$\sum_{n=1}^{\infty} \frac{n(n+1)/2}{(2n+1)!!^2} = \frac18$

Current mood:

class Circle:
pass

circle = Circle()
circle.circle = circle

$\sum_{n=1}^{\infty} \sin^2(\pi n! e) < \infty$

I wrote a Python script to look for circle packings. I can fit 20 circles of diameter 1 inside a circle of diameter 5.124. This is very close to the best known solution, which has diameter 5.122. Maybe .I can find a new record if I keep searching. mathstodon.xyz/media/-owErmTna

Proof without words that a pentagonal number is 1/3 of a triangular number. mathstodon.xyz/media/_eUukzGyW

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