Thursday, July 23, 2009

A meditation on Archimedes to satisfy the needy

Why Archimedes is Awesome

  • Started calculus
  • Made the best estimate of pi up to that time
  • Was completely in love with math

Archimedes has always been a figure who impressed and intrigued me. I got an opportunity in 11th grade to really explore him and that led me to writing an essay on him and the depth of his love of math. His life is a model of beautiful passion, something we are all capable of but which many of us are afraid to explore.

An essay for American Literature class

Written 1/1/02

Few men have understood the glory of living. Thorton Wilder calls those few “poets and saints.” While not all poets and not all great men truly understand this glory, some understand and that is what compels them to do great things. They understand that every moment is worthwhile, that the grimmest part of life is still life and is still beautiful. Most will never have that understanding, most understand only after they can look back on their entire life, and that can only happen at death. “It takes life to love Life,” Edgar Lee Masters once wrote. And for most that is true, but for a very few, understanding comes naturally and it makes them glorious. One of these great men was Archimedes1 of Syracuse. He was an ancient Greek mathematician, considered to be one of the three greatest mathematicians of all time2 (Golba, online). He revolutionized math in the ancient world and his contributions directly inspired new discoveries more than a 1000 years after his death. The elegance and beauty of math and pure logic amazed him. He was always contemplating the magnifigance of the universe in his symbols and numbers. He loved truth, understanding, and figuring out things. Math was his passion and he served his passion well (O’Connor and Robertson, online). Archimedes will always be remembered, because he could connect a grain of sand with the universe, and figure the mind of God plus or minus a sin function. Archimedes understood the beauty of life and that made him a very great man.

Archimedes was born around the year 287 BC. His father, Phidias, was a Greek astronomer, and he raised him in a house of math (Bendick 1). His city was Syracuse, a major city on Sicily, and a bustling seaport. He was likely related to the king of Syracuse, King Hiero II (Rorres, online). This suggests that he was moderately wealthy and so it’s not surprising he had enough to travel to Alexandria to study math in all its shapes and forms (Bendick 24). Math as a science was just beginning (Benedick 16). However, it was growing and mathematicians were gathering their information together in Alexandria; thus started for the first time a mathematical community (Bendick 26). Archimedes joined this community and dug in to every field he could. This was the beginning of Archimedes’ long and amazing career in math. He began sending out work to his colleages and gained a reputation for being top-notch. He eventually left Alexandria, leaving behind a considerable legacy including the Archimedes screw, an irrigation device (O’Connor and Robertson, online). He returned to Syracuse, but his math work did not stop. He became an expert engineer, revolutionizing the field of the lever, creating pulleys upon pulleys upon pulleys, and building some of the largest catapults the world had ever seen. He even once created, some say, a reflective mirror that burned enemy ships (Rorres, online). Most of his inventions went straight to the war room where King Hiero and his successors used them in Syracuse’s ongoing wars with Rome, a power just beginning to bloom (Golba, online). Archimedes’ inventions3 saved Syracuse the initially from a powerful seige, but Syracuse was taken by a suprise attack by Rome and was conquered (Rorres, online). Archimedes died when Rome took over Syracuse, killed by a soldier, despite orders that said to spare the mathematician’s life (Bendick 128).

While Archimedes was known for his inventions, that wasn’t his field of choice (Golba, online). His greatest works were in the fields of arithmetic, geometry, and physics. Nine of his works have survived, On plane equilibriums (two books), Quadrature of the parabola, On the sphere and cylinder4 (two books), On spirals, On conoids and spheroids, On floating bodies (two books), Measurement of a circle5, The Method, and The Sandreckoner. It is known that he did much more; his name is used in many, many works of his contemporaries and his successors. He developed the basis of integral calculus, he examined every geometric shape from the spiral to the circle. And yet Archimedes also treasured the ideas of others, using some of the newest of the time, like the sun-centered universe6 (O’Connor and Robertson, online). He loved ideas and the truth. Archimedes went far beyond just proving new math to be true, he wrote his methods down for the ages, and he also invented a new numeral system to express numbers that Greek numerals couldn’t. This number system came in handy when Archimedes calculated the number of sands of grain needed to fill the universe7, or at least the concept of the universe at the time (O’Connor and Benedict, online). This was not practical but it was a work of love, for Archimedes truly treasured the order and logic of the universe through math.

Archimedes’ art was math and he loved his art. Yet math is not an art of creation, it is an art of discovery. The laws of math have been true since the beginning of existence and Archimedes reveled in them. He would go without eating, start scribbling while bathing, writing down math as fast as he could. If he could ever find a surface to draw upon, even if it was simply the dirt with a twig he would start drawing figures (Golba, online). In the end these figures led to his death. Accounts of his death8 claim that he was scribbling math in the dust during the invasion of Syracuse when he was confronted by a Roman soldier, he told the soldier “don’t disturb my figures” and the enraged soldier killed him (Rorres, online). Archimedes was in such rapture about the joys of discovering new truth that he did not noticed the burning of his city around him. He did love his city and gave it some of his finest inventions, but math was his true love and so he could not waste time fretting over a city when the secrets of the universe were at stake. It was through this love that he loved life. He found that the universe had in it unlimited wonder and was continuously trying to find that wonder through math. His love of math was his love of life, his math was but an expression of life’s logic. Archimedes worked to his last moment, savoring every second, and then died forever a mathematician in love with the order of the universe.

Archimedes lived a life of math. Being a mathematician was nothing special especially with an astronomer for a father. Yet he is the greatest of all the mathematicians of antiquity, perhaps of all time. He figured out the relationship between the volumes of a sphere and a cylinder, he figured out the workings of water displacement, he understood the secrets of conics and a great deal more (Rorres, online). He was great, but what drove him was a love of math. This love of math was a forever wonder about the mysteries of life, and in this way Archimedes understood life.

1-Archimedes was his full name, most Greeks only had one name (Bendick 1)

2- The other two are Newton and Gauss (Golba online)

3-In addition to the inventions already mentioned Archimedes employed a large metal contraption that would rake ships at sea, he also booby traped the walls of Syracuse (Rorres, online)

4-This work concerned the ratio between the two and Archimedes requested that ratio be engraved on the door of his tomb (Golba, online)

5-In this book he calculated the most accurate pi at the time (Bendick 91)

6-Archimedes used the universe constructed by his father, Eudoxus, and Aristarchus, (O’Connor and Robertson, online). He later made a mechanical model of this universe that lasted 200 yr.s (Benedict 78)

7-the number of grains needed to fill the universe is approximately 8*10^16 (O’Connor and Robertson, online)

8-One account says he was carrying mathematical equiment that looked like gold and that is why he was killed (Rorres, online)

Works Cited

Bendick, Jeanne. Archimedes and the Door of Science. Warsaw, North Dakota: Bethlehem Books. 1995.

O’Connor, J. J., Robertson, E. F. “Archimedes of Syracuse.” January, 1999. University of St.Andrews. Online. Internet. Dec 21, 2001.

Golba, Paula. “Archimedes.” 1994. Interactive Real Analysis, ver. 1.9.3. Online. Internet. Dec 21, 2001.

Rorres, Chris. “Archimedes Home Page.” 1995. Drexel University. Online. Internet. Dec 21, 2001.

Good Archimedes links

Good overview

Lots of info

A Good starter

Archimedes writings

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