Q:

What are the notable mathematical problems that feature pi?

A:

Some mathematical problems that feature pi are the area of a circle, a circle's circumference, arc length and the different surface area and volume formulas for a cone, sphere and cylinder. In mathematics, the ratio between a circle's circumference and diameter is given as pi.

While the circle's circumference is given by the formula 2 x radius x pi, its area formula is pi x radius squared. Similarly, many of the area and volume formulas for different geometric solids were formulated with pi as a term in them. For example, the area of a sphere is 4 x pi x radius squared, and its volume formula is 4/3 x pi x radius cubed.

The history of pi dates back to the ancient Babylonians and Egyptians. Babylonians estimated pi as 3.125, and the Egyptians approximated pi to be 3.1605. However, it was the Greek mathematician Archimedes that calculated pi to be between 223/71 and 22/7. A general estimate for pi is 22/7 or 3.14.

In 1706, William Jones was the first to introduce  a Greek letter for pi, which was later adopted by the mathematician Euler to represent the ratio between a circle's circumference to its area. Later mathematicians extended the number of decimal places in this irrational number through rigorous calculations. In the computer age, pi has been estimated to its two-quadrillionth digit.


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