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6 days ago · The hockey stick identity gets its name by how it is represented in Pascal's triangle. In Pascal's triangle, the sum of the elements in a diagonal line starting with \(1\) is equal to the next element down diagonally in the opposite direction.
3 days ago · The Fibonacci numbers are the sums of the diagonals (shown in red) of a left-justified Pascal's triangle. The Fibonacci numbers occur as the sums of binomial coefficients in the "shallow" diagonals of Pascal's triangle:
5 days ago · Given an integer n >= 0, generate the length n+1 row vector representing the n-th row of Pascal's Triangle. Examples: pascalTri(0) ans =. 1. pascalTri(1) ans =. 1 1.
5 days ago · Stirling numbers of the first kind appear in the formula for Gregory coefficients and in a finite sum identity involving Bell number n ! G n = ∑ l = 0 n s ( n , l ) l + 1 {\displaystyle n!G_{n}=\sum _{l=0}^{n}{\frac {s(n,l)}{l+1}}}
2 days ago · Application. If we have a quadratic polynomial in the form ax^2 + bx + c , ax2 +bx+c, then we can use the formula x = \frac { - b \pm \sqrt { b^2 - 4ac } } { 2a} x = 2a−b± b2−4ac to find when it equals zero. (Note the plus-or-minus means there are two solutions, not just one.)
4 days ago · Commissioners' Plan of 1811. The Commissioners' Plan of 1811 was the original design for the streets of Manhattan above Houston Street and below 155th Street, which put in place the rectangular grid plan of streets and lots that has defined Manhattan on its march uptown until the current day.
5 days ago · You are currently signed in to your district account. Lou Frey Institute
