2
votes
5answers
824 views

Circumference of convex shapes

Here is a puzzle I found in "Mitteilungen der DMV" (roughly "Letters of the German Society of Mathematicians") issue 19/2011. It was posed by Alfred Schreiber in "Wie man Hasen fangt" (How to catch ...
23
votes
3answers
2k views

An elementary problem in Euclidean geometry [closed]

This problem was first put to me by Luke Pebody (who did not know the answer at the time) and after some work I am yet to find a proof or counterexample. I would be grateful of any insights. Call a ...
3
votes
1answer
452 views

Is always possible to slice a pizza in a fair way

Given a pizza, represented by the unit disk $D_1(0,0)=\{(x,y)\in\mathbb{R}^2\mid \|(x,y)\|\leqslant 1\}$, and given $N$ slices of $r$-pepperoni, represented by disks ...
8
votes
1answer
551 views

Sticks and thread

In this recent question Math puzzles for dinner we had a nice time as we were asked to provide new maths puzzles for dinners. I suggested the following: Given three equal sticks, and some ...