Extended binomial coefficients and the Pascal triangle
Date of Publication
2000
Document Type
Bachelor's Thesis
Degree Name
Bachelor of Science in Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Abstract/Summary
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.
Abstract Format
html
Language
English
Format
Accession Number
TU10034
Shelf Location
Archives, The Learning Commons, 12F, Henry Sy Sr. Hall
Physical Description
93 leaves
Recommended Citation
Ting, G. B., & Velasco, F. C. (2000). Extended binomial coefficients and the Pascal triangle. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/17006
