The Pythagorean Theorem

The Pythagorean theorem is named after the Greek mathematician Pythagoras (ca. 570 BC—ca. 495 BC), who discovered the Pythagorean Theorem and its proof.m. There is evidence that Babylonian mathematicians understood the formula, but there lack of evidence that they used it at the times.

The Pythagorean theorem is often used to find the measures of the sides of a right triangle. It works the following way. Picture a right triangle, the side that is opposite from the right angle is know as the hypotenuse. The two sides left are known as the legs.

According to the book "A Problem Solving Approach to Mathematics for Elementary School Teachers," "interpreted in terms of area, the Pythagorean theorem states that the area of a square with the hypotenuse of a right triangle as a side is equal to the sum of the areas of the squares with the legs as sides."

The formula for the Pythagorean theorem as stated above is

Lets perform the following. Let  a=24 b=18, we must find the hypotenuse or c^2.

So, 18^2 + 24^2 = c^2
     324 + 576 = c^2
        900 = c^2
       √900 = 30

c=30


Pick's theorem

Today I have a little trick theorem for you guys. Have you ever bumped into a "weird" shape and have gotten stuck trying to find the area of the shape? Well if you have I will show you how to get rid of these problem. Pick's theorem gives an a very accurate approximation of the area of a bizarre shape.

Formula:
             A = B/2 + I - 1            (B: border Points, I: interior points)

Note: This theorem can only be performed if the shape is shown on either a geoboard or a dotted paper because is the only way to find the interior angles.