Number Theory

Question: What ancient mathematician from Syracuse in modern-day Sicily is credited with making the first calculation of “pi”?

Answer: Archimedes

Anyone can measure a slice of pie. But calculating the value of “pi” is something that eluded mathematicians for thousands of years. Archimedes of Syracuse (287–212 BC), arguably the greatest mathematician of the Ancient World, is credited with creating an algorithm that calculated the first few decimals in pi—a breakthrough that would begin the never-ending calculations of this never-ending number.

At first glance, it doesn’t sound all that complicated. You start with a circle. Then you measure its outside (the circumference). Then you measure the distance across the circle’s widest point (the diameter). Divide the circumference by the diameter—but what you get is a series of decimals that go on forever without repeating themselves, making it impossible to calculate the actual value completely. Adding to the mystique of pi is that no matter how big the circle is, the value is the same. Knowing that ratio has remarkable applications in geometry and physics. It’s crucial in things like calculating the area and volume of circles, spheres, cylinders, and cones. Without it, NASA wouldn’t have gone to the moon.

The whole concept of pi didn’t originate with Archimedes, however. It is believed that Babylonian and Egyptian cultures had introduced the concept all the way back in 2,000 B.C. So, what was Archimedes’ big breakthrough? What he did was draw a hexagon in a circle. Then, he doubled the sides until he had a 96-sided polygon inside the circle. Using this method, he was able to conclude that pi was greater than 3.14084 and less than 3.14286—which is an extremely close approximation of the actual value of pi, which is 3.14159265 ...

By calculating its upper and lower limits, Archimedes was the first mathematician to bound pi this way. While refinements were made down through the years, no one would improve upon his method of using inscribed and superscribed polygons for calculating pi for another 2,000 years. Archimedes is credited with turning the search for the value of pi into a science.

It wasn’t until early in the 18th century that the symbol “π” was introduced to represent the magical ratio we call pi. In Archimedes’ day, it was known as quantitas in quam cum multiflicetur diameter, proveniet circumferencia—medieval Latin for “the quantity which, when the diameter is multiplied by it, yields the circumference.” (That batch of words seems to stretch almost as long as pi itself!)

As for Archimedes, he deserves a few more words because pi was just one of his many discoveries and inventions that have stood the test of time.

Archimedes by the numbers ...

Archimedes was born in Syracuse (then, a Greek colony), on the island of Sicily, around 287 B.C. His father, Phidias, was an astronomer and mathematician. When he turned 18, Archimedes traveled to Egypt to study at the Library of Alexandria, the center of the scientific world at the time. After returning to Syracuse, he would spend the next fifty years developing a series of groundbreaking theories that covered a wide range of topics including the fundamental principles of mechanics; methods for finding the center of gravity, surface area, and the volume of geometric figures; the principle of buoyancy; and of course, an estimate for the value of pi.

By all accounts, Archimedes was obsessed with math. Like our vision of the typical absent-minded professor, he was heavily bearded, cared nothing about clothes, would often forget to eat, and seemed to always be lost in thought. When he discovered his principle of buoyancy while taking a bath, he was so excited, he leaped out of the tub and ran naked through the streets of Syracuse shouting, “Eureka! Eureka!” 

His head may have been in the clouds, but Archimedes also had a sense of humor. He often sent his theorems to associates in Alexandria, but there were a few mathematicians he felt were arrogant. Knowing they were likely to claim credit for his discoveries, Archimedes would slip in a few false propositions so when they tried to pawn them off as their own, they would repeat some theorems that were impossible.

He was the Da Vinci of the Ancient World

Archimedes isn’t just known as the greatest mathematician of the Ancient World, he is also known as the greatest inventor of the Ancient World. When he wasn’t solving the most complex mathematical problems of the day, he was inventing things like the Archimedes screw, a device for raising water. Back then, it was used to pump water out of ships and for irrigation, but the design is still used today.

Archimedes also invented a batch of devices to defend a city called his “engines of war.” Coming in handy during the Roman invasion of Syracuse, these included cranes to drop rocks, giant claws to lift ships out of the water, and machines that fired wooden missiles. He also came up with a set of mirrors that focused sunlight on enemy ships to set them ablaze. Unfortunately, it was during that same siege of Syracuse in 212 B.C. that Archimedes met his untimely end—and his math obsession is partly to blame for it.

An account by Greek philosopher Plutarch said that Archimedes died while solving a math problem. The Roman general in charge of the siege had forbidden his soldiers to harm Archimedes due to his stature, but he was killed by a Roman soldier who confronted Archimedes in his study—completely oblivious to a battle raging around him. His last words are said to be “Nōlī turbāre circulōs meōs!,” which translates to “Do not disturb my circles!”—a reference to the geometry problem he was working on.

With his boldness and vision, the theorems Archimedes discovered raised mathematics in the Ancient World to a new level of understanding. His ideas deeply influenced the birth of modern science. More than any other scientist of the Ancient World, Archimedes inspired everyone from Galileo to Albert Einstein. When talking about the three greatest mathematicians that ever lived, many scholars include Sir Isaac Newton (1642-1727), Carl Friedrich Gauss (1777-1855)—and Archimedes (287-212 B.C.). 

Whether your thing is numbers or the baked variety, you can’t go wrong with pi/pie day, no matter how you slice it.

A few more servings of pi trivia for number lovers out there

·        That’s not rational—Pi is classified as an irrational number, which means that its decimal representation goes on endlessly without repeating. But for most applications, it isn’t necessary to calculate the value of pi to infinity—scientists at the Jet Propulsion Laboratory (JPL) only calculate it to the 15th decimal (3.141592653589793) for accuracy. Using just 39 places past the decimal of pi enables scientists to determine the spherical volume of the entire universe.

·        See how pi measures up—Rounding pi to just 9 digits after the decimal point to calculate earth’s circumference yields incredibly accurate results. For every 25,000 miles, the error will be just one quarter of an inch.

·        Birthday pi—It seems somehow fitting that two of the world’s most legendary minds had associations with Pi Day: Albert Einstein was born on Pi Day, March 14th, 1879, and Stephen Hawking died on Pi Day, March 14, 2018, at the age of 76.

·        Even nature loves pi—Pi appears in many unexpected places in the natural world, from the structure of spirals in seashells and galaxies to the shape of rivers and frequencies of musical notes.

·        I have trouble memorizing my phone #—The record for memorizing the greatest number of decimal places of pi was achieved by Rajveer Meena at VIT University, Vellore, India, in 2015. He was able to recite 70,000 decimals while blindfolded for the duration of his recall, which took 10 hours.

·        Got you beat!—As impressive as someone memorizing Pi to 70,000 digits, the current record for calculating pi on a computer stands at 62.8 trillion decimals.

·        Tech support—One of the most crucial roles for pi in the modern era is in technology, especially for computer algorithms and cryptography. The unending and non-repeating digits of pi serve as building blocks for secure communication and efficient computation.

·        Pi goes on trial—In the O.J. Simpson trial, the defense attorney and an FBI agent squared off over the value of pi. An FBI agent’s argument about a piece of evidence revolved around the value of pi—but his findings hit a snag after he was shown by the DA that he used pi inaccurately. 

·        Highly illogical—In an episode of Star Trek, Spock outsmarts an evil computer by challenging it to calculate the final digit of pi.

·        Pi talk—The best advice we can give anyone on Pi Day is to try not to start a conversation with anyone about it. Why? Because it will go on forever ...

Visit the birthplace of Archimedes during Sicily’s Ancient Landscapes & Timeless Traditions.