3:00 pm Thursday, July 8, 2010
Student Geometry Seminar: Steiner's Porism
by Thomas Motter and Henry Gorman (Rice University - Mathematics Department) in HB 423
We will discuss the proof of Steiner's porism. The theorem is as such: we are given two circles, one of which is inside the other. At any point on the inner circle, we construct a circle that is tangent to both the inner and outer circles. Then, we proceed to construct a circle tangent to that circle and the other circle, and continue going around until we get to a circle that either intersects or touches the first circle that we drew. It turns out that this is invariant with respect to where we draw the first circle. We will prove this through strategic use of inversion of both circles. Host Department: Rice University-Mathematics
Submitted by mathweb@rice.edu |
