- I like the 4-5-6 theorem:
pi^4 + pi^5 = e^6
Well, to five decimal places, anyway. Some other good ones: e^pi - pi = 20
sqrt(2) ln pi = phi
There are also famous "almost integers" such as this one discovered by Ramanujan: e^(pi sqrt(163))
Which is an integer to 12 decimal places.Edit: I just remembered I have public JupyterLite notebooks for both of these:
https://notebooks.oranlooney.com/lab/index.html?path=fake_ma...
https://notebooks.oranlooney.com/lab/index.html?path=heegner...
by lifthrasiir
2 subcomments
- The second fact, pi^2 ~= g, is famous enough that it has a separate section in Wikipedia [1].
[1] https://en.wikipedia.org/wiki/Mathematical_coincidence#Gravi...
- More advanced slide rules typically have a set of “folded” scales, that can sometimes save a calculation from ending up off scale. In theory, these should be offset by half the scale length, i.e. sqrt(10). However, since the folded scales also offer a convenient way to multiply with the offset factor, most slide rules offset them by π instead, since it’s almost the same as sqrt(10), and multiplication by π is a more useful thing to have around.
by renyicircle
0 subcomment
- My first thought was "well of course it is, since pi is a little larger than 3" but it was cool to see an actual derivation of how much pi squared differs from 10 as a nice, closed form series.
- I remember discovering that pi x 10^7 is very close to the number of seconds in a year while at uni.
One of my tutors was convinced this had to be more than coincidence, but I always figured it was just chance and a nice but sometimes useful shortcut...
- This first became apparent to me when I got a slide rule. Pi is often marked on the various scales and an x^2 scale is often nearby the x scale.
- 6! is the number of minutes in 12 hours and the number of hours in a 30-day month.
- > In the US and countries with a similar date format
Humm that's like 2 or 3 countries?
by BrandoElFollito
0 subcomment
- As an ex-physicist, pi^2 is 10. Like g.
I get it that this is a nice calculation with the Zeta function and everything, but 3 and a small something squared will be near 10 so it is 10.
- I was a little disappointed that the upper range of gravity on earth only goes to 9.8337. Just a little more and there would have been somewhere on earth that was an exact match.
It would have been the ideal (if chilly) place to start a cult.
- Pi^0 is exactly 1.
- If you don't unblock scripts from cdn.jsdelivr.net.cdn.cloudflare.net, the math code won't work.
- The author wants tau=2*pi, but in the Greek alphabet, tau has one vertical stroke, and pi has two.
So, visually in Greek, pi=2*tau would seem an improvement.
Oh, well.
- Also number of McDonald's in the world divided by number of McDonald's in US is close to pi. Within 1%.
by awinter-py
0 subcomment
- need a countdown for when it gets there
- pi^2 ~ 10, well known to anyone who used slide rules.
- at this rate, pi square is close to 'g'
- 987654321 / 123456789 = 8 (to the 7th decimal place) is another nice one
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