Unexpected Factorial

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When you use an exclamation mark with a number, you’re actually implying it’s not a normal number any more. It’s a factorial!

Ok, so how does this work?

5!=1×2×3×4×5=120

6!=720

These numbers get really large. For example:

15!≈1.3×10^12

So, next time you see a headline with 2000! in it, you’ll know what to expect.

There are also double factorials (n!!) and iterated factorials (n!)!, and they aren’t the same thing. Just add more exclamation marks and you get multifactorial. Check wikipedia to see how spicy it gets.

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Hamartiogonic@sopuli.xyz

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270! degrees (sopuli.xyz)

submitted 1 month ago by Hamartiogonic@sopuli.xyz to c/unexpectedfactorial@sopuli.xyz

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Which is roughly 6.7*10^540.

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[–] Applesause@mander.xyz 3 points 1 month ago (1 children)

So everything after 89!° is corotational with 0?

[–] msfroh@lemmy.ca 4 points 1 month ago* (last edited 1 month ago) (1 children)

The bar should actually be a lot lower than that. The "90 and 4" factors just jumped out at me because the thread was already talking about 90 degree rotations. 45 and 8 would be another valid option, for example.

360 = 2x2x2x3x3x5.

With 2 and 4, all of the 2s are covered. With 3 and 6, all of the 3s are covered (and we pick up an extra 2). Then with 5, we've covered the whole thing. (You can see why we defined degrees to put 360 of them in a circle -- lots of small factors makes it easy to slice into 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, etc parts.)

So, starting with 6!, they're all multiples of 720, and therefore multiples of 360.

[–] Applesause@mander.xyz 1 points 1 month ago

That sounds just mathy enough to be believable, and said with such confidence I don't even need to check your work!

Thanks for the explanation.