Pythagoras

Friday, February 27, 2009
Pythagoras
  • legs
  • hypotenuse
  • R.A.T
  • Greek
  • theorem

The legs of a triangle are called sides A and or B These 2 can be switched around. C on the other hand must be the longest side. A hypotenuse is the longest side of a right triangle, the side opposite the right angle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. R stands for right A stands for angle and the T stands for triangle together it is called the right angle triangle. Greek is Where people live now or did but the letters can be used az zeta and beta.A thorem is a problem that can be be shown or proven the answer.

here are some Videos :D

pythagoras




Pythagoras was a famous Greek mathematician who was famous for his ingenuity, his creativity and the fact that no one really knows if he actually did all that he is known for.

Definitions
R.A.T it is the abbreviation for right angled triangle
Theorem is a theory
Greek is a culture that Pythagoras was from
Legs are the two shorter parts of a triangle that make up a right angle
Hypotenuse is the longest side of the triangle

do you see the right angle on this triangle, it is 90 degrease and if you add up all of the corners it makes 180 degrease

this is just a basic diagram of the theorem of (A) (B) (C)

now i will show you a square

if you see, there are four right angle making the whole thing equal 360 degrease

Pythagoras........

Thursday, February 26, 2009








Hi this is Carlo... And that dude a the left is called Pythagoras... This guy was a famous Greek mathematician... Well,.. exactly he was just like a myth or not it depends... This guy was in factually smart at the time...


These are the things that he got smart for...,. If you'd be kindly look at the paragraph below this you'll be just fine...And some stuff we leared for the past few weeks....




DefinitionZ
R.A.T: this is just a short abbreviation for right angle triangle if you were thinking of an animal,DON'T!!!!!....
Theorem: this is just a basic theory or formula that can be proven or whatnot....
Greek: it is just a place called Greek which humans live in either in the past or the present doesn't matter....
Legs: if your thinking about the human well don't... This is all about math nothing more, it means the two shorter parts of a triangle that make up a simple right angle...
Hypotenuse: if your thinking about this word and say this word is difficult well your just dirty wrong... This means it is the longest side of a triangle, the only longest... And it is the opposite side of the right angle
See!!!... Those thing ain't that bad but you'll have to understand it quite clearly.....






Okay these are just examples on what am i talking about in the last paragraph...ON TRIANGLES!!!!!!!!....


You see this triangle has a right angle... Which eventually is 90 degrees but if you add all the crazy stuff there the triangle will equal 180 degree... TA DA!!!!!!!!...


















Now this is just a basic diagram of the theorem of sides (A) (B) and (C)... See!!! If you get this math you'll understand... It's all pretty and whatnot...


Now that the triangle learning is over... Time for the squares of doom!!!...








This square of "doom" is just basic... It has a right angle, actually four of them... So it equals 360 degrees... SEE!!! Its super simple...






Now these are some example I should show you for this scribe, I'll just choose two because I'm lazy...




Okay firstly you people have to check what is (A) and (B)... Simple do the square root of it, you should have 15 as an answer, right?!...To figure out C you must do the (A) and (B) square first so it'll equal 225 for both... Then square root the 450 which gives you the answer 21.213


Here's a recap if you don't understand

a(2)+b(2)=C(2)
15(2)+15(2)=c(2)225+225=c(2)
450=c(2) ( predend that your square rooting it)
C = 21.213


Okay you see how theres a question mark there,.... This is how you solve it in my eyes of point of view....
Here's the formula... c(2)-b(2) =a(2)
The numbers that are showned are pretty straight forward... 10(2)-8(2)=c(2)
now just square it!!!..100-64=c(2)
all equals 36=c(2) then use the square root on it...!...
And the final result is 6 on both sides.....
Now that were done examples...... We will watch my groups video then it'll be the end.....






And that all I got...I might got errors but its okay.... Peace!!!!....

Pythagras therom

OH NO! MR.Harbeck has amnesia! What ever will we do??? Its a good thing he left us these word and artifacts!

Hi my name is Camille and I will be your teacher for today! Most of you already know what I'm going to be talking about but to some of you this is NEW information. So if okay so Lets start!


This week we have been learning about the Pythagoras Theorem . We have been given an assignment to help our teacher Mr. Harbeck, remember what he was suppose to teach us.The assignment involves us to understand 4 pictures. But I'll get to that a little bit later. We were also given a list of vocabulary words here they are :
  • legs
  • hypotenuse
  • R.A.T.
  • Greek
  • theorem
Legs- shorter than the hypotenuse , comes out of the right angle, so each right triangle always has 2 legs.

Hypotenuse- is the largest leg in a right angle, triangle and is always opposite to the right angle.

R.A.T- the word R.A.T is a shorter way of saying right angle triangle.

Greek- some one who has the ethnic background of Greece. or a native or inhabitant of Greece.

Theorem- it is a idea that has been proven true.


This is the artifacts
one is a Greek man called Pythagoras, a square, a right angled triangle and a2+b2=c2.

First we will be discussing the right angled triangle or also known as R.A.T.
Here is what a right angled triangle loo
ks like:
















A right angled triangle has 3 sides: side A which is the long side on the left and side B which is just under the box also know as 90. then their is side C which is also referred to as the Hypotenuse. The Hypotenuse or C is always the longest side on a R.A.T
Here is a square:

















A square has four equal sides. All 90•.

Another artifact that was found was a formula related to the Right Angle Triangle, that Pythagoras mad. It looks like this :









PYTHAGORAS! This is the Greek Dude we have been learning about!



















Pythagoras was a great mathematician. He is know for the therm, he made - the Pythagoras therm .

~ an interesting fact about Pythagoras was that some people did not believe he was a real person, that the Pythagoras therm was made by a group of people called the Pythagorean.

Pythagoras questions:
Problem 1 This diagram shows the game plans for a game designed by Harbeck Toys INC. The board is made up of
a square and four identical right triangles.


If the central square has an area of 225 square centimeters what is the perimeter of the board game? To answer this question we first need to write what were already know:
we know that 225 cm2 is the area of the square and that all the legs are even.
So first we find out what the square root is for 225 cm is.
it equals to 15cm
So now we know all of the legs or sides equal to 15cm.
Now we need to solve for the Hypotenuse: so we use the Pythagoras therm which we were talking about before
.
a2+b2=c2
so if we were to put in the numbers it would look like this:
(15x15)+(15x15)=c2
225+225=c2
450=c2
450 square root is 21.213

(15x4)+(21.213x4)
60+84.852=144.852cm


Word Problem 2
A) The square's diagonal is 4.2 cm.
each square is 3x3 so we use a2+b2=c2
3(squared) + 3(squared) = C2
9+9=c2
18=c2
18[square root] = 4.2 cm

b) the length of the hypotenuse is
the square has 64 squares, 64 divided by 4(sides) is 16
so the square is 16x16, from there we use a2+b2=c2
16(squared)+16(squared)=c2
256+256=c2
512=c2
(square root 512)
22.627 = c
22.627 cm2













OUR VIDEO!!!! :P






















Here is part DEUX !!

Pythagoream Theorem

An "uber" smart mathematician. Pythagoras was a philosopher from Greek. They say that he was the greatest genius whoever lived. But they weren't sure if he actually existed because there was no trace of him being alive.

Triangle










Square






Pythagorean Theorem is the sum of the areas of the two
squares on the legs A & B which equals the area of the
square on the hypotenuse C.

definitions:

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 thatfrom ancient modern Greece.


Theorem: A theoretical proposition, statement, or formula, something to be proved from other formulas.

Pythagoras





A square has 4 equal sides. // The rat has a hypotenuse (the longest side) the hypotenuse is always opposite of the right angle.














Pythagoras was a famous Greek Mathematician alot people also didnt know who he was or if he really exsited or not.
that was born on Samon, A greek island in the eastern Aegean. Pythagoras was the first man who called himself a '' Philosopher '' and was a lover of wisdom. He was born on 580-72 BCE and died near 500-490 BCE.

legs - It connects together to make a right angle.
hypotenuse - It is the opposite of 90d. and the longest side
R.A.T - Its a right angle triangle
Greek - someone that came from greek.
theorem - A theorem is a statement that is prove by many people.

Pythagoras Theorem


Pythagoras is a Greek Mathematician, who is "uber" smart. People said that Pythagoras is a philosopher from Greek. They have said that Pythagoras might have not existed because there was no evidence of him alive.













Legs: the legs are always shorter than hypotenuse. All triangle's has two legs.the 2 legs can be in either side. The legs create a right angle.

greek:a person who was in ancient or modern greek.

Theorem: a formula or a theory that can be proven.

R.A.T: stands for right angle triangle.

Pythagoras- Pythagorean Theorem

Wednesday, February 25, 2009
Pythagorean Theorem

Pythagoras

-He was a great Mathematician and Scientist
-He is known for the Pythagorean Theorem (We care because it's math)
-First to think that the Earth was not flat but round
-He discovered square numbers(Square roots)
-He was a Greek Guy
-We don't have any of his work(proof that he was alive)
-Some people say that he didn't exist
-Very smart(I mean very!)



legs
There are two legs in a right triangle. The legs are shorter than the hypotenuse. The legs make the 90 degree angle. The legs are labeled as A or B. It doesn't really matter which leg you label A or B.














Hypotenuse

The hypotenuse is the most important part.The hypotenuse is the longest side of the triangle. The hypotenuse is located opposite of the 90 degree angle. You label it as C.














R.A.T
R.A.T stands for Right Angle Triangle. You can tell if it's a right triangle because the square on the 90 degree angle. A Right Angle Triangle has a total of 180 degree. Two Right Angle Triangles can make a square or a rectangle. The two angles that connect the hypotenuse make 90 degrees.















More about the Pythagorean Theorem...










































This picture is showing the Pythagorean Theorem. It's saying that A2 and B2 will equal the C2.

Squares are important in the Pythagorean Theorem. It will be easier if you know the relationship between a square and a right angle triangle. As you know a square has four equal sides. It has for corners, and those four corners are 90 degree angles. If you have four corners then 90x4=360. then the whole square has an angle of 360. If you cut a square up like you see in the picture, you will get two right angle triangles. And those triangles will contain a 90 degree angle, two equal legs, and a hypotenuse.

Question 1
How do you solve this?
First you label witch side will be A,B, and C. Then look at the information you have. The long line that's 10mm is C so is the other side. It's 10mm. In the inside of the triangle you see a line that is 8mm. That is B. Then on the bottom, we don't know how long it is. We'll call it A. You see that the middle line(B) cuts the triangle in half to make two smaller triangles.We'll solve one side of the triangle first.
C2-B2=A2
lO2-82=C2
(10x10)-(8x8)=C2
100-64=36
36=C
Then you use the square root. The square root of 36 is 6, so 6=A BUT we only solve half of it. You just have to add 6+6 to get 12 because those two sides are the same. It has the line of symmety on A. So The answer for this question is A=12.

Onto question 2....

This diagram shows the game plans for a game designed by Harbeck Toys INC. The board is made up of a square and four identical right triangles. If the central square has an area of 225 square centimetres what is the perimeter of the board game?

Question 2

Well I think that this one is harder than the first. So first lets take 225 and find the square root. The square root is 15 right? To make sure we got it right, we need to check. 225 is the area of the square. To get area you need to times length by with but in this case you need to times side by side. Now our answer was 15. So 15x15=225.
So that means that all the sides of the square is 15. And that also means that the legs for the right triangles are 15 too! now all we need to figure out is the Hypotenuse.

Like for the last question, we need to label. The Hypotenuse is C and the bottom(base) is B and the other one is A.
A2+B2=C2
152+152=C2
(15x15)+(15x15)=450
450=C
Now we need to find the square root of 450. The square of 450 is... 21.213.20344 but we only need 21.213. So the Hypotenuse is 21.213....We are not done yet! The question said that we need to find the perimeter of the board game. So we have to add the sides up.
21.213x4=84.852
15x4= 60
_____________
144.852

So the answer to this question is 144.852.

Here's a video that explains the Pythagorean Theorem(better than I do...)



And...this is the video that I did in class...



Pythagoras !

This week, we were assigned to make a blog post about the Pythagoras Theorum and Pythagoras himself. Plus define a few words.

Pythagoras was one of the most greatest genuises ever lived. He was an uber smart mathmatician and philosopher. Pythagoras was from Greek, but we are not 100% sure that Pythagoras actually existed because he made no records.

Legs
The legs are the shorter parts of a triangle. The legs create the right angle of the triangle.

Hypotenuse
Hypotenuse is the longest side of a right triangle, it is the opposite side of the right angle.

R.A.T
R.A.T is just short for Right Angle Triangle.

Greek
A person born or living in ancient or modern Greek.

Theorem
A theory that can be proved.

The Pythagoras Theorem
Pythagoras created the Pythagoras Theorem. It is the sum of the areas of the 2 squares on the legs which is a and b, equals the area of the square on the hypotenuse(c).

Then we have to explain some artifacts that Mr.Harbeck posted for us. The first article is the picture above this. The picture represents the Pythagoras Theorem. The definition for it is above the picture.

This is the 2nd article.






This is a Right Triangle. It has a 90 degree angle, and all together it has 180 degrees.This triangle is also known for a R.A.T.How do you know when it's a right angle ? Well, if it has a little square in the corner, then it means it is a 90 degree angle.



(no picture because everytime i clicked the picture icon, it would freeze.)

Well, the picture is sopposed to be a simple square. A square has 4 right angles which is 90 degrees each, and all together it would equal 360.

(no picture because everytime I clicked
the picture icon ..it would FREEZE)



(I could not get the rest of the post done because the computer at home was super slow:( )

Our next assignment was to make a video on how to solve the problem's on the videos.

This is the video I made with Kim C. and Courtney.

2nd Video:

Pythagoras Post

This past week weve been given a project to do a post on Pythagoras and in this post i will be explaining the pythagorian therom.



This is pythagoras he has done many amazing things in his life but there isnt really any evidence from his life just from what his friends said so maybe pythagoras never excisted and was just made up by people sometimes reffered to as the "pythagorians"

Now heres some important vocabulary that you need to know.

Hypotenuse:The side of a right angle that is the longest and is on the opposite side of the right angle.

R.A.T:A R.A.T is an abreviation to Right Angle Triangle. A right angle triangle is 90 degrees

Greek:A greek is a person who lives or was born in Greece Legs:The legs are the two shorter sides of the triangle that make up the angle

Theorem:A theorem is a theory that has been proven.

Another thing we were asked to do was explain these artifacts



The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).



Right Triangle: This is a right triangle. The right triangle has a right angle which equals 90 degrees. All together the triangle equals 180 degrees



Square: This is just a plain square 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
video
video

Pythagoras


Pythagoras

Pythagoras is a really smart guy.
People don't really know if he existed or not because there is no evidence of him ever being alive.

The artifacts were the pythagorean theorom, a square, and the R.A.T.








From last Friday, and all of this week, we have been learning about Pythagroas, and his theroey named Pytagorean Theroem. His theory is that on a R.A.T ( right angle triangle) , you can find the hypotenuse (the longest side of the triangle right on the opposite side of the right angle) by using the the measuraments of the two legs ( the two legs are what make up the right angle in the triangle). To make this easier for you to understand, we will call the two legs a and b, and the hypotenuse c. The thoroem is a squared plus b squared equals c squared. For now, I am going to say that side a is 2cm and side b is 3cm. So, since we know what sid e a and b equal already, we can put it down in our equasion. Now the equasion says, 2 squared plus 3 squared equals c squared. Since we want to get rid of the exponents, we square the numbers to get, 4 plus 9 equals c squared. Now lets add the numbers together to get an equasion of 13 equals c squared. To finish things off, lets put square roots on both sides so we can get rid of the exponent on the c. Now we come up with an answer of 3.605. Below is the same example i have just told you but in picture.



























Below you is more examples of this thorey.

A checker board has 64 small squares that each have a demension of 3cm X 3cm. The 64 squares are arranged in eight rows of 8.

a. What is the length of the diagonal of a small square?
b. What is the length of the diagonal of the board?

For this equasion, i am going to cut the small square and the big square in half. First with the little little square.






























Here is another example ofthe pythagorean theorom.

This diagram shows the game plans for a game designed by Harbeck Toys INC. The board is made up of a square and four identical right triangles.

If the central square has an area of 225 square centimetres what is the perimeter of the board game? Show how you know.

For this example, I am first going to find the square root for 225 so I can get side length for a and b. I got an answer of 15. Now I am going to solve for c since I already know that they both are 15. I got an answer of 21.213. Now that I know what side c is, I can find out the perimeter of the board. All I have to do is multiply side c and side b by four, and then add the two answers that I get. I got an answer of 144.852cm. So now you know that the perimeter of the board is 144.852cm.






















-Oops! Side c is suppose to be 21.213.







Now for the last example of the post.

For this example, I am going to only use one of the triangles to solve for a. The answer to a is 6.





-Oops again! The b side is suppose to be 8 cm.

























These are some words that I will explain if you didn't know what they meant earlier when I said them:

Hypotenuse: The side of the triangle that is right across from the right angle. It is also the longest side. (You know that you have got the answer wrong if the hypotenuse isn't the largest side of the triangle.)

R.A.T: This stands for right angle triangle.

Legs: The sides that make up the right angle in a triangle.


Here are some things that you should know about shapes.

Rectancle: Has four right angles. All of the angles put together equal 360 degrees. It is also 2

R.A.T that has all different lengths.

Square: The same thing I said for the rectangle except it is 2 R.A.T that have the same lengths for side a and b.

R.AT (different lengths): Has one 90 degree angle, and all the angles put togther equal 180 degrees. Has two legs. (all R.A.T has to have 2 legs or else it isn't a R.A.T)

R.A.T (a and b are the same length): The same thing that I said for the other R.A.T except the
hypotenuse is always going to be 45 degrees.

Here are the videos that me and my friends made to help you understand what I was trying to teach you in this whole blog post even better.