### Sutchai's Pythagoras Post

Thursday, February 26, 2009
So... Harbeck fell and had amnesia and we have to help him and explain some artifacts that were left in his backpack. Luckily, he has some students that will actually HELP him. (:

Right Angle Triangle

This is a Right Angle Triangle (R.A.T.), it has legs and a hypotenuse. It is called a right angle triangle because it has a right angle in it. Do you see that little square in the corner of the triangle? That's where the right angle is located. The legs of the triangle make up the right angle. You can label these "a" or "b", it doesnt matter which side "a" or "b" goes on, as long as one is on one side of the right angle and vice versa. The hypotenuse is the longest side of the triangle, it is directly across from the right angle. It is labelled "c". It has one right angle and two other angles that make up 90 degrees. The two acute angles that make up the 90 degree angle are called "complimentry angles". They can also be called "theta" and "beta" because theta and beta make up 90 degrees. Theta and beta are located at the two acute angles.

Square
This is a square. How do we know that it's not a rectangle? Because it has lines of symetry. The lines of symetry are the lines on each side of the square. The lines of symetry indicate that all sides are equal. A sqare has four 90 degree angles. It is in each corner of the square. This whole square adds up to 360 degrees. How do we know? Because 4 x 90 degrees = 360 degrees. It has two right angled triangles in it. How do we know? Because when you cut the square in half from opposite corners, you will get two right angled triangles (R.A.T.). Also, since the triangle adds up to 180 degrees, 2 x 180 degrees = 360 degrees.

Pythagoras
This is a Greek man who figured out the "Pythagorean Theorem". He was also known as the father of math. He hung out in Egypt and he was a vegan (someone who eats only non-living things). He figured out the circumference of the earth and he also found out that the earth revolves around the sun. He figured out the cure for sick people, harmonics. Pythagoras liked to make words for a huge group of things like for all the planets and stars he made the word cosmos.

Pythagorean Theorem
This is the "Pythagorean Theorem". It was created by Pythagoras. He came up with this theorem to figure out an unknown side of a triangle. For example, when you know the sides "a" and "b", you can plug them into the theorem and multiply "a", multiply "b" and add them up together. Then, find the square root of the product and find the square root of "c" squared. Then you have what "c" equals. When you prove it using squares, it should work out if you cut out the squares to fit the "c" squared. The R.A.T. in the middle proves that it is the length of the unknown side.

Mr.Harbeck, I personally think that we should care in grade 8 math because it will be heading our way when we get to a harder level in math, and we'll need to know these things already in order to learn more advanced stuff.

Now, for the 2 problems I chose to solve.

Here's the first one:

To find the base of the triangle, first you must find out the base of one side. Then, after you find the base of one side of the triangle, double the base of that one side, and you'll get the base of the whole triangle. You have to double it because you know that both sides of the triangle are equal.

Here's the second problem:

To find the perimeter of the game board, first find the sides of the square. Then, once you know the side of the square, you'll know sides "a" and "b" on the triangle, since they're both equal. Since you know both sides "a" and "b", you have to now figure out what the hypotenuse is ("c"). Once you figure out the hypotenuse, you now know all sides of the triangle and you can add up all sides of the game board.

Here are the math videos that Michelle and I made:

1. peachy 8-41 said...

Hi Sutchai. :)
I like how you explained the triangle and how you evenly put all the information together, especially the part where the Theta and Beta are located, I had a lot of problems with that, because I couldn't explain it properly, but you did it beautifully with wonderful vocabulary. :) And by vocabulary, I mean math vocabulary! "Acute". Haha. You have more then 5 points in your square, so you get a perfect 5 marks. You explained the square well, but again, same as dean's, you could have added how to find the area and perimeter, since Harbeck was pushing us to find that a few math classes ago. But, still. It's very well done. I like how you drew how to solve the first problem on a piece of paper and took a picture of it, we all know that Harbeck is very fond with that. It's a great way to show your work because it's faster than paint, and sometimes clearer than paint. Keep up the orignality. Same with what you did in the second problem. I like how you showed the picture for the second problem, then explained how to get the answer. It was clear and well done. Good job with the math videos, you must think I say this way too often, but you explained it well and clear. I like how you drew the steps out, I do think it was a lot easier for everyone to understand. Keep up the great work Sutchai. :) Oh, but for the words that Harbeck gave us, I think you should have written them out and found the meanings? Just to make a litle clear. But it's fine. ;) The words are still in your post. Keep it up! :D
ONE mistake I found
- symerty, I think it's spelled with 2 ms, like symmerty. I'm not sure, but that's how a lot of other people spelled it. Haha