Abraham de Moivre was born in France in 1667, a year after the Great Fire in London. de Moivre arrived in London in the late 1680s. Leading up to his emigration, life in France for Huguenots, i.e. French Protestants, was growing ever more uncomfortable. As Louis XIV consolidated power, he grew to see religious tolerance as a … Continue reading de Moivre’s Shortcut
To square a complex number, square the length, and double the angle. A vector is a directed line segment, an arrow if you will. Think of a complex number, z = a + bi, as a vector from the origin (0,0) to the point (a,b). In polar form, z can be written in terms of r, the distance from the … Continue reading Square of a Complex Number
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
Just south of Mueller in Austin is the J.J. Seabrook Greenbelt. It is hugged by Pershing Drive and will soon have a trail connected to the trail at Mueller. The creek bed has been re-engineered and, just a few days ago, a bridge arrived ready to span the creek. It was a sight to see the bridge … Continue reading Pershing Pedestrian Bridge
New Orleans LA In graduate school, I spent a fair amount of time getting familiar[z] with the Riemann zeta function. Courses in complex analysis and special functions along with reading a couple of pop math books[e] increased my familiarity with zeta as well as the Riemann hypothesis. In answer to the gentleman’s question in New Orleans, “It … Continue reading Riemann Zeta Function
Austin TX 2013/06/16 This post and the previous are sort of farewell gifts to my students who just finished their first year studying calculus. I love creating lectures (as you might imagine), but they hungered for something else. They challenged, inspired, and reminded me what I love about teaching. For me, the gift of teaching is … Continue reading Euler’s Formula
This post was in the works for over a month. The chalk happened in one evening, but the research and writing took time. Taylor series make for a meaty topic, and Brook Taylor had a full life. Plus, infinity took me on a few tangential journeys. The big idea here is approximation, in particular the evolution … Continue reading Taylor Series
Barton Springs PoolAustin TX2013/06/02 There are so many books, articles, websites, poems and cartoons about π; I considered not chalking it. I have been working on an upcoming post on Taylor series, but π just keeps saying, “Hey, after all I have done for you, will you please just spend some time with me?” So, here … Continue reading π
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 