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The Romans finally invaded Syracuse and overtook the city Archimedes was drawing circles in the dirt. When a soldier commanded Archimedes to surrender, Archimedes instead drew his sword and told the soldier that he wanted to finish the proof he was working on before surrendering. The soldier became angry and killed Archimedes. This shows that Archimedes was so committed to his expertise that he took the chance to dying in order to work on his last problem. Archimedes was so thoughtful with the study of math, and because of it, it led to many important discoveries and principles for us today.

There are 13 Archimedean solids. Although they are named after their discoverer, the first surviving record of them is in the fifth book of the Collection of Pappus of Alexandria. The duals of the Archimedean solids (made by replacing each face with a vertex, and each vertex with a face) are commonly known as Catalan solids. Apart from the Platonic and Archimedean solids, the only other convex uniform polyhedra with regular faces are prisms and antiprisms. This was shown by Johannes Kepler, who also gave the names generally used for the Archimedean solids.

Archimedes produced formulas to calculate the areas of regular shapes, using a revolutionary method of capturing new shapes by using shapes he already understood. For example, to estimate the area of a circle, he constructed a larger polygon outside the circle and a smaller one inside it. He first enclosed the circle in a triangle, then in a square, pentagon, hexagon, etc, etc, each time approximating the area of the circle more closely. By this so-called “method of exhaustion” (or simply “Archimedes’ Method”), he effectively homed in on a value for one of the most important numbers in all of mathematics, π.

He did not just study existing literature involving mathematics, but he also initiated and pioneered a number of fields of science such as hydrostatics, pycnometry and static mechanics. He also did a lot for integral calculus and mathematical physics, so much so that he is called “the father of integral calculus” and “the father of mathematical physics”. His findings, theories and results of his studies are forever preserved in his published works that include The Sandreckoner, On Spirals, On Conoids and Spheroids, Quadrature of the Parabola, On Plane Equilibriums, On Floating Bodies and Measurement of a Circle.

Archimedes is credited to have estimated the value of pi, a factor used in calculating the area of circles and volume of spheres and cylinders. He was able to prove that the area of a circle is actually equal to pi multiplied by the square of the circle’s radius. He was able to achieve an accurate estimation of the value of the square root of 3. He was also able to prove that the surface area and volume of a sphere is 2/3 that of a cylinder, including the bases. He had many other mathematical achievements in higher mathematics such as geometry, trigonometry and calculus.

The Archimedes Screw was also developed due to a task given by King Hieron II. Archimedes is said to have been asked to make sure that a huge ship called Syracusia would not sink due to excess water in each hull. The Archimedes Screw was designed to remove this water. It was turned by hand. It looks like a tube with a screw-shaped blade within. This type of screw is still used today to pump liquids.

Archimedes inventions include great works like the golden crown, Archimedes screw, Archimedes heat ray etc. His other inventions include block and tack pulley, principle of leverage, odometer etc. Archimedes though not the inventor of lever, had a great insight into the principle of lever and said that ‘Give me a place to stand on, and I will move the earth’.

As a young man, Archimedes is believed to have studied in Alexandria, Greece. In his writings, he mentioned that he knew many Alexandrian mathematicians. In fact, he considered a man named Conon of Samos, also a mathematician, as his close friend. In his writing entitled “On Spirals”, Archimedes related an event in Alexandria wherein some mathematicians would claim his work as their own. Therefore, instead of sending real proofs of theorems, Archimedes included two false proofs, in order to discourage those who pretended to know but really did not understand.

Born in the beautiful seaport of Syracuse Sicily, Archimedes is famous for his birth land and is commonly known as Archimedes of Syracuse. Though we do not possess any personal details of this great man, Plutarch in his work Parallel Lives, mentions the relation between Archimedes and the ruler of Syracuse, King Hiero II. It is said that they were relatives and fast friends and hence Archimedes was compelled to invent war machines and equipments to protect Syracuse against the Roman siege.

Archimedes was born in Syracuse, Sicily around the year 287 BC. Little is known about his family, only that his father was named Phidias. It is thought that his father, an astronomer, was related to the king of Syracuse at that time, Hieron II. As for whether Archimedes married and had children, nothing is certain. It is suspected that he studied in Alexandria, Egypt and he was probably a student and follower of Euclid.

The most famous story of Archimedes life involves the discovery of Archimedes' Principle. The story begins when King Hieron asking a goldsmith to construct a gold wreath to the immortal gods. After some time, the king came to suspect that the wreath was not pure gold but rather filled with silver. In order to end his suspicion, the king asked Archimedes to determine whether the wreath was pure gold or filled with gold without destroying it. Archimedes agreed to try to solve the king's problem. Then one day, while he was taking a bath, Archimedes noticed that the water level rose in the bath as he entered the water. Archimedes was so excited by this discovery that he jumped out of his bath and ran naked through the streets yelling, "Eureka, Eureka!!” meaning, I have found it. Archimedes had discovered that a body immersed in a fluid displaces its weight of fluid. This principle in turn helped Archimedes prove that the gold wreath was not solid gold.

Allison Chen

61 Knowledge Cards

I had to make the 13 Archimedean solids for a school assignment. They are all actually truncated versions of the 5 platonic solids and of themselves, despite their completed words (like rhombicosadodecahedron). Here is a great chart that organizes all of the polyhedra. http://www.friesian.com/polyhedr.htm