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Pythagorean Triples

curiousCharacter — Wed, 21 Jul 2010 17:30:54 +0000

When math textbooks need an example of a right triangle, they frequently use a triangle with sides of length 3, 4, and 5, since the numbers work out so nicely: by the Pythagorean theorem. If that gets tiresome, 12, 5, 13 might be used: . Clearly, multiplies of these numbers work also, e.g. [...]

What is e, and Why is it Important?

curiousCharacter — Tue, 09 Mar 2010 02:34:22 +0000

This post is to give some background about the constant e. Math students normally encounter e (2.7182818284590452…) in their Precalculus chapter on exponentials and logarithms, and they often wonder where this rather odd number comes from, and what is special about it.

The Greatest Formula in Mathematics

curiousCharacter — Sat, 30 Jan 2010 01:52:09 +0000

It’s usually called Euler’s Identity, after the great Swiss mathematician Leonard Euler, and several polls of mathematicians and physicists have bestowed on it titles such as “the greatest equation ever”

Newton Verifies the Law of Gravity

curiousCharacter — Thu, 14 Jan 2010 16:20:09 +0000

Although much of Newton's work is accessible only to specialists, some of his results can be understood and appreciated by the rest of us. In this post I will describe one such investigation – his effort to determine how the force of gravity decreases with distance from the earth. The results were very significant in a scientific sense, and the way he carried out the work shows astonishing insight and imagination.

The Wonders of WolframAlpha

curiousCharacter — Fri, 08 Jan 2010 07:27:58 +0000

It is unworthy of excellent men to lose hours like slaves in the labor of calculation. Gottfried Wilhelm Leibniz I have often told students that becoming good at math is a lot like becoming good at a sport or at playing an instrument – practice is extremely important. Hours and hours of practice. However, there is a [...]

How Many Prime Numbers Are There?

curiousCharacter — Wed, 25 Nov 2009 00:59:36 +0000

Are there an infinite number of prime numbers? Or maybe there is a largest prime number, and every number after that is composite. To get a little insight into this, we might start listing the prime numbers, beginning 2, 3, 5, 7, 11, …, to see if any pattern emerges. About all that is [...]

How Math Ended Signal Distortion

curiousCharacter — Sun, 04 Oct 2009 04:48:01 +0000

On the morning of August 2, 1927, a young electrical engineer named Harold Black was riding the Lakawanna Ferry across the Hudson River on his way to work in Manhattan, where he was employed by Bell Laboratories. Black was pondering an important problem that he had wrestled with for several years without making any progress. [...]

The Mathematics of Monsters

curiousCharacter — Fri, 02 Oct 2009 03:21:49 +0000

Here is the familiar image of King Kong atop the Empire State Building. There’s something profoundly incorrect in how he is depicted, a problem that is shared with almost all giant creatures in the movies, be they flies, dragons, or humans. The problem involves some math, which is why I’m discussing it here. Before I can [...]

Formula Driven Problem Solving

curiousCharacter — Thu, 23 Jul 2009 16:19:10 +0000

This post is the first of a series of hints and techniques for students of math, all based on my experience as a math tutor and teacher… Much of what a student must learn in a math course amounts to mastering the steps in a well defined procedure. For example, multiplying two binomials (e.g. (x-3)(y2+z) ) [...]

Pythagoras and His Theorem

curiousCharacter — Fri, 03 Jul 2009 04:04:52 +0000

One of the most important and famous formulas in mathematics is the Pythagorean Theorem: for a right triangle, the square of the long side (hypotenuse) is equal to the sum of the squares of the other two sides. Using a diagram: As I have pointed out in other posts, proofs of major results like this are [...]