Monthly Archives: August 2009

Geometry and Probability


Posted in Conferences, Probability | Tagged , , | 4 Comments

Igor Pak’s “Lectures on Discrete and Polyhedral Geometry”

Here is a link to Igor Pak’s  book on Discrete and Polyhedral Geometry  (free download) . And here is just the table of contents. It is a wonderful book, full of gems, contains original look on many important directions, things that … Continue reading

Posted in Book review, Convex polytopes, Convexity | Tagged , , , | 4 Comments

Test Your Intuition (9)

Click on the picture if you wish to read about the “Mars effect”   A) You want to test the theory that people who were born close to noon on July 7 are unusually tall. You choose randomly 100 Norwegian men over 25 years old and discover … Continue reading

Posted in Statistics | 5 Comments

The Polynomial Hirsch Conjecture: Discussion Thread

This post is devoted to the polymath-proposal about the polynomial Hirsch conjecture. My intention is to start here a discussion thread on the problem and related problems. (Perhaps identifying further interesting related problems and research directions.) Earlier posts are: The polynomial Hirsch … Continue reading

Posted in Convex polytopes, Open discussion, Open problems | Tagged , | 115 Comments

Polymath4 – Finding Primes Deterministically – is On Its Way

  After two long and interesting discussion threads polymath4, devoted to finding deterministically large prime numbers, is on its way on the polymath blog.

Posted in Open problems | Tagged | Leave a comment

Impossibility Result for “Survivor”

Consider a set of agents and a directed graph where an edge means that agent supports or trusts agent . We wish to choose a subset of size of trustworthy agents. Each agent’s first priority is to be included in … Continue reading

Posted in Computer Science and Optimization, Economics | Tagged | 11 Comments

School Bus to Ramle

We had just come back to Israel from Palo Alto after spending a sabbatical year there and my child was starting school. I walked down with him to wait for the school bus. To my great surprise it was a yellow school … Continue reading

Posted in Taxi-and-other-stories | Tagged | 2 Comments

Buffon’s Needle and the Perimeter of Planar Sets of Constant Width

Here is an answer to “Test your intuition (8)”. (Essentially the answer posed by David Eppstein.) (From Wolfram Mathworld) Buffon’s needle problem asks to find the probability that a needle of length will land on a line, given a floor … Continue reading

Posted in Convexity, Probability, Test your intuition | Tagged | 6 Comments

Test Your Intuition (8)

Consider all planar sets  A with constant width 1. Namely, in every direction, the distance between the two parallel lines that touch A from both sides is 1. We already know that there exists such sets other than the circle … Continue reading

Posted in Convexity, Test your intuition | Tagged | 14 Comments