Trigonometric identities are like a set of high quality knives, staying sharp even when asked to slice, cut, and chop day after day. In Sine Squared, I used a Pythagorean identity to coax the value from an integral. An identity is an equality statement. x = x is an identity; x equals x for any value of the variable x. This is distinct from an equation … Continue reading Pythagorean Identities
Life stands up to the downward force of gravity every day. From table legs to your legs, perpendicularity provides balance and strength. Perpendicular lines played an important role in finding the center of the arc of the bridge in the Pedestrian Bridge post. In writing the equation of those perpendicular lines, I used a concept I picked … Continue reading Perpendicularity
There is only one way to choose nothing. If there is no thing to choose, you have a choice: choose nothing. If there are two things from which to choose, choosing nothing is still a choice. Austin, TX I used to tell my students a story about counting goats as the birth of mathematics. They knew … Continue reading Pascal’s Triangle
It all started with a square. Just a simple square. Over two thousand years ago, in a small Greek colony in southern Italy, someone noticed something was not quite right about the distance along the diagonal. Life for that someone, and their friends, was never quite the same. That someone was a member of a religious … Continue reading Square Root of 2
the triangle Austin, TX 2011/07/17 A couple of years ago, I wrote a little program about triangles. The program calculates the area of a triangle given the base and the height. No great feat, right? Except, I did a little something special with the user interface. The triangle is graphed in a good old Cartesian … Continue reading Triangles
Madison Square Park, NYC5/28/2011 I was in NYC for a friend’s wedding. Big plans for the city: food, subway rides, Central Park, the Upper East Side, and chalk. On Saturday morning, I hopped a train to midtown and headed into Madison Square Park. The park had a large sculpture from Jaume Plensa. It stopped me … Continue reading Hexagons
Footpath Math: Chalk it up to a math geek 