Archimedes’ Constant And March 14

For many sports enthusiasts March 14 is the day before March Madness begins. For many others globally it is Pi Day—not for the lovers of pies but for the lovers of mathematics.

Of course, one could have their glorious (π) and eat their delicious pie as well if they choose. Nothing on this planet traversing the cosmos would prevent that sumptuous duet.

A smidge about this sui generis day founded by Physicist Larry N. Shaw at the Exploratorium in San Francisco:

Founded in 1988 at the Exploratorium, Pi (π) Day has become an international holiday, celebrated live and online all around the world. The numbers in the date (3/14) match the first three digits of the mathematical constant pi (π).

What is π, anyway? Divide any circle’s circumference by its diameter; the answer (whether for a pie plate or a planet) is always approximately 3.14, a number we represent with the Greek letter π. Keep calculating π’s digits with more and more accuracy—as mathematicians have been doing for 4,000 years—and you’ll discover they go on literally forever, with no pattern.

Greek Letter π

The mathematician Archimedes used polygons with many sides to approximate circles and determined that Pi was approximately 22/7. The symbol (Greek letter π) was first used in 1706 by William Jones. A ‘p’ was chosen for ‘perimeter’ of circles, and the use of π became popular after it was adopted by the Swiss mathematician Leonhard Euler in 1737. In recent years, Pi has been calculated to over one trillion digits past its decimal. Only 39 digits past the decimal are needed to accurately calculate the spherical volume of our entire universe, but because of Pi’s infinite & patternless nature, it’s a fun challenge to memorize, and to computationally calculate more and more digits.

Archimedes’ Constant

One of Archimedes’ many significant contributions to mathematics was his approximation of the value of pi. He was the first mathematician to establish a theoretical calculation for pi instead of an estimation. By inscribing and circumscribing polygons on a circle, he was able to constrain the value of pi between 3+10/71 and 3+1/7.

Rather than trying to measure the polygons individually, he used one of Euclid’s theorems to develop a faster numerical procedure. This process enables one to get a result as accurate as desired. It is a unique idea because he eliminated the geometrical aspect of it and turned it into an arithmetic procedure. Throughout Archimedes proof for this process, he makes references to several square roots. He does not say where he got the approximations. This premature ability to calculate irrational square roots is remarkable.



Another slice of March 14 is the birthday of another physicist—Albert Einstein. This is another harmonious duet.

On Star Trek: The Original Series’ episode Wolf In The Fold dealt with Pi in a very “fascinating” fashion. An ageless, violent entity takes over the USS Enterprise’s computer system, and Mr. Spock comes up with an innovative way to defeat it.

Mister Spock: “Computer, this is a class A compulsory directive. Compute to the last digit, the value of pi.”

Of course, even the 23rd Century starship’s computer cannot calculate the endless value of Pi. The entity is driven from the computer back into its dead host and transported into the cosmos where hopefully its atoms would be beneficial instead of malevolent in their eventual reformation.

Before March Madness begins as well as St. Patrick Day, explore Pi Day with its numerous components. If so inclined, have a piece of your favorite pie from the bakery or homemade.

G. D. Williams © 2020
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A Slice of Pi (π) Day History

Physicist Larry N. Shaw

Until his passing in 2017, Shaw, affectionately known as the Prince of π, led π Day parades yearly at the Exploratorium. Today, the Exploratorium continues the tradition by hosting an annual π Day, a public celebration that features a π-themed activities, antics, rituals, and—and, of course, plenty of pie.

One of the first details we read about Archimedes (287-212 BCE) in almost every account of his life is the famous scene where he runs wet and naked through the streets of Syracuse shouting “Eureka!, Eureka!” (“I have found it!”). This nudist episode, however, fails to capture the respect that the life of the greatest Greek mathematician and mechanical engineer of antiquity deserves. Archimedes was a pioneer in mathematics and engineering, many centuries ahead of his contemporaries. He was the son of an astronomer named Phidias, lived in the Greek city of Syracuse, studied in Alexandria under the successors of Euclid, and was on intimate terms with King Hieron II, the ruler of Syracuse.

During the Roman conquest of Sicily in 214 BC Archimedes worked for the state, and several of his mechanical devices were employed in the defense of Syracuse. Among the war machines attributed to him are the catapult and – perhaps legendary – a mirror system for focusing the sun’s rays on the invaders’ boats and igniting them. After Syracuse was captured, Archimedes was killed by a Roman soldier. It is said that he was so absorbed in his calculations he told his killer not to disturb him.

Not much information about his personal life is available but historians believe that he breathed his last somewhere around 212 B.C or 211 B.C. This was when Syracuse was conquered by Roman general Marcus Claudius Marcellus and Archimedes was killed by a Roman soldier.

Archimedes was working on a mathematical diagram when a soldier approached him saying that the general wanted to meet him, but he refused saying that he had to finish his work first. This enraged the soldier and killed Archimedes with his sword.

Going by Plutarch, Archimedes might have been killed while he was surrendering to the soldier. Archimedes was carrying mathematical instruments which the soldier interpreted to be precious gems.

As pi is an irrational number – there are an infinite number of digits after the decimal point that never repeat – we will always be able to calculate new digits. Even though we have done this for trillions of digits of pi, we still aren’t sure if some digits appear more often than others.

If no digit of an irrational number appears more frequently than any other when written as a decimal, it is called “normal”. A lot of people are interested in the normality of pi, but proving it either way is unlikely to have much real-world impact, says Wadim Zudilin at the University of Newcastle in Australia.

“We care more about pi itself, because it’s so famous, that solving another arithmetic mystery of this number is an attractive task,” he says.

With trillions of extra digits to play with, Trueb examined what the distribution looked like. “Each of the numbers from nought to nine appeared 10 per cent of the time, which is what you would expect if pi is normal,” says Trueb.

Star Trek The Original Series: Wolf In The Fold

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