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> In my opinion the circle should be positioned in an infinite plane, then random vectors should be drawn on the plane and ignored unless they intersect the cir
by sampo 11y ago
> In my opinion the circle should be positioned in an infinite plane, then random vectors should be drawn on the plane and ignored unless they intersect the circle.
After looking at the Wikipedia page, it seems that your method would be equivalent to the "random radius" aka "1/2" aka "ninja" method.
https://en.wikipedia.org/wiki/Bertrand_paradox_(probability) https://en.wikipedia.org/wiki/Bertrand_paradox_(probability)
This is a good demonstration of the paradox here. You phrase your method as "random vectors in an infinite plane", but even when it is equivalent to the "ninja" method, the ninja method doesn't seem right to you.
- dstyrb 11y agoI don't think so, like say you had a point outside the circle, and from that point you equally selected angles to slice the space in. You would get systematically longer slices than if all your slices are cut parallel to each other (and you ended up with the same number slicing the pizza). edit: I worked it out and you're right, I get the same answer as the ninja one.
- Dylan16807 11y ago>You would get systematically longer slices than if all your slices are cut parallel to each other (and you ended up with the same number slicing the pizza). You're only cutting once per pizza, so there's no parallel slices, so no such effect. And allowing a dense set of possible parallel vectors from every angle is equivalent to rotating the pizza. Which obviously doesn't affect the sizes.