# 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.

## On the Irrationality of the Square Root of 2

Consider a triangle with two legs of equal length which meet at a right angle. What is the proportion of the length of the Hypotenuse to the length of one Leg?