Timeline for What theorem can be used to explain this occurrence?
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8 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2017 at 15:56 | answer | added | Liviu Nicolaescu | timeline score: 1 | |
| Mar 17, 2017 at 12:23 | comment | added | Benoît Kloeckner | You cannot use only diameter either, as is shown (less dramatically) by a disk as first object and as second object a thin rod slightly longer than the disk's diameter. The rod has additional available positions, where it is almost aligned near the inner circular boundary. However if the two objects you compare have the same shape but different scales, then your obvious observation is true, basically thanks to Thought 2.5 in Pat Devlin's answer (Thought 2 extends beyond disks, but has an issue if the object is not star-shaped en.wikipedia.org/wiki/Star_domain) | |
| Mar 17, 2017 at 12:23 | comment | added | Benoît Kloeckner | You have to be careful when you consider the size. There exist two objects, the first of much larger area than the second, such that the probability of the first lying entirely in the inner circle is much larger than the probability of the second lying entirely in the inner circle. Indeed, you can take a smallish disk as first object, and a very very thin seastar with very long arms. | |
| Mar 17, 2017 at 8:41 | comment | added | Qiaochu Yuan | In isolation it is a straightforward observation about probability and geometry (maybe "geometric probability" if you really want to go there): if you throw a small circle of radius $r$, it fits into a circle of radius $R$ if and only if its center is at least a distance $r$ from the boundary, hence if and only if its center lands in a concentric circle of radius $R - r$. Do you have other examples of this type that you want to understand? | |
| Mar 17, 2017 at 6:59 | comment | added | Carlo Beenakker | if you phrase it as "how many objects can I fit in the circle", the "field of mathematics" you are looking at is that of packing problems | |
| Mar 17, 2017 at 6:50 | answer | added | Pat Devlin | timeline score: 2 | |
| Mar 17, 2017 at 6:10 | review | First posts | |||
| Mar 17, 2017 at 6:25 | |||||
| Mar 17, 2017 at 6:06 | history | asked | Rohan Arora | CC BY-SA 3.0 |