Pascal's Triangle From Top To Bottom - the binomial coefficient website


	Your one-stop place to shop on the Web for all your binomial coefficient needs^®

				Our Mission
			Terms, Symbols and FAQ		History
		Applications and Applets		Identities and Proofs		Modern Algorithms
	Reliable Sources		Other Websites		Contributors		Page Statistics
Stuff for High School Students		Stuff for High School Teachers		The Bottom? (e-mail us)		Stuff for Grad School Students		Recent Research

The pattern of numbers shown in the picture above has been studied for over 2,000 years by people all over the world. They are invaluable in the mathematical field of combinatorics, which is a fancy way of saying counting things. They are called the binomial coefficients because they are the numbers multiplying terms of the expansion of the binomial (a+b)ⁿ, which is a cornerstone of the study of algebra. The patterns and inter-relationships among the numbers fascinated people in ancient times, and are still essential today to the study of fields as modern as computer science.

This website has as its goal to be as comprehensive a resource as possible for anyone wanting to study any aspect of Pascal's Triangle. Much of the information here can be understood by students in high school, and can be a good resource for their teachers as well, but we also want to be of service to graduate students and working mathematicians looking for information about more esoteric aspects of this much studied set of numbers.

Major text sources for this website

Title	Author(s)	Publisher	Source for:
A=B (available in print and online)	Petkovšek, Wilf, Zeilberger	A.K. Peters	Algorithms
Concrete Mathematics	Graham, Knuth, Patashnik	Addison Wesley	Proofs
Enumerative Combinatorics	Richard Stanley	Cambridge University Press	Proofs
Pascal's Arithmetical Triangle	A.W.F. Edwards	Johns Hopkins Univ. Press	History
Proofs That Really Count	Benjamin and Quinn	Math. Assoc. of America	Proofs
Proofs Without Words	Roger B. Nelsen	Math. Assoc. of America	Proofs

We thank the authors and publishers of these works, most especially Johns Hopkins University Press and the MAA for kindly allowing us to reproduce artwork from the books by Edwards and Nelsen, respectively. All the books were also invaluable in our never-ending search for identities.

Other cool websites

Encyclopedia of Integer Sequences	Mathforum: Pascal's Triangle	Wolfram's World of Mathematics
MacTutor History of Mathematics	Pascal's original Treatise online	Math Words
	Knot in the Braid

Credits and Contributors

Website Designed, Programmed and Researched by:
Matthew Hubbard and Tom Roby
Logo by: Matthew Hubbard and Jodi Soares

Special thanks to:
Theo Dordea
Gagan Sekhon
Dan Jurca
Massoud Malek
Victor Manjarrez
Russ Merris
Stuart P. Smith
Jodi Soares
Art Velasquez
Kevin McGrath
Isaiah Lankham

Ten Most Recent Contributors:
Ron Ozer
Bill Everett
Angel Plaza
Bo Brinkman
Jonathan Burns
Martin P. Getz
Pieter H. Van Der Kamp
Sebastián Martín Ruiz
Gottfried Helms
Nina Horne

List of All Contributors

Page Statistics

Category	Number	Updated
Identities	200	01.01.08
Proofs	29	11.18.07
Hints	36	01.01.08
Applets	8	09.16.05
Number of times the author of this page has written or typed the first few rows of Pascal's Triangle	1300	01.01.08

The Google^TM Matrix the position for this website when Googling different combinations of text Date of last Google test: 01.01.08 Some positions are from Tom Roby's mirror site at the University of Connecticut (Thanks, Tom!)
combining text at top of column to the right with text at beginning of the row below	Pascal's Triangle	binomial coefficient	binomial coefficients
(blank)	9 (up from 15)	14 (down from 12)	14 (down from 13)
Identities	1	1	1
History	10	1 (up from 4)	2 (up from 8)