When Albert Einstein was born on March 14, 1879, no one but his parents made a fuss. Mankind had known the ratio of the circumference of a circle to its diameter for 4000 years, but we didn’t celebrate a formal Pi Day until 1988.

Now, mathematicians, high school math classes, and even the U.S. government stop to celebrate the most famous Greek letter.

## Calculating π

You can determine a very crude approximation to the value of π by inscribing and circumscribing squares on a circle and calculating the ratio of the perimeter of each square to the diameter of the circle.

If the diameter of the circle is one, the perimeter of the circumscribed square is four and the perimeter of the inscribed square is two times the square root of 2, or about 2.83.

These are the crudest limits of π.

If we just increase the inscribed and circumscribed figures to hexagons, we can narrow the limits to 3 and 3.46. By increasing the number of sides, we can approach the value of π.

Around 250 b.c., the Greek mathematician Archimedes used 96-sided figures to narrow the limits of π to 3.1408 and 3.1428. How he could do this without any calculating device boggles the mind.

## Calculating π More Precisely

Until the computer age, π had not been calculated to more than 1,000 decimal places. Now we know the value of pi to over twelve trillion decimal places.

## Memorizing π

Many have taken up the hobby of memorizing π, but, as with chess, only a very few excel. The current record holder is Chao Lu of China, who recited π to an astounding 67, 890 decimal places on Nov. 20, 2005. He broke a record that had stood for over a decade by an amazing 25, 695 decimal places. Mr. Lu took just over 24 hours to accomplish the feat.

## The Feynman Point

The first sequence of six consecutive identical numbers occurs in position 763, which is the first of six nines. This is known as the Feynman point after the famous physicist Richard Feynman who quipped that he would like to learn pi to 763 places and then say 9, 9, 9, 9, 9, 9, and so forth.

Interestingly, the second sequence of six identical numbers is also nines. Which brings up a question that has yet to be answered – and which could become the Fermat’s Last Theorem of the 21st century.

## Is π ‘Normal?’

One would think that everything that could be known about π is known. But though π is suspected to be a ‘normal’ number, no one has ever proven this.

A normal number is, in layman’s terms, an irrational number which, if you examine it to enough decimal places, will not favor any sequence of numbers over any other. Discrepancies besides the nines exist if one just examines a limited number of decimal places of π. For example, in the first million places, there are 811 more fives than sixes.

## The Einstein Connection to π Is More Than Just a Birth Date

The most famous equation in all of physics is E=mc^2. We can re-write the equation as c^2=E/m, a definition of the speed of light. Just as π is defined as the ratio of the circumference of a circle to its diameter, so the speed of light can be defined as the square root of the ratio of the Energy of an object to its mass. So let’s all raise a glass to π, c, and Einstein.

The most appropriate time to do this would be on Pi Day, March 14, at 1:59:27, which would be the Pi Second. Cheers.

Leslie R Storer says

Agreed, and what is the significance of π to Nature and to all the Pyramids around the world. It seems to me that we are taking a lot for granted, and that something still needs to be learned here/discovered. To much of a coincidence for my liking. When I see the Pyramid of Khufu built out of stone and is real, built on the ratio of π, I ask myself why and by whom and why at that location. I think someone is testing our intelligence and we haven’t found the answer as of yet. I believe there are probably many more clues on the earth and we have to find them to survive and figure out the purposes and meaning of it all. I am retired living in Thailand, feed me a bone so I can increase my knowledge and maybe help.

John Austin says

I think the comparison with Fermat’s last theorem is misleading. Fermat’s last theorem was believed to be true before it was mathematically proven, because nobody could find anything to contradict it, i.e. there was evidence. Statistically you can show that the digits of pi are randomly distributed out to a million decimal places or more. The differences you quote between digits are entirely to be expected on the basis of a binomial distribution, with variance sqrt(npq), where p = 0.1, q = 1 – p = 0.9 and n = 1,000,000. If you’re going to hint that the digits of pi may not be randomly distributed you need to supply evidence. Otherwise this is sensationalism.