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Visualizing first 1000 digits of π. Beautiful.

mathladyhazel's profile picture

Math Lady Hazel 🇦🇷

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36,143 views • 1 year ago •via X (Twitter)

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10 Comments

Nanjizal's profile picture
Nanjizal1 year ago

But what about plotting PI in other bases, is there any more obvious pattern.

Arkhnor's profile picture
Arkhnor1 year ago

And it's yet unproved whether pi is a normal number...

A. Hariharan's profile picture
A. Hariharan1 year ago

🫤 what why, why is this even worth plotting

Guido's profile picture
Guido1 year ago

It’s the law of large numbers

Bitcows's profile picture
Bitcows1 year ago

👁👁❤️

A I's profile picture
A I1 year ago

Tell me why

DULA's profile picture
DULA1 year ago

Do we know why this beautiful dance and balance? What about 1000 or 1 million digits ?

Serious Nonsense 🇵🇸's profile picture
Serious Nonsense 🇵🇸1 year ago

is this even useful?

David Cornwell's profile picture
David Cornwell1 year ago

I rarely repost anything without a wiseass comment of my own. Congrats! 🍾 🥂 🎉

Restu ˆ⌣ˆ's profile picture
Restu ˆ⌣ˆ1 year ago

I have the first 10 thousand digits of pi, any idea how can I visualize it?

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A square wave flipping between ±1 at multiples of π is the limit of f_N(t) = (4/π) ∑ sin((2k+1)t)/(2k+1) for k < N. Only odd harmonics appear, since f(t + π) = −f(t). Term k is a circle of radius (4/π)/(2k+1) turning 2k+1 times as fast as the first; the chain ends at height f_N(t). The sum overshoots each jump. Its first peak, at t = π/(2N), is 1.182 for N = 5 and 1.179 for N = 100, about 9 % of the jump. More terms narrow it, never remove it.
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