# Archimedes, A Mathematician With An Obsession

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*By Ashley Langham*

Archimedes was a Grecian mathematician, who was more famous for his mechanical inventions than his mathematical skills, during his time; yet, he was extremely skilled and enthralled with the study of geometry. He was also a skilled physicist, engineer, and astronomer.

He had many achievements in mathematics that led to modern day theories and studies. He famously calculated an approximate value of pi and his contributions led to the development of calculus.

One can still find his impact honored on the Fields Medal Award, an award for outstanding achievements in mathematics for young mathematicians. He is quoted saying, “Rise above oneself and grasp the world,” which is located at the bottom of the award.

Unfortunately, he was be so fixated by geometry, his obsession led to his murder. Read on to learn more about his work and life!

# Archimedes’ (287 BCE- ca. 212 BCE) Inventions

There is little known about Archimedes’ life because most of his personal writings were lost over the years. What we do know is that he was born in Syracuse, an island of Sicily. His father, Phidias, was an astronomer and likely influenced his son’s interest in the subject.

At some point in his life he had to have studied in Alexandria, Egypt, which was the ancient hub for science and mathematics, during his time. From his own writings that survived, he speaks of interacting and learning from his fellow mathematician friends and colleagues that were located there. Both Conon of Samos, a Greek astronomer and mathematician, and Eratosthenes, Chief Librarian at the Library of Alexandria, mentioned Archimedes in their writings as well, which would put him in Alexandria at some point during his young adulthood. However, at some point, he returned home to Syracuse and spent the majority of the rest of his life there.

What was known of Archimedes is that he was quite a talented inventor. He created an invention that was a screw for lifting water out of the ocean, that was later named after him. He also was instrumental in creating the war machines used to delay the Roman siege of Syracuse in 211 and 212 BCE. He also was attributed to have made a device that demonstrated the motion of the sun, the moon, and the planets in the galaxy; though the details of this device are somewhat uncertain.

He was supposedly commissioned by his town’s leader, King Hiero II, to find a method to properly assess the volume of an asset. Hiero II suspected that his goldsmith was cheating him out of making a solid gold crown for him. He suspected that his goldsmith used a bit of silver instead, which was a cheaper metal. Hiero II used Archimedes to find a method of determining whether his crown was solid gold or had bits of silver without destroying it. Archimedes devised a method for discovering the apparent scam by submerging himself in his bath water. He noticed from stepping into the bath, that the water levels rose, making it possible for him to measure volume. He was therefore attributed to have discovered the law of buoyancy. However, this story and the ability to measure volume was only attributed to Archimedes 200 years after the incident allegedly happened; written by Vitruvius, a Roman architect.

# Archimedes’ Mathematical Contributions

Archimedes made most of his contributions in the field of geometry. Apparently he wrote nine treatises, yet only fragments of two survived. In his *Measurement of the Circle* treatise, a fragment survived that measured the approximated value of pi between the limits of 3 10/71 and 3 1/7. He also states in this treatise that the area of any circle is equal to the area of a right triangle in which one of the legs of the right angle is equal to the radius of the circle and the other leg is equal to its circumstance.

In his *Sphere and Cylinder *treatise, he demonstrates that the surface area of a sphere is four times that of a great circle. It was his work in this treatise that makes him stand out the most as a mathematician. Despite how rudimentary mathematics was at the time, he was able to show the relationship between the volume of a sphere and that of a circumscribed cylinder.

In fact, in *Sphere and Cylinder *he gave instructions for his tomb to be marked with a sphere inscribed in a cylinder. However, no one knows the exact location of his tomb; though Cicero, a Roman philosopher, claimed he went there.

He also perfected upon two theories, the method of exhaustion and the reduction to absurdity. The former was a purely mathematical theory for finding the area, or volume, of a shape by inscribing it inside a sequence of polygons with increased numbers of sides. The latter was a philosophical theory whereby one attempts to disprove a statement by showing that it will lead to an absurd conclusion, i.e. 1=0.

# Archimedes Death by Geometry

Archimedes was fascinated by geometry; so much so he would often be so enthralled in the subject matter, he would have chosen studying geometry over bathing! Plutarch, a Roman writer, captures this adoration with this anecdote:

*“Oftentimes, [Archimedes] servants got him against his will to bathe, to wash, and anoint him, and yet being there, he would ever be drawing out the geometrical figures in the very embers of the chimney. And while they were anointing him with oils and sweet savors, with his fingers he drew lines upon his naked body, so far was he take from himself, and brought into ecstasy or trance, with the delight he had in the study of geometry”*

In 212 BCE, the Romans were in the process of capturing Syracuse in the Second Punic War. He was apparently captured while contemplating a mathematical diagram of circles. He was so entranced by his work, he turned down an ordered meeting with General Mercellus. He told the Roman soldier that summoned him, “do not disturb my circles.” Those would be his famous last words, because he was immediately killed because of his insubordination.

Since his death most of his work has been destroyed. We know a lot about his work due to other people’s written accounts. We know most of his work must have survived through the Middle Ages and the early Renaissance because: Galileo, Johannes Kepler, René Descarte, and Pierre de Fermat all wrote about Archimedes’ influence in their publications centuries later.

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