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# What is pi and why is it important?

Pi (pronounced “pie”; the symbol is π) is the ratio of the circumference to the diameter of a circle. Another way of looking at pi is by the area of a circle: pi times the square of the length of the radius, or as it is often phrased “pi r squared.” There are more ways to consider the value of pi: 2 pi (2π) in radians is 360 degrees; thus, pi radians is 180 degrees and ½ pi (½π) radians is 90 degrees. (For more about pi and radians, see “Geometry and Trigonometry.”)

What is the importance of pi? It was used in calculations to build the huge cathedrals of the Renaissance, to find basic Earth measurements, and it has been used to solve a plethora of other mathematical problems throughout the ages. Even today it is used in the calculations of items that surround everyone. To give just a few examples, it is used in geometric problems, such as machining parts for aircraft, spacecraft, and automobiles; in interpreting sine wave signals for radio, television, radar, telephones, and other such equipment; in all areas of engineering, including simulations and modeling of a building’s structural loads; and even to determine global paths of aircraft (airlines actually fly on an arc of a circle as they travel above the Earth).

Advances in architecture during the European Renaissance would not have been possible without similar advances in mathematics and a knowledge of the value of π (pi). This cathedral in York, England, is a prime example of what can be accomplished with mathematics.

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