Curves of Finite Total Curvature

We consider the class of curves of finite total curvature, as introduced by Milnor. This is a natural class for variational problems and geometric knot theory, and since it includes both smooth and polygonal curves, its study shows us connections between discrete and differential geometry. To explore these ideas, we consider theorems of Fary/Milnor, Schur, Chakerian and Wienholtz.Comment: 25 pages, 4 figures; final version, to appear in "Discrete Differential Geometry", Oberwolfach Seminars 38, Birkhauser, 200

Spartan Daily, March 5, 1999

Volume 112, Issue 27https://scholarworks.sjsu.edu/spartandaily/9384/thumbnail.jp

On the origin of the family

We present a game theoretic model to explain why people form life long monogamous families. Three components are essential in our framework, paternal investment, fatherhood uncertainty, and, perhaps the most distinctive feature of all, the overlap of children of different ages. When all three conditions are present, monogamy is the most efficient form of sexual organization in the sense that it yields greater survivorship than serial monogamy, group marriage, and polygyny. Monogamy is also the only configuration that fosters altruistic ties among siblings. Finally, our result sheds light to the understanding of why most religions center around the monogamous fidelity family