Web Reference: Pascal's triangle can be constructed easily by just adding the pair of successive numbers in the preceding lines and writing them in the new line. Pascals triangle or Pascal's triangle is shown in the image below. Here, we can see that any number is the sum of the two numbers just above that number. To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern. Each number is the numbers directly above it added together. (Here I have highlighted that 1+3 = 4) Let's build the first few rows: Try this yourself and see how far you can go. Due to its simple construction by factorials, a very basic representation of Pascal's triangle in terms of the matrix exponential can be given: Pascal's triangle is the exponential of the matrix which has the sequence 1, 2, 3, 4, ... on its sub-diagonal and zero everywhere else.
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