Mathematics is the ultimate game, where the players get to make up their own rules, with the only limitation being that the rules must be applied consistently.

Mathematics is the ultimate tool for understanding the world around us. Any thing that we can accurately describe with numbers we can understand through the relationships between those numbers.

Many of us were mislead during our educations to feel that mathematics means memorizing somebody else's rules, and that those rules limit our appreciation of the world around us. I hope that these musings help to dispel that misunderstanding. I hope that this helps people see that mathematics is NOT just a "left-brained" process of memorizing steps. Mathematics is a way of enhancing understanding of the world around you. Mathematics is a creative process requiring all forms of understanding including pattern recognition, visualizing, communication, and logical reasoning.

Is it possible to make Pascal's Triangle, fill a plane? See if you can beat the attempt.

Euclid's ancient proof that the list of primes must be infinite may be generalized into a method for searching for new primes. Can you develop this idea further?

The golden mean can be found using attractor methods. This show some interesting properties for number theory.

Mathematicians say it can't be done. It looks like it can! What is the error?

Why does this approximation technique show the value of pi to be four?

Radiation has nonlinear qualities. This may be observed in the current output of various types of detectors. (I observed it in the current of a neutron detector.) As a result our estimates of the impact of low level radiation may have significant errors.

A simple exercise with the fundamental constants of physics has some unusual implications about the universe itself. A quick approximation with a few basic concepts from physics may tell us why.

The Lorentz transformation can be easily shown to fit into a wave equation. Is this mathematically trivial or physically significant? You decide. Does this demonstrate wave-particle duality?

Einstein used gedanken (thought) experiments based in relativity to challenge quantum theory. Can quantum gedanken experiments challenge the limits of relativistic theory? Do you think these challenges are valid?

Wave equations can be utilized to analyze traffic flow.

Engineers: The distribution of incomes resembles a low pass filter. Look to see if you can figure out what causes the corner income. Also try to determine why the roll-off drops at higher incomes.

I created real-time software to read, filter and scale analog signals, and control an I/O panel menu using an indirectly addressed data structure approach. Many beginning programmers find indirect addressing difficult. Here's an overview.

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