**Mina Rees and the Funding of the Mathematical Sciences**

by Amy E. Shell-Gellasch

aa7423@usma.edu

Federal support for research in the mathematical sciences in the United States was essentially developed during the Second World War and the years immediately following. Through her work on the Applied Mathematics Panel during the war, mathematician Mina Rees (1902-1997) was instrumental in facilitating scientific research for the war effort. As Head of the Mathematical Sciences Division and Deputy Science Director of the Office of Naval Research following the war, she helped revolutionize the form and scope of federal support of scientific research, and guided much of the development of early computers. She was dedicated to creating an environment in the United States in which the sciences, and mathematics in particular, grew and flourished.

**Minimal Perimeter Triangles**

by Mark Levi

levi@math.psu.edu

Let *K* be an arbitrary closed convex curve in the plane. Of all the triangles circumscribed around *K*, let *ABC* be the one of least perimeter, and let *A*' be the point of tangency of the side *BC* with *K*. Similarly we define the tangency points *B*' and *C*'d . Then the lines *AA*' , *BB*' , and *CC*' are concurrent (i.e., they meet at a point). Moreover, the perpendiculars to the sides of the triangle at the points *A*' , *B*', and *C*' are concurrent as well. This latter property is much more general: it holds for triangles minimizing “most” other functions, such as the area, the sum of the squares of the sides, etc. I had first discovered these facts by an argument based on physics. This physical argument (along with a rigorous proof) is given in the article.

**Tangents and Subtangents Used to Calculate Areas**

by Tom M. Apostol and Mamikon A. Mnatsakanian

apostol@caltech.edu, mamikon@caltech.edu

A recent paper by the authors (*Amer. Math. Monthly*, June/July 2002) showed that subtangents can be used in practice to draw tangent lines, and it revealed that subtangents provide an unexpected connection between the tractrix and exponential curves. That paper also contains a rigorous justification of a geometric method of tangent sweeps developed by Mamikon Mnatsakanian that can be used to calculate area of many classical plane regions. This paper gives an alternate treatment for power functions, again using tangent sweeps and properties of subtangents. It finds (without calculus) the area of a parabolic segment, a hyperbolic segment, and all generalized ssegments arising from arbitrary real power functions. It also relates subtangents and the mean-value theorem for integrals.

**Problems and Solutions**

**Notes**

**Equilateral Triangles and Triangles**

by Richard P. Jerrard and John E. Wetzel

jerrard@math.uiuc.edu, j-wetzel@uiuc.

**An Easy Proof of Hurwitz’s Theorem**

by Manuel Benito and J. Javier Escribano

mbenit8@palmera.pntic.mec.es, jesbriba@boj.pntic.mec.es

**A New Short Proof of Kneser’s Conjecture**

by Joshua E. Greene

jgreene@hmc.edu

**Reviews**

**In Code: A Mathematical Journey**

by Sarah Flannery with David Flannery

Reviewed by Marion Cohen

mathwoman199436@aol.com