Triangles of Numbers
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Home > Art, Film & Photography > Triangles of Numbers: Binomial Coefficient, Lah Number, Pascal's Triangle, Pascal's Pyramid, Bell Number, Stirling Numbers of the Second Kind
Triangles of Numbers: Binomial Coefficient, Lah Number, Pascal's Triangle, Pascal's Pyramid, Bell Number, Stirling Numbers of the Second Kind

Triangles of Numbers: Binomial Coefficient, Lah Number, Pascal's Triangle, Pascal's Pyramid, Bell Number, Stirling Numbers of the Second Kind


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 33. Chapters: Binomial coefficient, Lah number, Pascal's triangle, Pascal's pyramid, Bell number, Stirling numbers of the second kind, Stirling numbers of the first kind, Pascal matrix, Eulerian number, Pascal's simplex, Singmaster's conjecture, Rencontres numbers, Narayana number, Lozanic's triangle, Gilbreath's conjecture, Boustrophedon transform, Leibniz harmonic triangle, Hosoya's triangle, Triangular array, Floyd's triangle. Excerpt: In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written, and it is the coefficient of the x term in the polynomial expansion of the binomial power (1 + x). Arranging binomial coefficients into rows for successive values of n, and in which k ranges from 0 to n, gives a triangular array called Pascal's triangle. This family of numbers also arises in many other areas than algebra, notably in combinatorics. For any set containing n elements, the number of distinct k-element subsets of it that can be formed (the k-combinations of its elements) is given by the binomial coefficient . Therefore is often read as "n choose k." The properties of binomial coefficients have led to extending the meaning of the symbol beyond the basic case where n and k are nonnegative integers with; such expressions are then still called binomial coefficients. The notation was introduced by Andreas von Ettingshausen in 1826, although the numbers were already known centuries before that (see Pascal's triangle). The earliest known detailed discussion of binomial coefficients is in a tenth-century commentary, due to Halayudha, on an ancient Hindu classic, Pingala's chandaḥśāstra. In about 1150, the Hindu mathematician Bhaskaracharya gave a very clear ex...


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Product Details
  • ISBN-13: 9781155813516
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 34
  • Spine Width: 2 mm
  • Weight: 82 gr
  • ISBN-10: 1155813510
  • Publisher Date: 25 Jun 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Binomial Coefficient, Lah Number, Pascal's Triangle, Pascal's Pyramid, Bell Number, Stirling Numbers of the Second Kind
  • Width: 189 mm


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