Geometry

The Geometric Proof of Infinite Primes

I was recently wondering why Euclid, the geometer, published a proof that there is an infinite number of primes. I should have known that his proof is geometric. It is: “Let A, B, and C be distinct lengths that cannot be…

Inscribed Right Triangle

Here’s a fun puzzle (via Brilliant.org): What is the area of the square $$ABCD$$? There may be a simpler approach; my solution wound up being more complicated than I expected. Since $$\Delta AEF$$ is a right triangle, $$AE = 5$$…

Geometry

Naming Variables

First of all, let me get this out of the way: “Hey, you kids! Get off my lawn!” In this post, I comment on the notational shifts from what I was trained in back in the 1980s and what textbooks…

Right Triangle Similarity

Today’s lesson in my Geometry class was on the use of the geometric mean when finding missing values of right triangles. For every right triangle, two of its altitudes are the legs and the third is perpendicular to the hypotenuse….

Al-Jabr (continued)

In my previous post, I looked at the first two detailed examples provided by al-Khowarizmi in his compendium, the title of which gives us the word “algebra”. Al-Khowarizmi discussed three types of mathematical objects: Numbers (N, constants), roots (R, unknowns),…