The Origin and History of Pi

1. The Origin and History of Pi CTAE Resource Network Instructional Resources Office Written by: Philip Ledford and Dr. Frank Flanders July 2009

2. Objectives • Study the history of pi. • Learn the meaning of pi. • Examine the development of pi along with the development of mathematics. • Evaluate some of the different formulas that pi is used in. • Explore professions that use pi.

3. Intro to pi • Ever wondered what that symbol means on your calculator. It is the first Greek letter of the Greek work meaning “perimeter”. It turns out that it is a very important symbol. • Pi = 3.1459. • Some of you may already know that pi is used in a lot of different mathematical formulas. • As you study pi keep in mind that for thousands of years people had to calculate pi by hand. This took an incrediably long time.

4. What is pi? Pi=3.14159 Pi is the mathematical constant whose value is the ratio of a circle’s circumference to its diameter. Circumference = The distance around a circle Diameter = The width of a circle.

5. How Pi was developed. • The history of pi is complicated. No one “invented” pi. It was discovered rather than made. The use of pi developed as the use of mathematics developed. • Ancient Egyptians and Greeks knew the ratio of the circumference to the diameter of a circle is the same for all circles and is slightly higher than 3. • Though the estimate of ancient civilizations was close to pi it was not until Archimedes, a Greek mathematician and physicist, who more accurately calculated pi.

6. How Pi was developed. (con’t) • Archimedes found that if he drew circles in polygons and calculated the inner and outer polygon’s perimeters and calculated the values that the estimate of pi was 3.1419. Polygon=geometric figure with three or more sides or angles. The second major advancement in understanding pi came with the development of calculus.

7. How Pi was made. (con’t) Isaac Newton was able to calculate 15 decimals in the pi series, it is said that Newton spoke about his work with pi saying he was ashamed how long it took him just to calculate the 15 digits without working on anything else.

8. How Pi was made. (con’t) • In 1706 John Machin developed a converging series for pi that calculated up to 100 decimal places. • By the year 1949 digital computers were invented and could calculate 100’s of decimal places of pi in hours. In 1949 John von Nuemann calculated 2037 digits of pi in 70 hours.

9. How Pi was made. (con’t) • As you can tell, pi has been very difficult to calculate. • It has taken 1000’s of years to estimate with 100’s of different algorithms (a set of rules for solving problems in a finite number of steps) that made it possible for mathematicians to more accurately define pi.

10. Using Pi Pi has mathematical applications in most professions. Can you think of situations where using pi might be important to you? As you probably already know you use pi for finding the Area and Circumference of a circle.

11. Using Pi (con’t) • Other applications of pi are finding the volume of something. Volume = The amount of 3-D space an object takes up. Everyone in the world at some time has used pi. Agriculturalist, engineers, architects, and construction workers are just a few of the professions that use pi extensively.

12. Area • Area=pi x the radius squared. • The radius of a circles is the distance from the center most point to the edge of that circle. • For example. Tim the architect has to build a circular column that has a radius of 5 feet. What would be the area of the entire column? • To calculate this Tim would take pi x 5 squared • 3.14 x 5 squared = 78.5 • Therefore the area of the circular column is 78.5 feet. <= radius

13. Circumference • Circumference is the distance around the outside of the circle. • To find distance we would use the formula circumference= pi x diameter • As you know diameter is the width of a circle. • For example Jim the engineer needs to design a metal tube that has a diameter of 15 feet. • Jim needs to find the circumference of the circle in order to make a metal tube to fit around it. Jim would use the formula c=pi x d • Circumference = 3.14 x 8 = 25.12 • The circumference Jim is looking for is 25.12 feet.

14. Volume • To find volume we would use the formula volume = pi x radius squared x height. • Tom the agriculturist needs to know the volume of a dipping vat for his cows to safely and comfortably fit in. • Before he can calculate he needs to know the radius and the height of the structure before he can begin building. • Tom measures the radius at 5 feet and the height at 9 feet. • Therefore Tom’s formula would look like Volume=3.14 x 5 squared x 9 • 3.14 x 5 squared x 9 = 706.5 feet cubed

15. Pi in the Professions. • Agricultural professionals may use pi to determine the area covered by a pivot irrigation system or storage facility. The would use the formula Architects and construction works would both use the formula for Area extensively. They also use the formula for volume extensively to fill columns of concrete and to know the space a building would take up.

16. Pi in the Professions. (con’t) • Engineers use advance formulas that include pi. These are just some of the formulas an engineer would use. Moving around structures such as landmasses and buildings would require the use of some of these formulas. Engineers would probably use pi more than other professions.

17. Summary • Pi is the mathematical constant whose value is the ratio of a circle’s circumference to its diameter. • The use of pi dates back to 1900 BC with ancient Egypt and Greece. • It has taken 100’s of different algorithms to help estimate pi’s number because it is a repeating decimal. • Pi has been developed along with the development of mathematics. • There are many different applications for pi. • Many different professionals such as engineers, agriculturalist, and construction workers use pi. • Pi day is celebrated on 3/14 of every year because pi = 3.14 