Pascal Triangle Research Paper

Real World Applications There are many real-world applications using the Pascal Triangle. The most popular is in algebra for expanding the binomial (x+y)ⁿ, where “n” is a specific exponent. Another way the triangle can be used is to calculate probability or determine the odds. The triangle is also full of interesting and functional mathematical patterns that can be used in solving a variety of other equations and figuring out numerical problems. “A polynomial equation with two terms usually joined by a plus or minus sign is called a binomial” (Russell, n.d.). Binomials are used in algebra and are most commonly represented by the letters (a, b) or (x, y). As you continue to multiply (a+b) by itself to solve the equation, mathematical

There are only two possible outcomes from a coin toss: heads or tails and the number of times you toss the coin will determine how many different combinations are possible. So, the question is “What is the probability of getting exactly two heads with only 4 coin tosses?” By looking at the 4th row of Pascal’s Triangle, the numbers are 1,4,6,4,1 and added together equal 16. The middle number is 6 so the probability is 6/16 or 37.5%. The long way to prove the answer is to write out all the possible outcomes and you can see from the chart below there are 16 possible outcomes for the 4 coin tosses and only 6 of them have exactly 2 heads which means the probability is 6/16 or 37.5% (Pascal’s Triangle,

It is surprising to see how the numbers in the triangle can be used logically in a variety of ways. Although expanding binomial coefficients is the most common mathematical use for Pascal’s Triangle, it has other applications. For example, calculating probability could take a long time to process by hand, but using the triangle can give a quicker result. There are also several mathematical patterns that are hidden within Pascal’s Triangle which include: diagonals, horizontals, exponents of 11 and squares. All of which explain an easier way of figuring out the same concept. The invention of Pascal’s Triangle changed the way individuals view math and paved the way for many others to challenge math and take it to the next level and for the mathematicians and scientists to create new theorems from their hard work. Math and mathematical concepts are all around and are all connected in some way. The same goes for Pascal’s Triangle as it is directly related the Fibonacci Sequence, the Golden Ratio and Sierpinski’s Triangle. Each explains a different topic, but when they overlap, that’s when math can really grab your