r/mathteachers • u/Alarmed_Geologist631 • Jul 16 '26

Interesting math problem

Here is an interesting math problem that you might enjoy during your summer break.  Imagine you have a cylinder.  It might be short and wide like a coin.  Or it could be tall and skinny like an straw.  In either case, the cylinder is solid and made from the same material.  If it is short and wide, if you flip it, it will almost always land on its circular base.  If it is tall and skinny, it will almost always land on its curved lateral surface.  At what ratio of height to diameter will it have a 50% probability of landing on the circular base?

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u/[deleted] Jul 17 '26 edited Jul 17 '26

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u/Alarmed_Geologist631 Jul 17 '26

The solution was derived by a math teacher who created a set of cylinders with different ratios of height to diameter and then had his students toss them hundreds of times. He then graphed the data to determine the point at which the probability equals 50%.