### Pythagoras POST

In his backpack he found

a triangle

a square

So the first thing we are going to talk about is THE TRIANGLE .

The triangle is a right angle triangle also know as the R.A.T. The sides make 90 degree which is the legs. The longer side of the triangle is the hypotneuse. You'll always find the hypotneuse across from the little square inside the triangle.

The square is next in line.....

The square is always equal. All the sides are the same. It all makes up 360 degrees.

### Pythagoras

vid 1

### Pythagaros

The first artifact is a a right angle triangle, also known as 'R.A.T'. The square in the corner is the right angle, and it's not called a right triangle because it's on the right side (in this case its not on the right!) The right angle is an angle of 90 degrees. The triangle is made up of legs: A and B, and the longest side of the triangle or the part of the triangle that is diagonal from the right angle is called the hypotenuse. The acute angles are going to be Theta and Beta. Theta and Beta are called complimentary angles because together they form a 90 degree angle.

This is a statue of Pythagoras. He is the great greek man that made the Pythgorean Theorem and many more. He was the first known westerner to say that the Earth revolves around the sun. He was the only westerner to be allowed in pyramids, only one to speak fluent Egyptian language.

**Pythagoras:** The greatest genius ever lived. He is a "uber" smart mathematician, he was a Greek geek. It wasn't for sure that he was really alive or even existed.

**Legs:** These are connected to create the right angle of the right angle triangle a.k.a sides "A" and "B". They are also smaller than the hypotenuse.**Hypotenuse:** The hypotenuse is the longest side of the right angle triangle, its the opposite side of the right angle also.**R.A.T:** stands for Right Angle Triangle.**Greek :** A person that from ancient modern Greece, also means that you lives or was born in Greece.**Theorem:** A theoretical proposition, statement, or formula, something to be proved from other formulas.

In this problem that Mr.Harbeck gave us, we had to find the base of the triangle. This picture explains how I solved 'c'.

Problem#2:

First, you need to find out how long each side of the square is. Then that will give you side "A" and "B" for the triangles since they're both the same length. Okay so, like a normal question find the length of the hypotenuse, which is 'c'. Once you have gott that you can now label the triangle and add up all the sides to find the perimeter.

### Pythagoras

-NOTE- Pay attention to the words that are PURPLE because those words are related with the artifacts found with Mr. Harbeck.

1st Artifact

This shape is called a right angle triangle, R.A.T. for short. The bottom left corner is a right angle, or a 90 degrees angle. The lines connected to it are called legs. These legs are usually labeled "A", and "B". "A" is usually the one that stands upright because it stands for altitude, and "B" is usually on the bottom because it stands for base. However, it doesn't matter, it could work either ways. The longest side of the triangle is called the hypotenuse, and labeled side "C". You could find the hypotenuse across from the right angle. The two angles connected to the hypotenuse are labeled Theta and Beta. These two angles added together equal 90 degrees. That makes those two angles called complimentary angles.

2nd Artifact

This artifact is called a square. What makes it a square is the lines of symmetry. The lines of symmetry are the lines that go through each side of a square. This indicates that all sides of the square is equal. Each corner of a square is 90 degrees angle. If you add up all of the corners you will get 360 degrees. Which means that this square is 360 degrees. If you cut this square in half from corner to corner, you will have two R.A.T.'s.

3rd Artifact

This is the pythagorean theorem. It was created by a guy named Pythagoras. I will talk more about him soon. Anyways, he came up with this equation to find the unknown side of a right angle triangle. Say we know side A, and B of a triangle. What we wanted to find out was C. All we have to do is use the pythagorean theorem. First we square side A and B. Next you add both of them up. And lastly, you find the square root of the sum on the left side, and you find the square root of the C squared on the other side. The number that your left with, should equal to side C.

4th Artifact

This is a statue of the famous Pythagoras. This is a Greek man that created the pythagorean theorem. He also came up with many other conclusions and theories. Because of this, he is often called the father of math. He figured out that the earth revolves around the sun, and the circumference of the earth. He spent a lot of time in Egypt, and he was the only westerner to be buried in a pyramid. He was also fluent in Egyptian language. Another interesting fact was that Pythagoras was a vegan. A vegan is someone that only eats non-living things.

Here are the two videos Joseph, Adrian and I made.

Thanks for reading and watching, please comment if I missed anything. Thanks and goodbye!

### Sutchai's Pythagoras Post

**Right Angle Triangle**

Square

Square

**Pythagoras**

**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:

### Scribe Post For February 26, 2009

These are my videos with Carrie and Krissia.

Part One:

### Phythagoras Post

Right Triangle:

**a²+b²=c²**

### Pythagoras

Hypotenuse - The hypotenuse is on the opposite of the right angle and is the longer side of the triangle.

Legs - Are the shorter sides of the triangle.

R.A.T. - Right Angle Triangle.

Theorem - A theorem is a demonstrated statement that has been proved or needs to be proven. Pythagoras' theorem was a² + b² = c² .

Greek - A native or citizen of Greece. and that's it for the vocabulary.

Pythagoras was a Greek who lived 2500 years ago. He was an "uber" smart mathematician. He is the one who came up with the theory of a² + b² = c². Pythagoras is important because his mathematical theories and formulas are still used today.

This shape is a right angle triangle (R.A.T.). The legs are the shorter side of the triangle (a and b). Across the right angle, is the hypotenuse. The hypotenuse is always the longest side. The hypotenuse is c. The formula for a right angle triangle is a² + b² = c². a can either be the vertical line, or the bottom line. The same goes to b.

This shape is a square and it has four right angles. The lines on the square just help you see that its equal on all sides. All together the square equals 360 degrees and to get that all you do is time 90 degrees by 4 which is 360.

You need to find out how long each side of the square is. Then that will give you side 'a' and 'b' for the triangles since they're both the same length. So then find the length of the hypotenuse, which is 'c'. After you find that out you can now label the triangle and add up all the sides to find the perimeter.

### Pythagaros

__TRIANGLE__

So this is a right triangle also known as R.A.T. It is called a right triangle because it has that little square that tells you it's 90°. Well the 90° is made by two parts of the triangle, that is θ (theta) and B (beta). Those two angles make 90° are called complementary angle. Hypotenuse is the longest side which is often called or labeled as "C". Just remember that is it across from the right angle. The two smaller sides are often labeled as "A" or "B", it doesn't matter which side it is on but now across the right angle.

__PYTHAGOREAN THEOREM__

__PYTHAGORAS__

__VOCABULARY__

Problem #1

Problem #2You need to find out how long each side of the square is. Then that will give you side "A" and "B" for the triangles since they're both the same length. Ok so, like a normal question find the length of the hypotenuse, which is 'c'. Once you have got that you can now label the triangle and add up all the sides to find the perimeter.

These are my videos with Carrie and Arielle.

### Pythagoras

Next is the Pythagorean Theorem....

My video on Pythagoras

### Pythagoras

Mr.Harbeck said that he found these artifacts that was left in his backpack. So right now I'm going to explain what these artifacts are and this vocabulary that was left on a piece of paper and how they are linked to these artifacts.

Do you know why these words are related to the artifacts? I DO ! The word legs relate to the right triangle because well you know the small square in the corner? That's the 90 degree angle. In other words its called 'A' and 'B' , which are the legs. If they can make a right triangle, they are called complimentary angles.

The word hypotenuse relate to side 'C' of the right triangle. Side 'C' is the longest side of the right triangle. It is always across from the 90 degree angle.

The next word R.A.T stands for Right Angle Triangle. It means that a triangle has a right angle (90 degree angle).

The word Greek relates to Pythagoras. Pythagoras was a greek person that was the father of math.

The word theorem relates to a formula, a² + b² = c² or a theory that can be proved.

The first artifact is a triangle. This triangle is a R.A.T (right angle triangle) because it has a 90 degree angle. You can tell if its a right triangle because of the square at the corner. This right triangle has two sides that are the legs, which are 'a' and 'b'. It also has two angles which are theta and beta. These angles create a complimentary angle because together they create a 90 degree angle. The longest side of the triangle which is 'c' is called the hypotenuse.

The second artifact is a square. To be sure it is a square, we have to put lines on each four sides because that tells us that each side are equal and that it's a square. The four sides of the square are called lines of symmetry. This square has four right angled triangles at each corner. You can also get two right triangles from one square because if you cut the square in half, you get two right angled triangles. The whole square equals to 360 degrees (4 x 90 = 360).

The third artifact is the Pythagorean Theorem. This is a formula that is related to 'a', 'b' and 'c'. In other words the 3 sides of the right triangle. Pythagoras was the one who came up with the theorem. This is a picture how we use the Pythagorean Theorem. Here is a square that is 3x3, another square that is 4x4 and another one that is 5x5. The 5x5 square is the one that was made from both 3x3 and 4x4 squares. The 5x5 square which has a square in it is the 4x4 square and the squares outside of it is the 3x3 square. So, the pythagorean theorem works because 3x3=9, 4x4=16, 5x5=25 and 9+16=25.

The last artifact is a picture of Pythagoras. He was greek and a very intelligent mathematician. Pythagoras was known has the father of math. He was the one who created the Pythagorean Theorem, a² + b² = c². Pythagoras is a vegan (vegetarian), a person that doesn't eat a live things. He was the one who discovered the circumstanes-cosmos of the earth and that the sun goes around the earth. He was into harmonics which meant that he loved music. Pythagoras thought that he could make a square into four triangles and that he could make a triangle out of 3 squares.

Video#1:

Video#2:

Video#3:

PROBLEM#1:

In this problem that Mr.Harbeck gave us, we had to find the base of the triangle. This picture explains how I solved 'c'.

Problem#2:

First, you need to find out how long each side of the square is. Then that will give you side "A" and "B" for the triangles since they're both the same length. Okay so, like a normal question find the length of the hypotenuse, which is 'c'. Once you have gott that you can now label the triangle and add up all the sides to find the perimeter.