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
 Monday February 19: Quantum Coding and High Dimensional Expanders
 Alef’s Corner: There is Still a Small Gap in the Proof
 My Argument Against Quantum Computers: An Interview with Katia Moskvitch on Quanta Magazine
 The Semester Break activities of the High Dimensional Combinatorics and Expanders Special Year
 Akshay Venkatesh Lectures at HUJI – Ostrowski’s Prize Celebration, January 24&25
 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 completed the proof of the 2to2 Games Conjecture
 Interesting Times in Mathematics: Enumeration Without Numbers, Group Theory Without Groups.
Top Posts & Pages
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 Quantum computing: achievable reality or unrealistic dream
 Alef's Corner: There is Still a Small Gap in the Proof
 TYI 30: Expected number of Dice throws
 Believing that the Earth is Round When it Matters
 If Quantum Computers are not Possible Why are Classical Computers Possible?
 Monday February 19: Quantum Coding and High Dimensional Expanders
 Elchanan Mossel's Amazing Dice Paradox (your answers to TYI 30)
 Subhash Khot, Dor Minzer and Muli Safra completed the proof of the 2to2 Games Conjecture
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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