Pascal's triangle. Pascal's Triangle, named after French mathematician Blaise Pascal, is used in various algebraic processes, such as finding tetrahedral and triangular numbers, powers of two, exponents of 11, squares, Fibonacci sequences, combinations and polynomials. We have situations like this all of the time. Suppose that we want to find the expansion of (a + b) 11. So one-- and so I'm going to set up a triangle. Pascal's Triangle can be displayed as such: The triangle can be used to calculate the coefficients of the expansion of by taking the exponent and adding . It has a number of different uses throughout mathematics and statistics, but in the context of polynomials, specifically binomials, it is used for expanding binomials.. Properties of Pascal's triangle For example, say you are at an ice cream shop and they have 5 different ice creams. So Pascal's triangle-- so we'll start with a one at the top. Application - Combination• Pascal’s triangle can also be used to find combinations:• If there are 5 marbles in a bag, 1 red, 1blue, 1 green, 1 yellow and 1 black. We use the 5th row of Pascal’s triangle: 1 4 6 4 1 Then we have. All I have been able to find has been related to probability. For instance, when we have a group of a certain size, let's say 10, and we're looking to pick some number, say 4, we can use Pascal's Triangle to find the number of ways we can pick unique groups of 4 (in this case it's 210). Some of my students are trying to find "practical uses" for Pascal's triangle. Binomial Expansion Using Factorial Notation. Pascal’s Triangle is a triangular array of numbers where each number on the “interior” of the triangle is the sum of the two numbers directly above it. Pascal's Triangle or Khayyam Triangle or Yang Hui's Triangle or Tartaglia's Triangle and its hidden number sequence and secrets. In this post, we explore seven of these properties. https://medium.com/i-math/top-10-secrets-of-pascals-triangle-6012ba9c5e23 Practical Uses for Pascal's Triangle Date: 2/27/96 at 20:14:58 From: Andrew Cotton Subject: Help with Pascal's Triangle Hi, I teach 7th grade math. And one way to think about it is, it's a triangle where if you start it up here, at each level you're really counting the different ways that you can get to the different nodes. The triangle was actually invented by the Indians and Chinese 350 years before Pascal's time. One use of Pascal's Triangle is in its use with combinatoric questions, and in particular combinations. So if I … there are alot of information available to this topic. some secrets are yet unknown and are about to find. Expand Using Pascal's Triangle (x+3)^4. The coefficients will correspond with line of the triangle. How many different combinations can I make if I take out 2 marbles• The answer can be found in the 2nd place of row 5, which is 10. 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