Tuesday, February 24, 2009
Pythagoras was a Greek mathematician a long time ago. Some people say he is just a made of mathematician made up by people who are considered the "Pythagoreans".
These are the four artifacts that link together. The reason these artifacts are linked together, is because it all has to do with the Pythagorean Theorem.
The first artifact is a R.A.T, or also known as the Right Angle Triangle. It is called that because it has a right angle (90 degree angle) in it. The legs are the two sides of the triangle that make up the right angle. Those legs are the legs that go horizontal, or vertical, but that is only in this picture, it is not always horizontal/vertical. That little square verifies that the triangle is a R.A.T. Both legs are often known as "A" or "B".
Wondering where "C" is? Leg C is the leg that is usually "unknown". In this artifact, it is the one that goes diagonally. There's a special name for this leg, and it is called the hypotenuse. There are two important things you must know about the hypotenuse: It is always the longest side of the triangle, and it is always on the opposite side of the right angle (little square). Well that's enough for the R.A.T.
The second artifact is a carved stone statue of the Greek mathematician, Pythagoras! He is the one who came up with this whole theorem. Still, no one knows if he was real or not..
The third artifact is a square. It's a simple square, but you're probably wondering why there are lines all around it. Well, those lines are called Lines of Symmetry. Those indicate that all the sides of the square are equal. Also, a square is 360 degrees all the way around, because it has four 90 degree angles in each corner.
Finally, the last artifact is a formula. This formula was created by Pythagoras himself, it was his method to find the hypotenuse of a R.A.T. You will need to substitute "a" and "b" with the numbers on the triangle you are going to solve.
We should care right now about this Pythagoras dude because what we are learning right now will be used later on in our future lives!
This is one problem for example. It is asking us to find the base of the triangle. To start this off, lets find the formula to solve this problem.
√36 = B
Alright, now that solved half of the triangle, but that does not give us the base because it is only half. If it is half of it, we need to double it.
So the length of the base is 12mm long.
Now this is a word problem, it starts with words, so it must be answered with words.
The length of the diagonal of a small square is _4.2cm_
Let C = length
The length of the diagonal of the board is _11cm_
Here is a video to help you understand :