Pi squared is nearly 10

48 points48 comments7 hours ago
olooney

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...

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Pinus

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.

lifthrasiir

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...

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renyicircle

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.

verzali

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...

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leni536

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.

ivolimmen

> In the US and countries with a similar date format

Humm that's like 2 or 3 countries?

tshaddox

6! is the number of minutes in 12 hours and the number of hours in a 30-day month.

BrandoElFollito

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.

Lerc

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.

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Dwedit

If you don't unblock scripts from cdn.jsdelivr.net.cdn.cloudflare.net, the math code won't work.

dvh

Also number of McDonald's in the world divided by number of McDonald's in US is close to pi. Within 1%.

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amelius

Pi^0 is exactly 1.

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awinter-py

need a countdown for when it gets there

smitty1e

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.

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mac3n

pi^2 ~ 10, well known to anyone who used slide rules.

wiz21c

at this rate, pi square is close to 'g'

gntech

987654321 / 123456789 = 8 (to the 7th decimal place) is another nice one