A famous use of Pascal's triangle is in the Binomial Expansion, themultiplication and simplification of brackets. Less well known, however, is thereason why this intriguing link between these two seemingly unrelated areas ofmathematics actua...英国华人论坛
One of the most famous patterns that can be found in Pascal's triangle isthe triangle numbers, which can be found in the diagonals of Pascal's Triangle.In this article, I explain in a variety of different ways what triangle numbersare, as we...英国华人论坛
Pascal's tetrahedron or Pascal's pyramid is an extension of the ideas fromPascal's triangle. Many of the properties of Pascal's triangle can be applied(with a little modification) to Pascal's Pyramid. However, in this article, Idiscuss only...英国华人论坛
Expanding brackets can be a nightmare; even something like (a+b)^4 can takeages to multiply out and simplify. In this article, I explain how Pascal'striangle can come to the rescue by helping to expand powers of (a+b) as high as(a+b)^10 in a...英国华人论坛
Of all the patterns and discoveries Blaise Pascal made from examiningPascal's triangle, it was perhaps its link with probability that made thetriangle so interesting to him and other mathematicians of his time. In thisarticle, I discuss how...英国华人论坛
Pascal's trianglecontains a vast range of patterns, including square, triangle and fibonaccinumbers, as well as many less well known sequences. In this article, however, Iexplain first what pattern can be seen by taking the sums of the row i...英国华人论坛
Aninteresting property of Pascal's triangle is that the rows are the powers of11. I have explained exactly where the powers of 11 can be found, including howto interpret rows with two digit numbers. Later in the article, an informalproof of...英国华人论坛