The Simplex, Duplex and Pascal's Triangles: Relatives of Pascal's Triangle, With Excursions Into Hyperspace

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9781514677094: The Simplex, Duplex and Pascal's Triangles: Relatives of Pascal's Triangle, With Excursions Into Hyperspace

Prepare to be intrigued by the many facets of
the properties of the amazing array of numbers
known as Pascal's Triangle and its many relatives.
Some of the topics you will find:

  • Polytopes
  • Simplexes and the Simplex Triangle
  • Tetrahedral, and higher dimensional figurate numbers
  • Duplexes and The Duplex Triangle
  • Geometric Duplication - Cubes and Hypercubes
  • Vandermonde's Identity for the Duplex Triangle
    and the Triplex Triangle
  • Euler's formula for Simplexes and Duplexes
  • Recurrent Sequences in Pascal's Triangle and its Relatives
    Including the Fibonacci, Pell and Jacobsthal Sequences
  • Pythagorean Triples - Related to the Sequences Listed Above
  • Properties Involving String Products
  • and more.

There is a comprehensive index that will allow readers to easily search for topics of their interest.

One goal is to provide a vehicle to the discovery of some higher mathematics related to higher dimensional geometric figures, at an entry level for the young beginning researcher by including many exercises that ask for verification of a pattern by testing specific cases and conjecturing a generalization of the pattern.

Another major goal was to make available source materials for mathematics teachers to use in their classes. Included are many topics suitable for introducing students, at the pre-college level, to the sense of satisfaction one receives while exploring and discovering significant parts of advanced mathematics.

I hope you will enjoy exploring this amazing Arithmetic Triangle and its relatives as much as I have. There is still much more to be discovered, of that I am certain.

Teachers and students are eligible for special discounts for purchases of this book. Send an email to tgreen0001@gmail.com for information on qualifying for a discount code to use before ordering.

"synopsis" may belong to another edition of this title.

About the Author:

Thomas M. Green was born in New York State, raised in Pennsylvania, Texas, and California.
He received his Master's Degree in Mathematics in 1962 from California State University, Long Beach. He did post-graduate study at Stanford University in the late 1960's and early 1970's as a fellow in two different National Science Foundation projects in Mathematics and Computer Science.
He has authored or co-authored several mathematical papers, textbooks, the book Pascal's Triangle and Pascal's Triangle, 2nd Ed. (with Charles L. Hamberg), and Texas Hold 'Em Poker Textbook.
Tom is now professor emeritus of Mathematics at Contra Costa College. He lives in California with his wife Sandra.

Also, by this author:

Pascal's Triangle, 2nd Ed.
https://www.createspace.com/3626370
or
http://www.amazon.com/Pascals-Triangle-2nd-Thomas-Green/dp/1479289841/
Texas Hold 'Em Poker Textbook https://www.createspace.com/3486256
or
http://www.amazon.com/Texas-Hold-Em-Poker-Textbook/dp/1453839348/

"About this title" may belong to another edition of this title.

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Book Description Createspace, United States, 2015. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****. Prepare to be intrigued by the many facets of the properties of the amazing array of numbers known as Pascal s Triangle and its many relatives. Some of the topics you will find: Polytopes Simplexes and the Simplex Triangle Tetrahedral, and higher dimensional figurate numbers Duplexes and The Duplex Triangle Geometric Duplication - Cubes and Hypercubes Vandermonde s Identity for the Duplex Triangle and the Triplex Triangle Euler s formula for Simplexes and Duplexes Recurrent Sequences in Pascal s Triangle and its Relatives Including the Fibonacci, Pell and Jacobsthal Sequences Pythagorean Triples - Related to the Sequences Listed Above Properties Involving String Products and more. There is a comprehensive index that will allow readers to easily search for topics of their interest. One goal is to provide a vehicle to the discovery of some higher mathematics related to higher dimensional geometric figures, at an entry level for the young beginning researcher by including many exercises that ask for verification of a pattern by testing specific cases and conjecturing a generalization of the pattern. Another major goal was to make available source materials for mathematics teachers to use in their classes. Included are many topics suitable for introducing students, at the pre-college level, to the sense of satisfaction one receives while exploring and discovering significant parts of advanced mathematics. I hope you will enjoy exploring this amazing Arithmetic Triangle and its relatives as much as I have. There is still much more to be discovered, of that I am certain. Teachers and students are eligible for special discounts for purchases of this book. Send an email to for information on qualifying for a discount code to use before ordering. Bookseller Inventory # APC9781514677094

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Thomas M Green
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Book Description Createspace, United States, 2015. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****.Prepare to be intrigued by the many facets of the properties of the amazing array of numbers known as Pascal s Triangle and its many relatives. Some of the topics you will find: Polytopes Simplexes and the Simplex Triangle Tetrahedral, and higher dimensional figurate numbers Duplexes and The Duplex Triangle Geometric Duplication - Cubes and Hypercubes Vandermonde s Identity for the Duplex Triangle and the Triplex Triangle Euler s formula for Simplexes and Duplexes Recurrent Sequences in Pascal s Triangle and its Relatives Including the Fibonacci, Pell and Jacobsthal Sequences Pythagorean Triples - Related to the Sequences Listed Above Properties Involving String Products and more. There is a comprehensive index that will allow readers to easily search for topics of their interest. One goal is to provide a vehicle to the discovery of some higher mathematics related to higher dimensional geometric figures, at an entry level for the young beginning researcher by including many exercises that ask for verification of a pattern by testing specific cases and conjecturing a generalization of the pattern. Another major goal was to make available source materials for mathematics teachers to use in their classes. Included are many topics suitable for introducing students, at the pre-college level, to the sense of satisfaction one receives while exploring and discovering significant parts of advanced mathematics. I hope you will enjoy exploring this amazing Arithmetic Triangle and its relatives as much as I have. There is still much more to be discovered, of that I am certain. Teachers and students are eligible for special discounts for purchases of this book. Send an email to for information on qualifying for a discount code to use before ordering. Bookseller Inventory # APC9781514677094

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Book Description CreateSpace Independent Publishing Platform. Paperback. Book Condition: New. This item is printed on demand. 176 pages. Dimensions: 11.0in. x 8.5in. x 0.4in.Prepare to be intrigued by the many facets of the properties of the amazing array of numbers known as Pascals Triangle and its many relatives. Some of the topics you will find: Polytopes Simplexes and the Simplex Triangle Tetrahedral, and higher dimensional figurate numbers Duplexes and The Duplex Triangle Geometric Duplication - Cubes and Hypercubes Vandermondes Identity for the Duplex Triangle and the Triplex Triangle Eulers formula for Simplexes and Duplexes Recurrent Sequences in Pascals Triangle and its Relatives Properties Involving String Products Pythagorean Triples and more. There is a comprehensive index that will allow readers to easily search for topics of their interest. One goal is to provide a vehicle to the discovery of some higher mathematics related to higher dimensional geometric figures, at an entry level for the young beginning researcher by including many exercises that ask for verification of a pattern by testing specific cases and conjecturing a generalization of the pattern. Another major goal was to make available source materials for mathematics teachers to use in their classes. Included are many topics suitable for introducing students, at the pre-college level, to the sense of satisfaction one receives while exploring and discovering significant parts of advanced mathematics. I hope you will enjoy exploring this amazing Arithmetic Triangle and its relatives as much as I have. There is still much more to be discovered, of that I am certain. Teachers and students are eligible for special discounts for purchases of this book. Send an email to tgreen0001gmail. com for information on qualifying for a discount code to use before ordering. This item ships from La Vergne,TN. Paperback. Bookseller Inventory # 9781514677094

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