c. John Bernoulli used to employ the Latin letter, c. So, presumably Euler first converged to Bernoulli's notation, i.e., from p to c, before finally popularizing a new
standard and declaring it to be $\pi.$

2. I have read similar things about people calling it Archimedes's number. I wonder if this is similar to the lazy journalism of "It has been said that..." when in fact the only people saying it are people saying that people are saying it.

I will confess, that the last sentence of my 2015 article "Circular Reasoning: Who First Proved That C Divided by d Is a Constant?" (https://www-tandfonline-com.dickinson.idm.oclc.org/doi/abs/10.4169/college.math.j.46.3.162) is "Because of these results about the nature of π and his very accurate bounds on the value, it seems fitting that we call π Archimedes’s number."

1. Oops. This is probably a better link. https://doi.org/10.4169/college.math.j.46.3.162

2. Even that is behind a paywall. I found the article on ArXiv: https://arxiv.org/abs/1303.0904.

3. (bill test) Wondering if commenters can use math. So I am trying it. PI is $$\pi$$

4. (bill) If you want to use math in a comment do the following:
slash \
open parenthesis (
math you want, for example slash then pi. DO NOT use dollar signs
slash \
closed parenthesis )

5. Georgios Stamoulis7:04 AM, December 21, 2023

Hi Bill, Lance,
I am Greek and in my Greek school years (30 years ago) π was introduced to us as "Aρχιμήδεια Σταθερά" (Archimedean Constant) by our math teacher.

6. When I look in Google Books Ngram nothing shows up for Archimedes constant (with or without hyphen, plural or possessive)
before 1966. For Archimedes number it is 1940.

7. (Bill) Georgios and Mike - Excellent points! It had no dawned on me that in Greece they WOULD call it Archimedias Constant (or close to that). And I had not through of rigously testing the hypothesis that it was really not used (on Google books, which is mostly English).