Archimedes was one of classical Greece’s best mathematicians, physicists, and inventors. He revolutionized the modern understanding of geometry, trigonometry, military mathematics, and physics. His concepts and theorems have effected every part of modern math and technology. However, through all these discoveries and all these titles and achievements, we know very little about who he was as a man. Because of this, he is strictly known as a natural scientist (physicist) and a mathematician, though these hobbies and endeavors still show some of his nature. We know him to be proud about his findings, vocal in their possibilities, and thoroughly able when backing up these possibilities with action and experiment. He was a master of applied physics with a strong reputation for success.[1]

Insight and Influences
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Archimedes lived and died in Syracuse from about 287 BC - 212 BC, though he was believed to have been educated in Egypt as a youth and young adult. Archimedes served as the military engineer for Syracuse during the second Punic wars, and many of his most important inventions both stemmed from this profession and delayed the Roman advance for a number of years. For example his self-named, Archimedes Screw³ was designed to aid Syracuse sailors in removing water from ships’ hulls. King Heiron of Syracuse is also said to have contributed to Archimedes’ discoveries. Because of the mathematician’s astounding reputation, King Heiron called on him often, giving him various tasks, which lead to numerous discoveries. Although he was an accomplished engineer, most of Archimedes’ contributions were self-motivated studies of math for the sake of studying math. His research on proportions of bodies as well as the majority of his math based discoveries had little inspiration except his own determination.

Major Contributions

In science classes and laboratories around the world, students and scientists find the volume of oddly shaped objects using a method currently called displacement³ . Archimedes is accredited with the discovery of this method of measurement, and, like most of his discoveries, this discovery accompanies an anecdotal story. King Heiron was given a crown, and wished to know if it was made of real gold. The problem with this commission was that Archimedes could not damage the crown or melt it down to find its mass. He quickly became perplexed and frustrated after much trial and error. One day, while taking a bath, he noticed that the water rose and fell as he got in and out of the bath. With a shout, he ran through the streets, naked, too excited to have put his clothes back on. Archimedes was one of the ancient fathers of modern math and geometry. His contributions form much of the college and high school curriculums for advanced math and geometry. When commissioned or challenged, Archimedes worked extensively with pulleys, levers, and physics, adding his creativity and knowledge to the growing machines of natural philosophy.

Affect and Effect

A Tanagram. Archimedes created a Stomachion, which is a similar puzzle comprised of Geometric Shapes. Image courtesy of
Archimedes achieved many great heights and made an abundance of new mathematical, geometrical, and physics based discoveries. Sadly many of his works are missing, either lost or destroyed. He was the architect for the Syricusia¹ , the largest ship of all ancient times- now decomposing wreckage at the bottom of the Mediterranean. He wrote a number of papers similar to the modern thesis called treatises. Some of his most famous treatises² included The Sand Reckoner, On Floating Bodies, On Conoids and Spheroids, and On Spirals -in which he states his discovery and understanding of his "Spiral of Archimedes² ." One piece of work with lasting effect and inspiration was Archimedes' Stomachion³ , a puzzle that he created similar to the modern Tanagram. The puzzle intrigued him, and he set about discovering how many ways it could be arranged in a square. Little oddities such as this show that the mathematician devoted his life to geometry and the maths. It was from study and learning that he drew his joy. History leads only to conclude that this was his only love. Though, history allows us to guess. There are no recorded documents remaining that give insight as to who Archimedes really was as a man. We do no know whether or not he was married or whether he had children. The only time he mentions family is when he mentions his father in The Sand Reckoner, Phidias¹ , a no-name astronomer. His father was likely an inspiration for Archimedes' adult studies on spheres. Archimedes' specific political views are lost with his history, but he faithfully served King Heiron for most of his adult life. Countless fables tell about how Heiron challenged Archimedes again and again eliciting some new discovery about the workings of natural philosophy. Provided the fables are true, King Heiron need be credited also with assisting the advancement of math and physics.

The Things He Left Behind

Look at any new text book in almost any school and on the cover of each will likely be a piece of photography or a graphic rendering of one of the
This Nautilus Shell contains the Spiral of Archimedes. Image courtesy of Crop Circle Geometry
concepts that Archimedes developed. The Spiral of Archimedes is a popular image for this, seen in the nautilus shell and many other natural formations, but any spirals- any complex loops or radial designs- are in some way descended from the Father of Geometry's original findings. His spiral, and the understanding of it,
help to make the high g-force loops and spins of large roller coasters that thrill seekers find in amusement parks around the world. An artistic theory states that the human eye sees more beauty in this shape than in others.
Another of his rotating forms, the Archimedes screw has a wide plane of modern uses. From the oil fields to science laboratories, and from ship hulls to fast food restaurants, the Archimedes screw has become a crucial part of the day to day life of millions. The simple machine brings oil from miles below the surface to be refined and used, but also churns the earth for hundreds of villages in third-world countries to provide them with water for drinking, bathing, and crops.
Mathematics text books today, while ornamented with the fruits of his findings, are stuffed full of concepts that Archimedes studied, furthered, and even developed. Parabolas, spheres, spirals and a large number of other complex shapes and figures grace the pages of geometry, trigonometry, and calculus books around the world. From these text books, students learn and grow and become productive scientists, engineers, inventors, and teachers, creating our entire world.


1. The Mathematical Achievements and Methodologies of Archimedes