Archimedean Principle-
Legend has it that: During Archimedes's life, a king consulted him to find out whether or not his crown was made of pure gold. Archimedes pondered of this question for a while. One day, when he went to the bath houses, Archimedes noticed that the water level rose when he submerged his body. this gave him such an inspiration that he ran out of the bath house and through the streets yelling "Eureka, Eureka" which means "I've got it, I've got it". He was happy that he forgot to put on and clothes!
Measurement of Pi-
Archimedes calculated the value of pi in his book Measurement of a Circle. He made his estimate by taking a circle and drawing a polygon inside. All of the angles touched the circle. He also drew another polygon outside of the circle. In the polygon, all of the line segments touched the circle. Archimedes used his knowledge of triangles to create a formula to calculated the perimeter of the polygons. He knew that pi was larger than the perimeter of the inner polygon, and smaller than the outer one. In the end, he had a 96 sided shape both inside and out. From this, he calculated that pie was smaller than 3 1/7 and and larger than 3 10/71. That means that he calculated pi as a number between 3.1428 and 3.14o8. The actual number of pi is 3.1415926535897932384626...!
On the Sphere and Cylinder-
Archimedes stated that a sphere and a cylinder that are the same height and width have a relationship in surface area. This "relationship" is that the ratio of the surface area of the sphere and cylinder is 2/3. This means that the surface area of the sphere if 2/3's as great as that of the cylinder. You can figure this out in three steps. (this is the same ratio for the volume of the same objects)
1. Calculate the surface area of the sphere using the following formula- 2╥r2.
2. Calculate the surface area of the cylinder using the following formula-2╥r2 + 2╥rh.
3. Calculate difference in values by making a fraction of the two numbers. You will be able to simplify down to 2/3.
Archimedes had any important discoveries. I did not list all of them for the fact that the list would be "a mile long". To find out more about Archimedes and his brilliant discoveries, go to your local library and take out books. I recommend:
*Archimedes and His Wonderful Discoveries- Arthur Jonas
*Archimedes, the Father of Mathematics- Heather Hasan
*Archimedes, Mathematical Genius of the Ancient World- Mary Gow
