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
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 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.
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.
Here are the two videos Joseph, Adrian and I made.
Thanks for reading and watching, please comment if I missed anything. Thanks and goodbye!
-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 ArtifactThis 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
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. (:
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.
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.
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.
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 ;)
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.
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
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:
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