A wonderful coincidence or an expected connection: why π² ≈ g

351–352 of 352 posts

Re: A wonderful coincidence or an expected connection: why π² ≈ g

#351

Post by rjmunro » Thu, Aug 15, 2024, 5:45 PM UTC

jcelerier wrote: post #298

mr_mitm wrote: post #229

Earlier quoted context omitted.

Pi doesn't vary. The ratio of circumference to diameter of a circle may vary depending on the geometry. Clearly everyone means euclidean space unless specified otherwise. Any other interpretation will only lead to problems, which is why it's not useful. There is really no ambiguity about this in mathematics. Mathematicians still use the pi symbol as a constant when they compute the circumference of a circle in a give…

> Pi doesn't vary. The ratio of circumference to diameter of a circle may vary depending on the geometry. Can you share some place where Pi isn't defined exclusively as being "the ratio of circumference to diameter of a circle"? I have never heard any other definition in my life, and couldn't find any other through the first few Google results

Pi is the "the ratio of circumference to diameter of a circle in Euclidian space". Everyone agrees that. What people are arguing is that when you have a circle in non-Euclidian space, so that the ratio of it's circumference to diameter is different, do we still call this new ratio Pi.

Most people would argue that we don't. They say "the ratio is not Pi" rather than "Pi is a different value".

Re: A wonderful coincidence or an expected connection: why π² ≈ g

#352

Post by CRConrad » Sat, Aug 17, 2024, 8:27 PM UTC

mananaysiempre wrote: post #133

ta1243 wrote: post #116

Earlier quoted context omitted.

I always find insolation and insulation to be such an interesting pair of words I guess the equivelent of "change the units" is "change the language". French: insolation et isolation German: Sonneneinstrahlung / Isolierung Spanish: insolación / aislamiento Chinese: 日照 / 绝缘 I guess coincidence

insolation sol , solis m "sun" insulation insula , - ae f "island" (apparently nobody knows where this one comes from) isolation isolation isolare isola isula insula , - ae f Spanish aislamiento aislar isla isula insula , - ae f Oh and the English island never had an s sound, but is spelled like that because of confusion with isle , which is an unrelated borrowing from Old French ( île in modern French, with the diac…

> Oh and the English island never had an s sound, but is spelled like that because of confusion with isle

So the German cognate (I assume) Eiland probably hasn't had one either. Makes sense, since the Nordic Eya / Øy / Ö never felt like they should, and they must be just northern variants that lack the -land (literally the same in English) suffix.

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