Editors' Note: Carl Barnett Allendoerfer was president of the Mathematical Association of America (1959–60) and won the Lester R. Ford Award for this article, published a few years after his presidency. (That was before the MAA had established the Allendoerfer Award for papers in Mathematics Magazine.)

Allendoerfer was an undergraduate at Haverford College, then after a stay at Oxford University as a Rhodes Scholar, he received his PhD from Princeton in 1937. He spent most of his career at the University of Washington in Seattle, where he was department chair between 1951 and 1962. He was a member of the Institute for Advanced Study in Princeton, 1948–49, and a Fulbright lecturer at the University of Cambridge, 1957–58.

A topologist by profession he also wrote several elementary textbooks, the most successful of which was Fundamentals of Freshman Mathematics (McGraw-Hill, 1959), coauthored with Cletus O. Oakley of Haverford College.

Professor Allendoerfer died in 1974.

Introduction

Since one of the most powerful methods in mathematical research is the process of generalization, it is certainly desirable that young students be introduced to this process as early as possible. The purpose of this article is to call attention to the usually untapped possibilities for generalizing theorems on the triangle to theorems about the tetrahedron. Some of these, of course, do appear in our textbooks on solid geometry; but here I shall describe two situations where the appropriate generalizations seem to be generally unknown.