Book Description
This survey explores the history of the arithmetical triangle, from its roots in Pythagorean arithmetic, Hindu combinatorics, and Arabic algebra to its influence on Newton and Leibniz as well as modern-day mathematicians.
Author : A.W.F. Edwards
Publisher : Courier Dover Publications
Page : 227 pages
File Size : 17,44 MB
Release : 2019-06-12
Category : Mathematics
ISBN : 048684076X
This survey explores the history of the arithmetical triangle, from its roots in Pythagorean arithmetic, Hindu combinatorics, and Arabic algebra to its influence on Newton and Leibniz as well as modern-day mathematicians.
Author : A. W. F. Edwards
Publisher : JHU Press
Page : 228 pages
File Size : 46,67 MB
Release : 2002-07-23
Category : Mathematics
ISBN : 9780801869464
"A fascinating book... giving new insights into the early history of probability theory and combinatorics, and incidentally providing much stimulating material for teachers of mathematics." -- International Statistical Institute Review
Author : Thomas M. Green
Publisher : Dale Seymour Publication
Page : 278 pages
File Size : 13,10 MB
Release : 1986-01
Category : Mathematics
ISBN : 9780866513067
Pascal's triangle and where to find it - Number patterns within Pascal's triangle - Figurate numbers and Pascal's triangle - Higher dimensional figurate numbers - Counting problems.
Author : Thomas M. Green
Publisher : CreateSpace
Page : 176 pages
File Size : 34,73 MB
Release : 2015-07-25
Category :
ISBN : 9781514677094
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 [email protected] for information on qualifying for a discount code to use before ordering.
Author : Brian Hopkins
Publisher : MAA
Page : 342 pages
File Size : 12,8 MB
Release : 2009
Category : Computers
ISBN : 9780883851845
Hopkins collects the work of 35 instructors who share their innovations and insights about teaching discrete mathematics at the high school and college level. The book's 9 classroom-tested projects, including building a geodesic dome, come with student handouts, solutions, and notes for the instructor. The 11 history modules presented draw on original sources, such as Pascal's "Treatise on the Arithmetical Triangle," allowing students to explore topics in their original contexts. Three articles address extensions of standard discrete mathematics content. Two other articles explore pedagogy specifically related to discrete mathematics courses: adapting a group discovery method to larger classes, and using logic in encouraging students to construct proofs.
Author : K. Ramasubramanian
Publisher : Springer Nature
Page : 639 pages
File Size : 20,54 MB
Release : 2019-11-08
Category : Mathematics
ISBN : 981131229X
This book includes 58 selected articles that highlight the major contributions of Professor Radha Charan Gupta—a doyen of history of mathematics—written on a variety of important topics pertaining to mathematics and astronomy in India. It is divided into ten parts. Part I presents three articles offering an overview of Professor Gupta’s oeuvre. The four articles in Part II convey the importance of studies in the history of mathematics. Parts III–VII constituting 33 articles, feature a number of articles on a variety of topics, such as geometry, trigonometry, algebra, combinatorics and spherical trigonometry, which not only reveal the breadth and depth of Professor Gupta’s work, but also highlight his deep commitment to the promotion of studies in the history of mathematics. The ten articles of part VIII, present interesting bibliographical sketches of a few veteran historians of mathematics and astronomy in India. Part IX examines the dissemination of mathematical knowledge across different civilisations. The last part presents an up-to-date bibliography of Gupta’s work. It also includes a tribute to him in Sanskrit composed in eight verses.
Author : Matthew L. Jones
Publisher : University of Chicago Press
Page : 404 pages
File Size : 41,80 MB
Release : 2008-09-15
Category : Science
ISBN : 0226409562
Amid the unrest, dislocation, and uncertainty of seventeenth-century Europe, readers seeking consolation and assurance turned to philosophical and scientific books that offered ways of conquering fears and training the mind—guidance for living a good life. The Good Life in the Scientific Revolution presents a triptych showing how three key early modern scientists, René Descartes, Blaise Pascal, and Gottfried Leibniz, envisioned their new work as useful for cultivating virtue and for pursuing a good life. Their scientific and philosophical innovations stemmed in part from their understanding of mathematics and science as cognitive and spiritual exercises that could create a truer mental and spiritual nobility. In portraying the rich contexts surrounding Descartes’ geometry, Pascal’s arithmetical triangle, and Leibniz’s calculus, Matthew L. Jones argues that this drive for moral therapeutics guided important developments of early modern philosophy and the Scientific Revolution.
Author : Walter William Rouse Ball
Publisher :
Page : 576 pages
File Size : 30,33 MB
Release : 1908
Category : Mathematicians
ISBN :
Author : Isaac Todhunter
Publisher :
Page : 338 pages
File Size : 13,60 MB
Release : 1865
Category : Probabilities
ISBN :
Author : Keith Devlin
Publisher :
Page : 210 pages
File Size : 26,25 MB
Release : 2010-03-23
Category : Mathematics
ISBN : 0465018963
Before the mid-seventeenth century, scholars generally agreed that it was impossible to predict something by calculating mathematical outcomes. One simply could not put a numerical value on the likelihood that a particular event would occur. Even the outcome of something as simple as a dice roll or the likelihood of showers instead of sunshine was thought to lie in the realm of pure, unknowable chance. The issue remained intractable until Blaise Pascal wrote to Pierre de Fermat in 1654, outlining a solution to the "unfinished game" problem: how do you divide the pot when players are forced to.