I like the 4-5-6 theorem: pi^4 + pi^5 = e^6 Well, to five decimal pla...

olooney • today at 1:59 PM • 3 replies • view on HN

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:

vitriol83 • today at 5:03 PM

the Ramanujan one has some relatively high powered mathematical explanation

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Y_Y • today at 4:57 PM

(e^pi - pi)/pi^4 ~= i^i

dylan604 • today at 3:53 PM

> Which is an integer to 12 decimal places

this isn't something I was expecting to read today. I guess this works with weak types? /s

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