The Internet is in a tizzy yet again about the evils of mathematics education. At least Common Core isn’t being demonized quite as front-and-center as in the recent past, but still. This time it’s about pizza. Which means every mathematics educator reading this will know it’s about fractions, because that’s why we ever mention pizza…
Month: March 2016
Inscribed Right Triangle
(Edit 6/18/23: The image has been lost, but I’ll leave the text in case I ever have the chance to reconstruct it.) 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 \(\Delta AEF\)…
al-Jabr: Integer Parameters
I was thinking about the third scenario described in al-Khwarizmi’s al-Jabr: \(x^2 = 3x + 4\). I was curious about the integer solutions of the general pattern, \(x^2 = ax + b\). It’s easy enough to demonstrate that this will hold if \(x = b = a + 1\), since that means \((a + 1)^2…
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 do now. I was reading Power Puzzles 2 by Philip Carter and Ken Russell when…
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. The length of the altitude is the geometric mean of the lengths of the two…