Extended binomial coefficients and the Pascal triangle

• Main Authors: Ting, Gwendalene B., Velasco, Faye Charmaine C.
• Format: text
• Language: English
• Published: Animo Repository 2000
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/17006
• Institution: De La Salle University

This thesis is an exposition of the articles Relating Geometry and Algebra in the Pascal Triangle, Hexagon, Tetrahedron, and Cuboctahedron Part I: Binomial Coefficients, Extended Binomial Coefficients and Preparation for Further Work' and Part II: Geometry and Algebra in Higher Dimensions: Identifying the Pascal Cuboctahedron by Peter Hilton and Jean Pedersen which appeared in The College of Mathematics Journal in May and September 1999. It presents some geometric features of the binomial coefficients in the Pascal Triangle such as Sliding Parallelograms and the Star of David. Binomial coefficients are extended to trinomial coefficients. Noticing that the Star of David Theorem still holds, a more general formula is given. The Pascal Triangle is also extended to three dimensions resulting in the Pascal Tetrahedron. The extension of the Pascal Hexagon to one higher dimension resulted to the Pascal Cuboctahedron.