# The Importance Of Patterns In Mathematics

The Pascal’s triangle in the mathematical word is a simple representation of numbers in an array and is a binomial coefficient. The Pascal’s theorem is said to be discovered by Bailey Pascal. Whereas historians

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Then we set the numbers accordingly. The corresponding number in the triangle is the value of the above added numbers, but keep in mind we do not do anything to the ones at the edges. Therefore in the below Pascal’s triangle we add the values of row one and we get two. (1+1=2)

As said earlier that it makes life easier for mathematicians in today’s world. The Pascal’s triangle is used in two major areas in math. They are Algebra and Probability.

Algebra

In this case let us say we use a polynomial x+2, and if we want to raise it to some powers like 1, 2,3,4,5 and so on.

Here is a chart below to have an idea. (x+2)^0 = 1 (x+2)^1 = x + 2 (x+2)^2 = x^2 + 4x + 4 (x+2)^3 = x^3 + 6x^2 + 12x + 8 (x+2)^4 = x^4 + 8x^3 + 24x^2 + 32x + 16 (x+2)^5 = x^5 + 10x^4 + 40x^3 + 80x^2 + 80x +

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6C2= 6!/(6-2)!.(2!) = 6.5.4.3.2.1/ (4.3.2.1) (2.1) =15 (does not match with the equation answer) 7C2=7!/(7-2)!.(2!) = 7.6.5.4.3.2.1/ (5.4.3.2.1) (2.1) = 21(does not match with the equation answer)

In this case only two match 6C0 and 7C0

Henceforth both the binomial theorem answers do not match to the quadratic equation answer.

Let us look at the Cubic line- On the calculator press the stat button and under edit press 1. Plug in all the numbers in L1 and L2, which will look like Again press stats and go to calc and press 6 for (CubicReg). This will take you to an open window and we press 2nd 1, 2nd 2 and then press VARS on the right side of the calculator. Click on Y- VARS- 1-1. You will get something like this. After this press enter and we will get our result.

Equation= -0.0011x^3+.094x^2+1.196x-0.3342

To find the X values we use the Quadratic formula x=(-b±√(b^2-4ac))/2a x=-0.094±√(〖0.094〗^2-4(-0.0011)(1.196) )/2(-0.00111) x= -11.142 Henceforth plugging in