Math Fun

This page is just for fun! We will investigate mathematical oddities, solve some puzzles, and get a glimpse into the wonder and beauty of mathematics.

The picture at the left is from "the good old days" when I was a young guy teaching math and physics at Wickenburg High School in Wickenburg, Arizona. What great fun we had with the "math club" and the "science club."
(Photo by Glen Alessi - Thanks Glen)

Definition: Fuzzy Logic - Two math majors sitting around drinking beer and working puzzles.
Been there, Done that!

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Math Fun 100: Interesting Puzzles
The Bookworm Puzzle

This is an easy puzzle, but very interesting in that it encourages you to approach problem solving differently. For this one I always say, "Be that worm!" In other words, get inside the problem!

The Bookworm Puzzle: Stated (pdf)
The Bookworm Puzzle: Solution (pdf)

The Two Cylinders Problem (Archimedes Crossed Cylinders or the Steinmetz Solid)

This one is so much fun! There are lots of complex algebraic and calculus-based solutions, but here we present a simple geometric approach. If two circular cylinders of equal diameter intersect at right angles, what is the volume common to both?

The Two Cylinders Problem: Stated (pdf)
The Two Cylinders Problem: Solution (pdf)

The Monk Problem:

This is such an interesting puzzle! At first you might think there is no way to prove it or that it will take some pretty advanced mathematics. But the solution is pretty simple and convincing. You just have to look at it from a different point of view.

The Monk Problem - Stated (pdf)
The Monk Problem - Solution (pdf)

The 9-Dot Problem

This puzzle is pretty easy but you have to "think outside the box" a little bit. Enjoy!

The 9-Dot Problem - Stated (pdf)
The 9-Dot Problem - Solution (pdf)

The Light Switch Problem

Here's another pretty easy one which requires you to "think outside the box."

The Light Switch Problem - Stated (pdf)
The Light Switch Problem - Solution (pdf)

The Durango Curve Problem

I lived in Phoenix, Arizona for many years, and every time I drove south on I-17 around the "Durango Curve" I noticed the shadow cast by the cement barriers on the east side of the freeway. This is a place where the freeway makes an abrupt 90 degree turn to the east.

If you are driving south in mid-morning when the sun is at 45 degrees, the east side barrier casts a shadow on the freeway that is the same height as the barrier. Then, as you drive around the curve, this shadow gradually gets shorter and eventually disappears. I know the freeway itself forms the quadrant of a circle, but what is the equation for the shadow?

The Durango Curve Problem (pdf)

The 12-Ball Problem

This is NOT an easy problem, but you can solve it. Don't just give up and look at the answer right away. The whole purpose of this puzzle is not to find the solution - the solution is already known and well documented. The purpose is to stretch your thinking and have the satisfaction of discovering it for yourself. I struggled with this one quite a while but I did eventually work it out!

The 12-Ball Problem - Stated (pdf)
The 12-Ball Problem - Solution (pdf)

Math Fun 200: Math and Nature
Fibonacci Spirals in Nature

Fibonacci numbers are simple to understand, but it's not so easy to understand why they are so prevalent in nature. Here's a little PDF document I put together to show a few examples I have come across while out hiking.

Fibonacci Spirals in Nature (pdf)

Regular Tilings of the Plane
The medium may be tile, carpet or wood, but there are only three regular tilings of the plane.

Regular Tilings of the Plane (pdf)

The "Group" is probably the most simple and most easily understood mathematical construct from Abstract Algebra, but it has many wonderful and  interesting properties! I hope to add several articles about Groups. This first one has to do with a non-numeric group relating to the appreciation of nature.

Groups in Nature (pdf)

Crickets Sing Like a Choir!

This MP3 file is an actual, untouched recording of crickets. It's just been slowed down. Adjusting our time-domain reference is similar to adjusting the number of dimensions we use to view data above. Many interesting and beautiful properties are revealed by looking at things differently!

Crickets Sing Like a Choir! (MP3 audio file)
Math Fun 300: Paradoxes
The Liar Paradox

This paradox is simply stated, but leads to some interesting logical discussions.

The Liar Paradox (pdf)
Math Fun 400: Catastrophe Theory
Much of mathematics treats events that are "well behaved." They are smooth and continuous, but not all things are like that. What about those things that are discontinuous or exhibit abrupt changes? Here's where Catastrophe Theory comes in. We are going to take a layman's approach to this fascinating study. So, don't be scared away if we use a little bit of technical jargon now and then. If I can understand this stuff - you can too!

The Cusp Sheet Surface

Think about a system that could have two stable states. We don't know how it is going to turn out but, as pressures build, all of a sudden, it jumps to the other state (like a clicker). Here's a way to visualize the dynamics.

Simple "Yes/No" Decisions Modeled by the "Cusp" Catastrophe (pdf)
Math Fun 500: Data Analysis: Finding Patterns
Mapping a One Dimensional Data Set into Two Dimensions

Many times when we look at a set of data differently we can start to see a pattern that wasn't obvious before. This short video illustrates a technique for looking at data from a different point of view.

Mapping a One Dimensional Data Set into Two Dimensions (video)
Math Fun 1200: Bibliography and References
There are thousands of excellent books about recreational mathematics! Here are a few of my favorites.

Bibliography (pdf)