## An Explanation of Pi. The Number Which Seeks to Define the Universe.

The number pi has intrigued great thinkers for millenia. Only recently have mathematicians and scientists been able to truly understand how it relates to nature.

The world is a fascinating, complex, interesting place. But that is not very remarkable in itself. What *is *remarkable is the fact that everything is ultimately confined to the strictest order, that everything can be so intricately defined by such human inventions as science and mathematics. Who would have thought that such seemingly random processes as go about structuring our present reality could be so well defined that humanity could begin to understand everything from the farthest parts of the universe to the smallest structures of atoms?

## The History of p

The Greek letter p was first used to define the relationship between a circle’s diameter and its circumference as late as 1706 by Welsh mathematician William Jones, but studies to determine the number to an ever higher degree of accuracy have been around since as early as ancient Egypt in the 19th century B.C. Of course, at that point the relationship (which can be very difficult to simply measure) was somewhere around 1/3.

It was the wonderful mathematician/inventor Archimedes in the 3rd century B.C. who first devised a systematic approach to define p by embedding a circle with polygons (whose circumferences are much easier to decipher. He found that by using polygons with ever greater numbers of sides, the circumference of the circle could be measured to greater and greater accuracy. Using a 96-sided polygon, it was determined that the value of p was somewhere around 22/7. While it is now known that this is not entirely accurate, it would be centuries still before better measurements were made.

While there are still some who have devoted entire mathematical careers to understanding this remarkable number, most people have accepted the fact that it is infinite and have decided (probably wisely) to move forward with their lives.

After all, 3.1415 should be good enough for most people.

## Math and the Universe

But none of this would be possible if the universe did not succumb so readily to the rigid numerical systems of mathematics that such geniuses as Pythagoras, Archimedes and Euclid have worked to establish.

Take the classic case of pThat number most students learn about in high school math classes which describes the relationship between a circle’s circumference and its diameter, which comes to approximately 3.14159 (though very few people, including myself, ever really memorized it past the first couple decimal places). Today, p has been established to more than 6 billion decimal places using modern computers, and the search inexplicably continues for even more.

## The Exact Value of p

The quest for ever more exact values of p is not, however, the search for an exact value. It is not the search for where the numbers might eventually end , giving us a final answer, for it is very well known (and has been mathematically proven) that none is coming.

The value of p is truly an irrational number, with absolutely no end, ever, as may be best shown by writing the number out in terms of a fraction: 4(1/1 – 1/3 + 1/5 – 1/7 + 1/9 – …)

Clearly, this same pattern will continue forever, bringing one ever closer to p. As inexplicable as it may seem, the infinite nature of p to mathematicians means that there is absolutely *no* exact relationship between a circle’s circumference and its diameter.

So why does this search continue? Mere curiosity, one must suppose. Once the value had been determined to a few million decimal places, it surely doesn’t make much practical sense to continue defining superfluous numbers. The first several are important for precision, but anything after that is quite useless. To put this in perspective, once p has been determined to 39 decimal places, it has been said that we could use this to measure the circumference of the entire universe to the precision of the width of a single hydrogen atom. This is very precise, and there really should never be a reason to know the value any further.

### p in Nature

Its infinite nature is surely not the most remarkable thing about p. Surely, the most remarkable thing about this number is the fact that it seems to crop up in the most unexpected places. Despite the fact that it is an irrational number, it has become clear that this number may very well be used to describe many fundamental aspects of the world around us.

For instance, Professor Hans-Henrik Stolum of Cambridge University once attempted to calculate the ratio between the actual distance of a river from beginning to end and the distance as the crow flies. He measured several rivers as they wound their way through the countryside, from their humble origins to the point where they funneled into the sea, and then he measured the exact distance from beginning to end as if the river was perfectly straight. One guess as to what he found the answer to be.

### That’s right. p.

Einstein discovered that p was a crucial element in both his field equations of General Relativity as well as his infamous “cosmological constant” which he developed later in life which defined the force which prevented the expansion of the universe. Heisenberg used p in his famous uncertainty principle of quantum mechanics, Coloumb used it in his law to define electrical force, and Kepler used it in his third law of planetary motion.

In science, in geography and in astronomy – p is all over the place, for some reason which eludes mathematicians and scientists to this day.