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by olooney 23 days ago
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...

3 comments

the Ramanujan one has some relatively high powered mathematical explanation

https://en.wikipedia.org/wiki/Heegner_number

Wikipedia also notes that “Ramanjuan’s constant” was actually discovered by Charles Hermite in 1859 and it was a 1975 April Fools article in Scientific American that attributed it to Ramanujan.
Stigler's Law of Eponymy strikes again!

https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy

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

That's why the time is Almost<T> instead of just T.