Mathematician Research Paper Archimedes

Mathematician Research Paper: Archimedes

It is no mystery that without the Ancient Greeks, math as we know it today would not be the same. It is mind blowing to think that people who had no access to our current technology and resources are the ones who came up with the basic principles of the mathematics that we learn and use today without any preceding information on the topic. One of the best examples of such a person is Archimedes. Not only did he excel as a physicist, inventor, engineer, and astronomer, but he is still known today as one of the greatest mathematicians of all time. His contributions to the field laid out many of the basics for what we learn today and his brilliance shocked many. Long after his time, mathematicians were still stumped as to how he reached the genius conclusions that he did. Nicknamed “The Wise One,” Archimedes is a person who can never be forgotten.

Archimedes is said to be born in Syracuse, a Greek City State in the island of Sicily, around 287 B.C. ("The Archimedes Palimpsest") His great level of intelligence was not totally surprising due to the fact that he was the son of Phidias who was a mathematician and astronomer himself. Some people believe that Archimedes may have been related to Hiero II, the King of Syracuse at the time, but it cannot be confirmed. ("Famous

Scientists") Although not much is known about Archimedes’s life outside of his work, it is said that he had an extremely curious mind and often studied with no clear purpose. When he had learned all that he possibly could from his teachers in Syracuse, he decided to travel to Alexandria to further his research. Located in Egypt and founded by Alexander the Great, Alexandria was reputed to be a great place for learning and furthering your knowledge of things. He studied there for some years, often sending his ideas in letters to his friend Eratosthenes, another brilliant mind, and then returned to Syracuse where he went on to make some of the greatest inventions and theorems of all time.
The majority of the contributions that Archimedes made to math were formed using his Theory of Exhaustion. With this method, he would develop a range in which the exact answer to a problem would be in and look for solutions that fell into that range. (Shuttleworth, Martyn) One of the most important discoveries that he made using this method was the first accurate value for pi. He did this by calculating the circumference of two ninety-six sided polygons, one outside and one inside of a circle. He purposely used polygons with so many sides so it would closely resemble the shape of a circle and concluded that pi was a value between 31/7 and and 310/71 which, as we now know, is very accurate. This discovery was extremely important and is something that is sure to be on the curriculum of most high school math students. I have learned about and used pi in algebra, geometry, and calculus. It can be used in real life for many purposes, an example being everyday telephone and radio use. In order to hear someone’s voice on the radio or phone, you need to use sine waves which have “a fundamental period of 2*pi.” To process sounds, engineers use frequency graphs that are displayed in multiples of 2*pi. (Keith)
Another one of Archimedes’s most famous contributions to the field is becoming the first person to calculate the volume and surface area of a sphere with proof that his formulas were correct. He is said to have thought of this as his “greatest personal achievement.” (“Famous Scientists”) He achieved this task by once again using his Theory of Exhaustion, deciding that by using a cylinder that had the same circumference as a sphere cut in half, he could get the formula for the surface area. To calculate the volume, he used a cylinder once again, determining that “the volume of a sphere is ⅔ that of it’s circumscribed cylinder.” (Shuttleworth, Martyn) These two formulas are extremely important and constantly used to this day. I learned about them in geometry class and used them throughout the year for multiple things. Both formulas are used to do numerous things that are a normal part of our lives. For example, a toy maker would use the formula for the surface area of a sphere to calculate the amount of material they would need to make a toy ball. Also, pharmacists need to calculate the volume of sphere shaped pills in order to put the correct dosage of medication in them.
Adding on to his list of achievements, Archimedes invented exponents. When he heard people say that there was no way to calculate the exact amount of the grains of sand on a beach, he decided to challenge himself. By inventing exponents, he could calculate exactly that and much more. He did this by making orders such as a first order, second, etc. Exponents are constantly used throughout the world every single day. I first learned about exponents in algebra class but used them afterwards in calculus as well. People in the real world use exponents for numerous purposes including everyday calculations for extremely large numbers such as calculating the population of people on this planet.
In conclusion, Archimedes has contributed tremendously to the field of mathematics.

Although I only mentioned three of his most famous contributions to math, there are many more. Archimedes was the person to prove that the area of a circle was equal to pi multiplied by the circle’s radius squared. He also calculated the volumes of parts of many other shapes including spheroids and conoids. The things that he came up with with little to no prior information to work with are used to help millions of people do different things. He was one of the most brilliant minds the world has ever known and without his work, math would not have come as far as it has

today.