### Pythagoras POST

Friday, February 27, 2009
Well..... harbeck sort of fell on his head and he can't remember a thing...

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

Well Mr harbeck fell and hit his head and now he has amnesia. all he was going to teach us is gone and all he has is a few artifacts that he found in his backpack so i will try and help him remember by explaining all the diffrent artifacts and how they are connected.

well this is on of the artifacts he found, it is a statue of Pythagoras. Pythagoras was a great mathematician many years ago he created the Pythagorean theoem. he also had many other mathematical theories and that is why he is reffred to as the Father of math. Pythagoras was greek man who lived to the age of 100(really really old for people back then) and he was a vegitarien, no meat of meat related products.

this is a 90* degree angle, there is a box in the corner of the triangle to show that it is a right or 90* angle. it has 2 legs commonly labled A and B. A and B switch some times. then the longest side that is facing outward is refered to as the hypotenuse.

this is Pythagorean theoem that pythagoras invented or you can think of it as more of a discovery and less as an invention. squared=~
that theoem states that A~ +B~=C~
so imagin a big square and then fill that square with blue blocks but leave 9 spaces around the edge of the square then fill those 9 spaces with red blocks. the red is A and the blue is B and the big square is C.

now this is the last artifact that was in Mr Harbecks backpack it is a perfect square. the way you can tell it is perfect is because of those small line on the side of the faces of the square. the lines means all sides are equal, that makes it a prefect square

that is my explination on Mr Harbecks artifacts

vid 1

### Pythagaros

Thursday, February 26, 2009

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 second artifact is a square, this is a special type of rectangle. A square has 4 equal sides. Those 4 equal sides are called lines of symmetry. A square is made up of 90° angles, one at each corner. So the square makes 360°because 4 x 90° = 360°. In this picture, there are 2 right angle triangles.

This third artifact is the Phythagorean Theoem. This means that, if you know side "a" and side "b", then all you do is square them. So, you have to add them together, which leaves you the c" squared. Then find the squar root of the answer from your calculator, that will give you the length of side "c".

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.

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.

### Pythagoras

Apparently, Mr. Harbeck slipped on ice and bumped his head. Trust me, it happens everywhere in the winters of Winterpeg. That accident has caused him to have amnesia. Now, as a class, he needs us to explain the artifacts he found in his backpack.

-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.

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

### Sutchai's Pythagoras Post

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:

### Scribe Post For February 26, 2009

Today we worked on our math videos for our Pythagoras blogposts.

These are my videos with Carrie and Krissia.

Part One:

Part Two:

The next scribe is ............. SUTCHAAI ! (: Good luck and have fun doing the next scribe ;)

### Phythagoras Post

Surprisingly, Mr. Harbeck fell and bumped his head on the floor. Now, he can't remember anything so he asks us to find out what these artifacts are to help him remember.

Right Triangle:

This is the right triangle. The sides that make up the 90 degree angle are called legs. The legs are labelled A and B. The hypotenuse is the C, and is the longest side of the triangle. You can always find it across from the 90 degree angle. Theta and Beta show at the top corner and the bottom corner of a right triangle. The top one is the Theta and the bottom one is the Beta. Complementry angles arPhye formed by Theta and Beta because Theta and Beta equals 90 degrees.

Square:

This is a square, which means that all sides are equal. There are four 90 degree angles in the shape which equals to 360 degrees. You can always find the area or perimeter of the square if you know the measurement of one side. If you know the measurement of one side, then you know the measurement of all sides because all sides of a square are equal. In this picture, one side is 5, so we know that all sides equal 5. 5x5 , which is LxW. The area is 25.

Phythagoras:

Phythagoras is the man who made the phythagorean theorem. Phythagoras was often called the Father of Math. He is a Vegan, someone who doesn't eat things that are alive. He loves Music just like how he loves Math. He believed that he could make a square out of four right triangle angles and that he could make a triangle out of three squares. Phythagoras was the person who discovered the circumfurance of the world.

Phythagorean Theorem:
a²+b²=c²

This is the Pythagorean Theorem. Pythagoras came up with the theorem to find out the length of a side of a right angle triangle. The theorem means is that, if you know side a and side b of a right triangle, all you do is square them. After that, you will need to add them together which will leave you with side c squared. Find the square root of the answer and that will give you the length of side c, the hypotenuse.
Heres the problem that Mr. Harbeck told us to use use for our post:

### Pythagoras

Vocabulary:
Hypotenuse - The hypot
enuse 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.

Theor
em - 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.

SQUARE

This is a special type of rectangle. A square has 4 equal sides. You can tell that it has 4 equal sides because it has those lines on the sides(lines of symmetry). A square is made up of four 90° angles, one at each corner. The whole square makes 360° because of the four 90° angles. In this square, there are 2 right angle triangles. You know this because if you cut a line from one corner to the opposite corner and it'll make the 2 R.A.Ts.

PYTHAGOREAN THEOREM
This is the Pythagorean Theorem. The length of a side of a right angle triangle. Well what the theorem means is that, if you know side "a" and side "b", then all you do is square them. From there, you will need to add them together, which will leave you with side "c" squared. Find the square root of the answer and that will give you the length of side "c".

PYTHAGORAS
-father of math
-hung out in Egypt
-harmonics
-vegan
-cosmos
-circumference of the Earth
-universe Earth around the sun

VOCABULARY
Legs: make the right angle. Legs of R.A.T. are (a) and (b).
Hypotenuse: is the longest side of a triangle.
R.A.T: this stands for Right Angle Triangle
Greek: is a person who lives or born in Greece.
Theorem: a formula or a theory that can be proven

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

Mr. Harbeck fell and he hurt his head somehow... and he needs our help to make him remember the thing he forgot...

He found his backpack and this is what he found...

This is a picture of Pythagoras. He is also known as the father of math. He discovered

that the earth goes around the sun. He found a cure for when people is sick and that is to play music. He is a Vegan. He also found the circumference of the earth. He is the one who came up with the Pythagorean theorem.

The next thing he found was a triangle... R.A.T

This is a Right Angle Triangle also known as the R.A.T. The side that makes 90 degree is called the legs. That you have to lable a and b. The hypotenuse is the C, and is the longest side of the triangle. It is always across from the little square inside the triangle.

This is What i mean....

Next is the Square.....

This is a square, all the sides are equal. There are four 90 degree angles in this shape, which equals up to 360 degrees all together. The sqaure is made up of 2 right angle triangles and those black lines on each of the side mean that it is a triangle. if it wasn't there i would mean that it is a sqaure.

Next is the Pythagorean Theorem....

My video on Pythagoras

### Pythagoras

Mr.Harbeck was suppose to teach us a new unit but apparently he slipped and bumped his head on the ice and now he has amnesia. So, we have to help him out and figure out what he was going to teach us so we could recover his memory.

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.