Yeah… Considering that 270! contains both 4 and 90 as independent factors (as there’s a x4 that has nothing to do with the x90), it means that it’s a multiple of 360. So it’s rotationally equivalent to 0.
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.
That would really be pretty neat. A bit unlikely though, but would be fun if it landed on the exact same angle.
Yeah… Considering that 270! contains both 4 and 90 as independent factors (as there’s a x4 that has nothing to do with the x90), it means that it’s a multiple of 360. So it’s rotationally equivalent to 0.
So everything after 89!° is corotational with 0?
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.
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.
LOL. The proposed new compass system has two norths, because apparently one just wasn’t enough.