It’s probably much too late for this, but the heart of the (geometric) analogy between circular and hyperbolic trigonometric functions is that circles and hyperbolas have internal symmetries visibly parametrized by a geometric area.
Now, obviously there are things the analogy does not capture, and there are things that obscure the analogy. For instance, the hyperbolic symmetry (which is a genuine symmetry!) does not play nice with the ordinary lengths of things in the plane; however, my
Wow. That was a big title. This post comes out of a number of conversations at Twitter Math Camp, but in particular a conversation with Justin Lanier, Michael Pershan, Malke Rosenfeld, and a rotating cast of others about the changing role of Twitter and blogs in the MTBoS. A topic we returned to a number […]
To call in the statistician after the experiment is done may beno more than asking hm to perform a postmortem examination: he may be able to say what the experiment died of. ~Ronald Fisher The 210th day of the year; (21, 20, 29) and (35, 12, 37) are the two least primitive Pythagorean triangles with different hypotenuses and the same area (=210). Students are challenged to find another pair of such PPTs EVENTS1654 Pascal wrote a letter to Fermat agreeing to a result of Fermat on a probability […]