In my previous post, I looked at the first two detailed examples provided by al-Khwarizmi in his compendium, the title of which gives us the word “algebra”. Al-Khwarizmi discussed three types of mathematical objects: Numbers (N, constants), roots (R, unknowns), and squares (S, squares of unknowns). Because he was limited to positive solutions, he was…
Month: February 2016
Al-Jabr
The word “algebra” comes to us from the title of a book, al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabalah written by Mohammed ben Musa al-Khwarizmi (there are variations in the transliterations of both the title and the author) around AD 825. He was not the inventor of algebra; indeed, his book was a compendium and extension…
Proof: Isosceles Triangles in a Quadrilateral
In my last post, I noted that it’s possible to create an isosceles trapezoid from four isosceles triangles, but I wasn’t sure if there was a way to construct a quadrilateral from isosceles triangles such that the quadrilateral was neither a rectangle nor an isosceles trapezoid. Now I know that it is not. Let’s reconsider…
Isosceles Triangles in a Quadrilateral
In this post, I’ll discuss two issues. First, I’ll look at a problem taken from a major textbook, and explain why the solution is wrong. Then, I’ll discuss why this particular problem bothers me in the greater context of mathematics education. First, the problem. This is a question from Pearson’s Common Core Geometry supplemental materials…