Piagno: Where are you running to, Hammer? Hammer: To get that pie I heard you talking about, Piagno! Piagno: I wasn’t talking about pie you eat, I was talking about the number Pi Hamster: If it’s a number, why is it called pie? Paigno: Pi is the Greek letter P . They used p for Perimeter

Hammer : The perimeter of what? Piagno: of a circle We call the perimeter, or edge around the circle, the circumference. You see Mathematicians found that when you divide the circumference of any circle by the diameter of the circle, the result is a value called “pi” or a number approximately equal to 3.14.

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273 724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609... Hammer: Why would they call a number a letter? Piagno: It’s an irrational number …a decimal that never repeats or terminates. The actual value starts out as: 3.1415926535897932384… For short, mathematicians usually refer to its value as 3.14, but that is not an exact amount. When working with the value of “pi” the only way to have an exact answer is to leave the symbol for pi in the number. Personally, I think most of the time we should be exact. Just a bias on my part I suppose, I accused my elementary school math teachers of making us multiply out by 3.14 by hand to keep us busy and give them a break for awhile, of course that was before calculators..:) Most of the time we don’t need to be exact so we can substitute 3.14 for Pi

5 inches Hammer: Why would they do want to do this, anyways? Piagno: Well, it is sometimes difficult to measure around something but if we measure the diameter we can calculate the circumference. Your wheel for instance when I try to measure it, I would have to wrap string around it and then measure the string. Imagine having to do that for all the circles in the world? It ‘s much easier to measure the diameter with a ruler. So if I measure the diameter. I can calculate the circumference. Hammer: how?

Piagno: The mathematicians did the first part for us when they discovered that the circumference divided by the diameter equals pi . We can use what we know about solving equations and multiply both sides by the diameter that gives us circumference equals pi times diameter which we can rewrite as circumference equals diameter times pi Symmetry allows us to rewrite the equation as: C= d pi, which makes it a little easier to use when we solve for the exact value of the circumference and leave pi in our answer.

5 inches Hammer: So if we measure the diameter we can get the circumference? Piagno: That’s right. If the diameter is five inches, we plug that into our formula. The circumference of your wheel is pi times diameter or the circumference is 5 pi. We don’t need to be that accurate so we can substitute 3.14 for pi but remember, if we do that we have to use the approximation symbol. Hammer: is that the sign that looks like an equal sign that got twisted? Piagno: yes it is called the approximation sign So 5 × 3.14 inches equals 15.7 inches. Your wheel’s circumference is approximately 15.7 inches

Hammer: In my math book it says c=2 pi r Piagno: What is the relationship between the radius and the diameter of a circle? Hammer: The diameter is equal to 2 times the radius. Piagno: We can use substitution and substitute the 2r for the diameter making the formula 2 times r times pi.

Radius= 4 inches Piagno: So, if you were given a circle with a radius of 4 inches, you know the circumference of that circle would be…2x4 x pi or 8pi inches. We can substitute 3.14 for pi which gives us 8 times 3.14 which means the circumference is approximately 25.12 inches.