MathOverflow is a remarkable recent platform for research level questions and answers in mathematics. Joe O’Rourke have asked over MO wonderful questions. (Here is a link to the questions) Many of those questions can be the starting point of a research project usually in discrete and computational geometry and sometimes in other areas. Many of the questions remained open, quite a few have led to definite quick solutions, and for many others substantial answers were offered. Usually Joe’s questions (and also his MO answers) contain beautiful and illuminating pictures. Amog the highlights: Joe’s question on Billiard knots; a poetic question about “light reflecting off christmantree balls“; rolling a random walk on a sphere – with a definite answer by S. Carnahan; Pach animals of high genus; Fair irregular dice (with a nice answer by Bill Thurston); Parabolic envalope of fireworks; Coiling rope in a box; A convex polyhedral analog of the pentagram map ; Randompolycubeshapes ; Which convex bodies roll along closed geodesics and many more. The 100th question is The rain hull and the rain ridge.
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Recent Posts
 Hardness of Approximating Vertex Cover, PolytopeIntegralityGap, the AlswedeKachatrian theorem, and More.
 Jacob Fox, David Conlon, and Benny Sudakov: Vast Improvement of our Knowledge on Unavoidable Patterns in Words
 Subhash Khot, Dor Minzer and Muli Safra proved the 2to2 Games Conjecture
 Interesting Times in Mathematics: Enumeration Without Numbers, Group Theory Without Groups.
 Cody Murray and Ryan Williams’ new ACC breakthrough: Updates from Oded Goldreich’s Choices
 Yael Tauman Kalai’s ICM2018 Paper, My Paper, and Cryptography
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 Third third of my ICM 2018 paper – Three Puzzles on Mathematics, Computation and Games. Corrections and comments welcome
 Second third of my ICM 2018 paper – Three Puzzles on Mathematics, Computation and Games. Corrections and comments welcome
Top Posts & Pages
 Hardness of Approximating Vertex Cover, PolytopeIntegralityGap, the AlswedeKachatrian theorem, and More.
 Subhash Khot, Dor Minzer and Muli Safra proved the 2to2 Games Conjecture
 New Isoperimetric Results for Testing Monotonicity
 Jacob Fox, David Conlon, and Benny Sudakov: Vast Improvement of our Knowledge on Unavoidable Patterns in Words
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 Can Category Theory Serve as the Foundation of Mathematics?
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 Elchanan Mossel's Amazing Dice Paradox (your answers to TYI 30)
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Joe has become quite renowned for his figures :). He also has two new books out (How to Fold It, Discrete and Computational Geometry) that are filled with many such great images, which are produced using Mathematica I believe.
Wow, I am truly honored, Gil (and thanks, Andrew)! Gil, I owe you one. Request refereeing, whatever … 🙂
GK: my pleasure Joe, keep the wonderful question comming
Wonderful post!
Would it be at all possible to tag this post “planetMO” so that it can be found via mathblogging.org/planetmo ?
Sorry about the typo, there’s a ” missing — here’s a working link planetMO