Pi Day Fun There are a lot of mathematical concepts in a slice of pie and a whole lot more in the full pie itself. If someone asks you how many degrees in a pie, the proper answer shouldn’t be it depends on how hot the oven was. A pie is circular and is not a polygon, (meaning, it has no sides). Therefore, it has a never ending or continuous edge, (meaning, every time one goes around it), it equals 360 degrees. If one started slicing a pie into pieces, it would change the degrees by what was cut and/or removed. For example, Judy cut a pie into two halves (that is kind of tough to remove from the pie pan). How many degrees were in each half? To find it, she would have to take 360/2 = 180 degrees. If Judy cut it again to make four pieces, she would 360/4 = 90 degrees, and if she cut it again to make 8 pieces, she take 360/8 = 45 degrees per slice. Pie also has a distance around the edge of the pan, it is called circumference. To find it, one must take the diameter, which is the measurement of the pan across and multiply it by the number pi (3.141592654…). In addition, the pan also has a bottom, where the crust is set. It is called the area of the dish. To find it, we use the radius, which is half of the diameter from the center of the dish to the edge, and square it (because all areas have two dimensions) and multiply it by the number Pi. If we were really insane, we could find the volume (inside of a solid) of a piece of pie, but only a piece at a time. It gets a little more complicated if someone tried to find the volume of the whole thing at once (we will figure this towards the end). That brings us to the number Pi, as mentioned earlier it is 3.141592654… We use it to find a lot of things in a circle. We use it to find circumference measured distance around the edge), arc length (a certain piece of the edge), area (inside of the circle), and the area of a sector (a certain piece of the inside). Pi is an irrational number, which means it has a non-­‐terminating and a non-­‐
repeating decimal, (meaning, it has no pattern of numbers and goes on forever and ever). It has been proved to be the circle’s circumference (measured distance) divided by its diameter. It’s confusing for most people to understand this concept because, we learn math in the opposite direction that it was discovered. In the old days, math had to be proven before it was calculated. Since it’s been proven for us, we teach our students how to calculate it first and later on in the advanced classes prove it. PI Day Fun Instructions 1. Take the pie and measure across the pan with an inch ruler to find the diameter in inches. 2. Use the diameter and times it by 3.14 to find the circumference of the pan. Another way to look at it, the circumference is taking the diameter and spinning it, which makes the outline of the circle or the pan in this case. 3. Next take the circumference and divide it by 8 (the number of slices we’re going to make). This tells us the length of the outer crust on each piece. 4. Okay, we talked about the distance around the pie, but what about the inside of the pan? Take the diameter and divide it in half and find the radius (similar to the circumference, the area is taking the radius and spinning it in a circle, which fills the inside of the shape). 5. Using the radius, times it by itself to square it, and then times it by 3.14 to find the area (don’t forget circumference has one outside dimension “ just the distance around” and the area has two inside dimensions the radius and it’s inside revolution or it’s spin). 6. Take the area and divide it by 8, which is the area of each slice. Wow very filling huh? 7. Now the real fun begins, you can actually take the pie and slice it into eight pieces. 8. Take the total degrees in a circle (360) and divide it by the number of slices (8). 9. You have 45 degrees of the pan in every slice, don’t you? 10. So you have a distance of the crust, an area of the slice, and the degrees of a slice, but it’s PI Day, so don’t think about it too much when you eat your slice. Don’t forget to ask for whip cream and enjoy!!!