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.

10Oct/070

Phi: It’s everywhere you look

Phi, also known as the golden ratio or the divine proportion, is one of the great mathematical constants. It is equal to a little more than 1.6 and is a most interesting irrational (but not transcendental) number. Phi has a fascinating connection with the Fibonacci series, it can be derived by solving a simple quadratic equation, and it reveals itself in simple but deep geometric constructions.

http://goldennumber.net provides the familiar background material on Phi and then goes much deeper, showing startling examples of how the golden ratio appears in art, architecture, music, poetry, proportions of the human body, and other surprising places.

A fun example of Phi appearing in unexpected places is in the dimensions of a credit card. The ratio of the two sides is very close to Phi.

Credit card dimensions in the golden ratio

Another surprising example, at the microscopic level, is the DNA molecule. Each double helix spiral is in the proportion of the golden ratio.

DNA molecules in golden ratio proportion

Check out http://goldennumber.net for more than you could every want to know about Phi, all beautifully illustrated.