Wild About Math! Making Math fun and accessible

13Oct/071

Fun Math explorations

Harvey Mudd College is renowned for its Math department and for its overall education. Harvey Mudd students perform remarkably well on the William Lowell Putnam Mathematical Competition, a very grueling 6-hour 6-question exam taken by roughly 3,600 undergrads in the U.S. and Canada every year.

Given Mudd's commitment to excellence in mathematics education I was quite delighted to stumble upon the Mudd Math Fun Facts page, created and authored by Harvey Mudd Math Professor Francis Su. I am mentoring a couple of gifted high school students in Math. I am guiding them in explorations to increase their comfort with challenging Math contest problems and, more importantly, I'm helping them to grow in their appreciation of all things Math. I'll definitely be using a number of the Mudd Fun Facts in our sessions as they all wow me with their elegant and often surprising statements and many draw me in to try to understand and explain why they're true.

Mudd Math Fun Facts are perfect for inquisitive high school students. They come in easy, medium, and advanced levels of difficulty so there's something for everyone. Each Fact contains a description, suggestions for guiding student exploration, the Math behind the Fact plus references for further study. With 190 Mudd Math Fun Facts as of this posting curious students can spend many many fun-filled hours in joyful exploration.

My very favorite Fact (so far) is Chords of a Unit Circle. Su states that you get an interesting results if you do the following:Mudd Fun Facts - Chords of a Unit Circle

  1. Take a unite circle (i.e. a circle of radius 1)
  2. Mark off n equidistant points along the circumference of the circle. (n=6 in the illustration.)
  3. Select one of the points
  4. Draw chords from the chosen point to the n-1 other points along the circumference
  5. Multiply together the lengths of the n-1 chords

See if you can find a pattern for the product of the n-1 chords for circles with n points by starting with n=2 (just one chord) and increasing n.