### Pythagoras

Thursday, February 19, 2009
Legs: Lines that come out of the right angle with one going up and the other to the side.
Hypotenuse
: The longest side of the triangle and opposite the right angle.
R.A.T
: Meaning Right Angle Triangle.
Greek
: Someone coming from Greece.
theore
m: A theory that can be proved.

These artifacts are all connected to each other through the Pythagorean Theorem.

Pythagoras: that uber smart Greek dude from Greece, but people are not really sure if he's a real dude because no records of his writing were found.

He was also a vegetarian.

The square and the triangle both relate to the Pythagoras Theorem because according to the theorem 4 triangles make a square.

a²+b²=c²
: This is the formula for the Pythagoras Theorem. It indicates that a small square (a²) and medium square (b²) equal to a larger square (c²). With a right angle triangle the formula states that the two legs (a and b) together make the hypotenuse (c).

The "mystery man" is Pythagoras, a MATHematician. We care in grade 8 MATH because it . . uh . . . well . . . . is MATH!

Let's make the 10mm (c) because both of them are equal which make them the longest side or hypotenuse. I will make the 8mm be (a). In order to find (b) we need to subtract (a) from (c). It will look a little something like this:

-a²=b²
10²-8²=b²
100-64=b
²
36=
b²
6=b

WORD PROBLEM:
A check board is made of 64 small squares that each have a dimension of 3x3 cm. The 62 small squares are arranged in eight rows of eight.

a) What is the length of the diagonal of a small square? Give your answer to the nearest tenth of a centimeter.

The picture below shows the diagonal of the 3x3cm square. Both the length (a) and width (b) are 3cm so we will have to solve for the diagonal (c). We all (should) know how to find (c) by now. a²+b²=c².
a²+b²=c²
3²+3²=c²
9+9=c²
18=c²
4.242=c

b) What is the length of the diagonal of the board? Give your answer to the nearest centimeter.

The whole board is made out of 64 3x3cm squares which are in eight rows of eight. To find the length (a) and width (b) we have to multiply 3 by 8. We multiply 3 by 8 because each square in a row of 8 is 3x3cm. 3x8=24. So now we know that the length (a) and the width (b) are both 24cm. Now that we know this we must solve for (c). Again, a²+b²=c².

a²+b²=c²
24²+24²=c²
576+576=c²
1152=c²
33.941=c

PYTHAGORAS VIDEOS: