# Achievements of Archimedes in context

Hello everyone! Hello! I am 황다은 and I am very small! In this presentation I want to explore the achievements of ancient Greek scientist Archimedes. One is that he discovered the principle of buoyancy. Two he studied the idea of the lever. And three he helped to develop geometry. Even though he lived more than two thousand years ago, our lives are more convenienttoday because of his ideas. His story of a scientist using his brain to defend a city against thousands shows the power of the human mind over weapons.

On the handout you can see that Archimedes lived on the island we call Sicily in the third century B.C. He was a mathematician and inventor. In his active years there, he lived during the Second Punic War, the war between Rome to the north and Carthage to the south. After his father King Hiero the First dies in 215 BC, his son, King Hiero the Second, switches sides and allies Syracuse to Carthage. Rome then assaults Syracuse using its navy by Marcellus. Archimedes’ outstanding brain terrified the Roman navy with original ideas like a giant crane. After a few years of harassing, Rome managed to invade and in 212 BC Archimedes, intense thinker, was killed by a Roman soldier.

Archimedes scientific achievements in that time were amazing. One, he understood the idea of buoyancy. Look at figure 2. Buoyancy is the result of the force of gravity pulling a block down and the force of water pushing the block up. The story is that one day the king asked him to inspect a crown of gold. Suspecting that the crown was not pure, he asked Archimedes to discover how much without destroying it. Archimedes did not know the answer and went to a bathhouse to think. He noticed that the water brimmed over when he stepped into it. Then he immediately shouted ABOUT HIS GREEN CARDS and ran home. He compared pure gold to a mixture of gold and something else and found the pure gold is heavier and pushes less water out. The lighter metal pushes more water out because it is less dense, so the volume will be bigger. Because the volume is bigger, the buoyancy force is bigger, the density is lower. When he compared gold and the crown, the crown pushes more water out and so there was less gold in it! By using this principle Archimedes found out the cheat! Two, Archimedes understood the principle of the lever, as shown in figure 3. He didn’t invent it but understood how to use it effectively. The principle is the distance between the supporting point and each point multiply with force is same. So, we can hold the object more easily if we understand the multiplication between distance and weight on one side and other. Heavier objects can be lifted with less force, but need a longer distance to do so. After knowing his he said to King Hiero, “Give me a place to stand on, and I will move the earth!” Using this idea, he defended Syracuse for Hiero by building cranes and catapults to harass the Romans, using the physics of the lever.

Three, he helped develop geometry. Geometry is the study of the relationship of the sizes and angles of lines and shapes. It is that the volume and surface area of a three-d circle or sphere is two-thirds that of a cylinder if they have the same height and diameter. Also, he could find how to find a parabola, which is a type of curved path that doubles in one direction but not in the other. Archimedes found on Syracuse that the shapes’s area which is surrounded by parabola and straight lines is the same as three-fourths of the triangle. If we draw a triangle and a circle, the shape divides into two parts. Se we can draw two triangles again. Repeating the process, the parabola is one. Archimedes was talented in playing with such abstract ideas.

But, what I talked about is only a small part of his achievements. But, anyway, the point is that he did all of this with motivation, creativity, and different style of thinking. Other Greek philosophers HATED HIM for this and called him A CHEATER and WEIRD. When he studied the number Pi, he drew larger shapes outside the circle and smaller ones inside those shapes. It had 96 sides. He did much to improve the number Pi.

Buoyancy, the lever, and mathematics have made our lives more convenient because of him. His work in weapons, those he was just a scientist, shows us how “the pen is mightier than the sword.” I found this information from the books, articles, and pictures listed in the handout. Everybody, have a wonderful night!

## See also

## Notes

- Livius, pp. 233-4, 295
- Walbank, p. 39
- Photo courtesy Wikipedia