Pythagoras Research Paper

Pythagoras was the ancient Greek philosopher and mathematician who lived in the sixth century B.C. In mathematics, the Pythagorean theorem is known as a fundamental relation in Euclidean geometry among the three sides of a right triangle. This theorem was named after him. For example, a right triangle is a triangle with a right angle; square corners adjacent sides also called square corners of the triangle beside it; hypotenuse is the side opposite the right angle. In the figure below, a and b are adjacent sides (square corners), c is the hypotenuse:
Pythagoras theorem stated his name in the plane geometry view via the purple square area (c) with a total area of red square (b) and blue (a).
Also, we have a reversed of Pythagorean theorem statement is for three positive real numbers a, b, and c, which satisfies a2 + b2 = c2, exists a triangle whose sides are a, b and c, and the angle between a and b is a square …show more content…
In the plane, the distance between two points (x1, y1) and (x2, y2) is given by the Pythagorean theorem as follows d=√((x_2-x_1 )^2+(y_2-y_1 )^2 ). In three-dimensional Euclidean space, the distance between two points (x1, y1, z1) and (x2, y2, z2) is d=√((x_2-x_1 )^2+(y_2-y_1 )^2+(z_2-z_1 )^2 ). In general, the distance between two points x, y in space with n-dimensional Euclidean R is calculated as follows d = |x - y| = √(∑_(i=1)^n▒|x_i-y_i |^2 ). For example, let A (0, 3) and B (4, 6) are two points, and AB is a distance between two points. So, we have d = AB, x1 = 0, y1 = 3, x2 = 4 and y2 = 6. By using the distance formula, we have AB = √((4-0)^2+(6-3)^2 ) = √(4^2+3^2 ) = √(16+9) = √25=5. Instead of using Euclidean distance formula, we can use the Pythagorean theorem. Let ∆x be the change in x and ∆y be the change in y. In other word, ∆x=(x_2-x_1), ∆y=y_2-y_1. Now, we can use the Pythagorean theorem that d2 = (∆x)2 +