Pythagoras Post

Thursday, February 26, 2009


Made By: Deb Russell

The Pythagorean theorem

The formula of the Pythagorean Theorem is A squared +B squared =C squared (or on the top left of the picture)





The Right Triangle:
The right angle had a 90 degree angle. Of course something has to make that 90 degree angle, the leg A and B make up that angle.
The line across the 90 degree angle is the longest side which is called the hypotenuse.
There is also two other things that are in the right triangle that equals 90 degrees, these two are called theta and beta.










The Square:
The square always has sides that are all the same, all sides equal 90 degrees. When you split a square by cutting once across the 90 degree angle it makes two right triangles.
Two angles that equals to 90 degrees are called Complementary.
Angles that makes a straight line equals 180 degrees. And two angles are called Supplementary.















This was all invented by a Greek man named Pythagoras. Pythagoras is a mathematician,and a teacher/philosopher. He is also one of the most important mathematicians in the world.


In math class we made a video about how to solve to the "C" i hope you like it.













But wait we also made a second video on how to solve the "B" this time. I hope you like it.










Pythagoras


















This man is Pythagoras.
Pythagoras made the proof of the right triangles. Pythagoras was a teacher and a Philosopher he is a very important person to mathematics. Pythagoras made the Pythagorean theorem which is:








This theorem is saying that A and B have a relationship with C:






















Now we move to Triangles

Triangles are also called R.A.T. a right angle triangle. A right triangle has a hypotenuse the longest side to a triangle. A R.A.T also has legs and the right angle. There are also symbols in the corners of the triangle called theta and beta. Theta looks like a circle with a slash in the middle and beta looks like a B with a tail.





















Now into Squares and Rectangles:

Squares and rectangles are in a group called quadrilaterals they have 4 sides and if you put 2 triangles you make a square or rectangle. They all make 360 degrees inside. A square has 4 equal sides and a rectangle has 2 long sides and 2 short sides.






















Now on to 2 math problem

This one you have to find the bottom length.

A²+B²=C²

8x8+BxB=10x10

B²=100-64.............36

square root b² is B and the square root of 36 is 6 but there are two so you add 6+6 and the length side is 12mm.
























Another Math problem

















Firstly you can see that going around isn't the answer you cut across the yellow square find the side of C.

AxA + BxB = CxC
10x10 + 12x12=CxC
100+144=CxC
244=CxC
Square root 244 and you will get 15.6

Now you have the purple square you just add the bottom length so 10mm+ 2mm= 12mm
That is the shortest distance to A and B.



























Movie will be uploaded soon.

Pythagoras



[photo taken from Mr.H's post]



This man is named Pythagoras. He was a teacher and philosopher in Greece, who was also vegan. Pythagoras was famous for calculating the circumference of the earth and realizing that the earth is a sphere and not flat. Pythagoras discovered the Pythagorean Theorem (a² + b² = c²).







This is the formula for the Pythagorean Theorem.


In this picture is a right triangle. R.A.T [ Right Angle Triangle]. The longest side of the triangle of the triangle is the hypotenuse. [side C= Hypotenuse]. The other two side are called the legs. [ side a & b= legs], and it doesn't matter which lines the letters go on. The legs both equal 90 degree angles. The square in the corner tells you that the lines equal a 90 degree angle. The sign in the corner that looks like a 'B' is called Beta and the sign that looks like a O with a line through it means theta.




This is a quadrilateral square. Quadrilateral means that all the side are the same length. The lines on each side of the chair indicate that each side is equal. In the corners of the square are the squares again, which means the sides make 90 degree angles. All the angles make up 360 degrees, therefore making the square equal 360 degrees.










pythagoras

Pythagoras Thereom

Pythagoras Theory

Wednesday, February 25, 2009




If you put any two triangles together you get a square or a rectangle like the one below.




These are quadralaterals they both have four sides and the



The sides that make up the angles can be called "legs" and can be called a or b so c is called the "hypotenuse."


make some cuts in "a" and arrange them around "b" to get "c"

And that is the jist of Pythagora's Theory

Pythagoras Post

This is Pythagoras :


Pythagoras is a greek mathematician. A teacher and a philosopher.
Pythagoras is one of the first important mathematician.

Pythagorean theorem :





Right triangle:

A right triangle has a 90 degree angle.
The leg a and b makes up that 90 degree angle.
From the 90 degree across, is where the long side is, the hypotenuse.
The theta and beta corners has to equal to a 90 degree to make a right triangle.


Square:

All sides of a square is the same. All the corners are 90 degrees.
When you split a square in half, it make 2 right triangles.

4= 90 degrees angles quadrilateral internal angles = 360 degrees.

Two angles that equals to 90 degrees are called Complementary. Angles that makes a straight line equals 180 degrees. And two angles are called Supplementary.

Were looking for the " a ". We know that " b " is 8 mm, and " c " is 10 mm.
So what i did is minus " b " to " c " and then I solved the exponents.
The when I got the exponents gone, I subtracted the answer of " c to b "
To get rid of the " a's " exponents you have to square root.
And what you do to the one side you do to the other side too .
So I square root the 36 and the " a " and got.. " a " = 6mm.
But were actually looking for two " a " because theres two triangles.
So you just added two " b's " which is " 6+6 " and got 12mm . " a = 12mm "











were trying to figure out what the diagonal is. So, i divided the square in half. and try to figure out what the long side. So we know that " a and b " is equals to 3 mm. So what i did is simplify " a and b exponents ". Then just add them together. And then, we square root to get the answer.





In this one, were trying to figure out the diagonal of the bigger square. I did the same thing as the first one. But instead of the " a and b " equals 3. In this one, " a and b " equals to 8mm.

Video:



video




video

Pythagoras

Tuesday, February 24, 2009




































I chose to do the second problem and the third problem.

1.























3.






























Phythagoras

Monday, February 23, 2009
Phythagoras




















Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it.













The Side A and Side B can be two different numbers but they both have to equal 90 degrees. These two sides are also called legs for the triangle. Once these 2 angles are added they are called Complementary Angles. There are also angles that are 180 degrees and make a straight line. This is called Supplementary.













In this picture there are two triangles that make one rectangle.
Two triangles
can also be used to make 1 square or other
quadrilateral.


Question Example -



a²+b²=c² - Theorem
16²+12²=c²

(16x16)+(12x12)=c²

256 + 144 square root of 400 20=c







To make sure that your answer is right
look
at the triangle and check the side or
the length
your working on and see if the other
sides and
shor
ter or longer.


Questions and Problems Problem 3 :









Answer :

Eunice's pythagoras post

Eunice Anne
February 26, 2009
8-16 (:










Pythagoras
is a Greek mathematician and scientist, born between 580 and 572, then he died between 500 and 490 BC. he founded the religion movement called "pythagoreanism". he's best known for the Pythagorean theorem. Pythagoras and his students believed that everything is related to mathematics and that numbers were ultimate reality and everything could be predicted and measured in rhythmic patterns or cycle. with very strict rules of conduct Pythagoras undertook a reform of the cultural life of croton, urging the citizens to follow virtue and form an elite circle of followers around himself called Pythagoreans. he and his students lived at the school he opened, the student is required to be vegetarians. Pythagoras is also the first man to use music as medicine. his disciples would sing hymns to Apollo together regularly. they used lyre to cure illness of the soul or body; they recited poems after sleeping to aid the memory. he died around 90 years old for unknown reason. it was sad that the influence of Pythagoras on Plato and other was so great that he could be considered the most influential of all western philosophers.


According to Pythagoras...

To understand Pythagoras, you must know the meaning of the sides of he right triangle and the right triangle itself.

  • Right Triangle- a triangle in which one of the sides measure 90 degrees
  • Legs- the two sides of the triangle that make up the right angle of the right triangle
  • Hypotenuse- is the longest side of the right triangle
  • R.A.T- is the right angle triangle
  • Greek- is the native language of Greece
  • Theorem- is a law or principle that is tested and argued



I care about grade 8 math because it is a preparation or introduction for the future lessons especially in math and in higher sciences. Also, I just want to have a good mark.






Square
- a square has all equal sides
- all sides of the square is 90 degrees
- a whole square has 360 degrees because if you add all of the 90s you get 360



- internal angles




R.A.T: Right Angle Triangle
- all right angles are 90 degrees
- whole triangle is equal to 180 degrees.






- right angle triangle
- right angle = 90 degrees
- triangle=90 degrees When two angles equal up to 90 degrees they are called COMPLIMENTARY angles that make a straight line equal 180 degrees and the two angles are called SUPPLEMENTARY.










RECTANGLE:
- all sides equal
- quadrilaterals
- internal angles

-sides are 90 degrees
- rectangle= 360 degrees







TRIANGLE:

- a and b make up the legs of the right triangle
- c= hypotenuse
= it is the longest legs of the right angle
- is always across the right angle











Pythagorean Theorem
- the Pythagorean theorem was started by Pythagoras
- it helps you find the c or the hypotenuse or the longest side of the triangle




- 4x4+3x3=25
this square used to be 2 squares. I added them both up to make an equal square. 4x4+3x3=25 then after I have to find a number that ...... (ask mom for help)





Pythagoras Theorem











Proof:




Another one proof:




Finding the sides of the square:













Pythagoras Homework:





















A checkerboard is made of 64 small squares that each have a dimension of 3 cmx3cm. The 64 small squares are arranged in eight rows of eight.



My videos:










Those are all the things that I have learnt in this whole Pythagoras unit. I hoped you liked the pictures and enjoyed my presentation. I apologize for future drawing mistakes if I have. I hoped I helped you understand Pythagoras. I sure did enjoy explaining and making pictures. x) Until next time... BYE! :) :D <3