Mathematical Pi

It is not difficult to construct a circle. With a little more effort, one can construct a square. The circle can be thought of as nature’s perfect form – it exists naturally everywhere by God’s design, and is associated with the concept of infinity. Conversely, the square can be thought of as man’s perfect form, and is associated with the concept of finiteness. The square is prevalent by man’s design, but rarely occurs naturally.

In early civilization, it was discovered that there was a special relationship between the circumference and the diameter of a circle. The ratio of the circle’s circumference to its diameter is represented by the symbol π (pi). (π is the sixteenth letter of the Greek alphabet, and is equivalent to the lower case English alphabetic “p”). It was discovered that this value could not be expressed as the ratio of two integers. As more and more accurate approximations of this ratio were achieved, it was discovered that there was not a repeating pattern of digits.

More puzzling, however, was the discovery that by using Euclidean theorems (compass and straightedge), it is impossible to construct a square that has the same area as a given circle. This is referred to as “squaring the circle” (it is also called the quadrature of the circle). It has been proven that this procedure is impossible, but that has not prevented many people who continue the futile effort. [Note: The ancient Greeks defined the two conditions for the circle squaring problem. In addition to using only compass and straightedge, the solution must be performed without using an infinite number of steps. Of course, if either of these two conditions is disregarded, it is a simple matter to square the circle. Using advanced mathematics, like calculus, a square equal in area to a given circle can be constructed quite easily].

For thousands of years it seemed natural and reasonable that a mathematical or geometrical relationship would be discovered between the circle and the square. It seemed logical that the circle could be measured as squares and rectangles are measured. That, however, is incorrect. And, our puzzling friend, the value called pi, is responsible for this perplexing situation. We continue to explore and examine additional digits of pi with the anticipation of discovering some clue to the complete and complex nature of this mysterious number.

Gravitation

I think it is singularly fascinating that only four fundamental forces have been discovered in our physical cosmos. Obviously, we are all aware of the effects of many different forces such as tides, wind, electric motors, volcanic and chemical explosions, and human muscles. All of these different kinds of forces, however, are versions of the four basic forces of the universe. Two of these forces, the strong nuclear force, and the weak nuclear force operate entirely within atomic nuclei. Therefore, we are not normally aware of them. The other two forces, electromagnetism and gravitation, account for almost all the forces that we encounter in our everyday lives.

The most powerful of the four forces is the strong force. It binds protons and neutrons together in the nuclei of atoms. It is the force that powers the sun. Although strong, this force is very short-ranged (only within the nucleus of the atom).

The next most powerful force is electromagnetism. This force acts between any particles carrying an electric charge. It keeps negatively charged electrons close to the positive nuclei of atoms throughout chemical reactions. This is the force that enables TV, the telephone, computers, radio, radar, microwaves, light bulbs, and dishwashers. This force is long-ranged, but much weaker than the strong force.

The third most powerful of the four forces is the weak nuclear force. Like the strong force, it also applies only at the subatomic level. The weak force is responsible for radioactive decay processes such as the emission of beta particles from certain nuclei. The weak force is harnessed in modern hospitals in the form of radioactive tracers used in nuclear medicine.

The weakest of the four forces is gravitation. Gravitation is the attraction between any two objects because of their masses. It is the force that keeps the planets in orbit around the sun. Although significantly weaker than the other three forces, the gravitational force acts over great distances.