Relating Geometry and Algebra in the Pascal Triangle, Hexagon, Tetrahedron, and Cuboctahedron Part I: Binomial Coefficients, Extended Binomial Coefficients and Preparation for Further Work

Abstract

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsPeter HiltonPeter Hilton (marge@math.binghamton.edu) is Distinguished Professor of Mathematics Emeritus at the State University of New York at Binghamton, and Distinguished Professor of Mathematics at the University of Central Florida at Orlando. His principal research interests are in algebraic topology, homological algebra and group theory; and he has long taken a close interest in problems of mathematical education, having been Chairman of the United States Commission on Mathematics Instruction. He has been First Vice President of the MM. He and Jean Pedersen have published four books and over 100 articles together since they began their collaboration in 1978, and are currently writing their fifth book.Jean PedersenJean Pedersen (jpedersen@scu.edu) is a Professor of Mathematics at Santa Clara University. She began her real study of mathematics with George Pólya in 1969, visiting him and his wife, Stella, weekly at their home from then until his death in 1985. Her main mathematical interests are polyhedral geometry, number theory and combinatorics. In 1978 she was asked by the MM to arrange for Peter Hilton and George Pólya to present a special session on the teaching of mathematics. The rest (see above) is history! She is a past Governor of the Northern California section of the MM and, in 1997, she received the Section's award for Distinguished Teaching.