Category Archives: Geometry

János Pach: Guth and Katz’s Solution of Erdős’s Distinct Distances Problem

Click here for the most recent polymath3 research thread. Erdős and Pach celebrating another November day many years ago. The Wolf disguised as Little Red Riding Hood. Pach disguised as another Pach. This post is authored by János Pach A … Continue reading

Posted in Combinatorics, Geometry, Guest blogger, Open problems | Tagged , | 13 Comments

Benoît’s Fractals

Mandelbrot set Benoît Mandelbrot passed away a few dayes ago on October 14, 2010. Since 1987, Mandelbrot was a member of the Yale’s mathematics department. This chapterette from my book “Gina says: Adventures in the Blogosphere String War”   about fractals is brought here on this … Continue reading

Posted in Geometry, Obituary, Physics, Probability | 6 Comments

Answer to Test Your Intuition (3)

Question: Let be the -dimensional cube. Turn into a torus by identifying opposite facets. What is the minumum -dimensional volume of a subset of which intersects every non-trivial cycle in . Answer: Taking to be all points in the solid … Continue reading

Posted in Geometry, Test your intuition | Tagged | 2 Comments

Test Your Intuition (3)

Let be the -dimensional cube. Turn into a torus by identifying opposite facets. What is the minumum -dimensional volume of a subset of which intersects every non-trivial cycle in .

Posted in Geometry, Test your intuition | Tagged | 10 Comments