Copasetic Flow

Dr. David Hestenes, (pictured to the left [2]), the original author of geometric algebra, (it was his PhD dissertation work at UCLA), will be speaking at A&M today [1]. We're learning how to do literature review matrices in our writing class, so I thought I'd try out the technique while reading Dr. Hestene's bio [2] last night.  Here are the key points I came away with 1.  Hestenes was inspired by Marcel Riesz's book " Clifford Numbers and Spinors "[3] One day in the mathematics– engineering library I looked at a shelf of incoming new books and pulled down and some lecture notes entitled “Clifford Numbers and Spinors” by Marcel Riesz. It was about Clifford algebra as a mathematical system. I read, I think, for about 15 minutes and all of a sudden I had an epiphany. I exclaimed “Gee, differential forms and the Dirac algebra have a common algebraic structure!”… 2.  Dr. Hestenes received the Oersted medal for his work on the force concept...

Just a few brief notes on circular and hyperbolic trigonometry today.  First, if there's anyone who'd like to offer, any clarifications, expansions, or other cool and interesting facts, please, you're more than welcome!  As usual, this is stuff that I learned in high school that didn't become blindingly clear and meaningful until it cropped up in grad school physics.  First, the equations for the circle and the hyperbola (picture 1) Notice that they differ only by a single negative sign.  Now, for their graphs, (picture 2). Each of these figures can also be expressed in parametric form as follows, (this is where the trigonometric and hyperbolic trig functions come in).  (picture 3) Now for the notes and other thoughts. Angular Arc Length and Angular Area Until just a few weeks ago, I had always wondered why the inverse trig functions were called arcsine, and arccosine.  The answer makes perfect sense, it just hadn't occurred to me.  T...