Hosted by The Math Forum


Problem of the Week 855

Dizzying Triangles

_____________________________________________
Spring 98 Archive || MacPOW Home || Math Forum POWs || Search MacPOW
_____________________________________________

Consider a grid of 16 points arranged in a uniform 4×4 array. If all orthogonal connecting lines were drawn there would be 9 small squares. For each square, draw its two diagonals. How many triangles are there that have each of its vertices on the grid, and each of its edges on the network of lines?

For enthusiasts: Find the general formula for f(n), which counts the number of grid triangles on the n×n grid (which has n2 grid points). For example: f(1) = 0, f(2) = 4.

Source: Harris Kwong, SUNY College at Fredonia (kwong@carol.cs.fredonia.edu or kwong@cs.fredonia.edu). He has a general formula and a proof, but would be interested in seeing other proofs; in particular, he wonders if there is an inudction proof.

© Copyright 1998 Stan Wagon. Reproduced with permission.

[Privacy Policy] [Terms of Use]

_____________________________________
Home || The Math Library || Quick Reference || Search || Help 
_____________________________________

© 1994-2014 Drexel University. All rights reserved.
http://mathforum.org/
The Math Forum is a research and educational enterprise of the Drexel University School of Education.The Math Forum is a research and educational enterprise of the Drexel University School of Education.

The Math Forum

2 October 1998