You may have met the complex numbers. Gauss named them in 1831, but our knowledge of complex numbers was born in the first half of the 16th century in northern Italy with attempts to solve cubic equations. Leveraging knowledge from Tartaglia, Girolama Cardano published his findings in his book Ars Magna in 1545. Complex numbers have a real part and an … Continue reading Polar Form of Complex Numbers
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
Rue Lagrange Paris, France 2013/03/12 On the flight to Paris, while I should have been sleeping, I was thinking about math. (Not entirely unusual apart from being some 30,000 feet above the Atlantic.) France is kind of a big deal for math history. One of the Paris’ oldest churches, St-Germain-des-Prés, entombs a portion of Descartes.0 … Continue reading Lagrange Four Squares
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
Footpath Math: Chalk it up to a math geek 