Problem of the Week 881

Minimize the Slopes

Find 881 points in the plane so that the lines between them determine as few different slopes as possible. Of course, they must not all be on a straight line.

For example: 3 points determine 3 slopes. Four points forming a square determine 6 segments, but only 4 distinct slopes. (Proof of optimality not requried -- though it is known.)

Source: A beautiful new book titled: "Problems from the Book" by Aigner & Ziegler (Springer-Verlag). The "book" refers to Erdos's mythical book that contains the BEST proofs of everything.


A report, with photo, of our mathematical entry at the 1999 Breckenridge Snow Sculpture Championships appeared in the Feb. 5 issue of SCIENCE.


I am leaving town for several weeks. The PoW program will be administered by my colleague Rob Leduc ( in my absence.

© Copyright 1999 Stan Wagon. Reproduced with permission.

23 February 1999