|Math Fun 100: Interesting Puzzles|
|The Bookworm Puzzle|
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)|
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:|
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|
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.
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|
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|
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)
"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|
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
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|
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
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|
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.|