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.
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.
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.