# Boxing Pythagoras

## On Wildberger’s “Inconvenient Truths”

Dr. Norman Wildberger of the University of New South Wales has a wonderful and prolific YouTube channel in which he discusses a great deal of very interesting mathematics. I have discussed Dr. Wildberger before, regarding a very similar subject, but I wanted to take a moment to discuss a video from his Math Foundations series entitled, “Inconvenient truths about sqrt(2).”

In the video, Dr. Wildberger claims that there are three different ways in which $\sqrt{2}$ is commonly discussed: the Applied, the Algebraic, and the Analytical. He does a fairly good job of discussing the manner in which the ancient Greeks discovered that there exists no ratio of two whole numbers which can be equal to $\sqrt{2}$, which is a topic I have covered here, as well. He then explains what he means by each of the above three categories.

We can use a function for just such a purpose. A function is a specific mathematical tool which allows us to describe an entire set of data points all at once which we symbolize as $f(x)$ (read “$f$ of $x$“). We encode the data by means of a mathematical formula. For example, our exemplary rolling ball might well have been encoded by the function $f(x)=\frac{1}{2}x$, where the $x$ represents the time, in seconds, that the ball has been rolling, and the value of the function, $f(x)$ tells us the distance in meters which the ball has traveled in that time. In this particular function, the coefficient of $x$ tells us the rate at which distance changes as time passes– that is, $\frac{1}{2}$ a meter per second. When the boy first rolls it, the ball is traveling at $\frac{1}{2}$ a meter per second; when it finishes it had been traveling at $\frac{1}{2}$ a meter per second; and at any single point during the journey the ball is traveling at $\frac{1}{2}$ a meter per second.