Great Scientists and their Inventions

Archimedes(Lived c. 287 BC – c. 212 BC)


Archimedes is the best known mathematician and scientist from ancient times. In addition to brilliant discoveries in mathematics and physics, he was also an inventor. Archimedes was born in the Greek city-state of Syracuse on the island of Sicily in approximately 287 BC. His father, Phidias, was an astronomer.

Archimedes may also have been related to Hiero II, King of Syracuse.

Archimedes’ Greatest Achievements

Invented the sciences of mechanics and hydrostatics.

Discovered the laws of levers and pulleys, which allow us to move heavy objects using small forces.

Invented one of the most fundamental concepts of physics – the center of gravity.

Calculated pi to the most precise value known. His upper limit for pi was the fraction 22⁄7. This value was still in use in the late 20th century, until electronic calculators finally laid it to rest.

Discovered and mathematically proved the formulas for the volume and surface area of a sphere.

Showed how exponents could be used to write bigger numbers than had ever been thought of before.

Proved that to multiply numbers written as exponents, the exponents should be added together.

Invented the Archimedean Screw to pull water out of the ground – the device is still used around the world.

Infuriated mathematicians who tried to replicate his discoveries 18 centuries later – they could not understand how Archimedes had achieved his results.

Directly inspired Galileo Galilei and Isaac Newton to investigate the mathematics of motion. Archimedes’ surviving works (tragically, many have been lost) finally made it into print in 1544. Leonardo da Vinci was lucky enough to have seen some of the hand-copied works of Archimedes before they were eventually printed.

Was one of the world’s first mathematical physicists, applying his advanced mathematics to the physical world.

Was the first person to apply lessons from physics – such as the law of the lever – to solve problems in pure mathematics.

Invented war machines such as a highly accurate catapult, which stopped the Romans conquering Syracuse for years. It’s now believed he may have done this by understanding the mathematics of projectile trajectory.

Became famous throughout the ancient world for his brilliant mind – so famous that we cannot be sure that everything he is said to have done is true.

Inspired what we now believe are myths including a mirror system to burn attacking ships using the sun’s rays, and jumping from his bath, then running naked through the streets of Syracuse shouting ‘Eureka’ meaning ‘I’ve found it’ after realizing how to prove whether the king’s gold crown had silver in it.


The Archimedes’ Screw

One of Archimedes’ marvelous inventions is the ‘Archimedean Screw.’ This device is rather like a corkscrew within an empty tube. When the screw turns, water is pulled up the tube, so the screw can pull water up from a river, lake, or well.

Archimedes is thought to have invented this device when he was in Egypt, where it’s still used for irrigation. It’s also helpful for lifting light, loose materials such as ash, grain, sand from a lower level to a higher level and is still used worldwide for a variety of purposes.

Archimedes was fascinated by curves. His powerful mind had mastered straight line shapes in both 2D and 3D.

He needed something more intellectually challenging to test him. This came in the form of circles, ellipses, parabolas, hyperbolas, spheres and cones.

Calculation of the Volume of a Sphere

He rose to the challenge masterfully, becoming the first person to calculate and prove the formulas for the volume and the surface area of a sphere.

The way he found his formulas is both amazingly clever and shows him to be a mathematician of the first rank, far ahead of others of his time, doing mathematics within touching distance of integral calculus 1800 years before it was invented.

Through his calculation, he found that the volume of the hemisphere must be equal to the volume of the cylinder minus the volume of the cone.

The formula for the volume of the cylinder was known to be πr2h and the formula for the volume of a cone was known to be 1⁄3πr2h. In this example, r and h are identical, so the volumes are πr3 and 1⁄3π r3.

Subtracting one from the other meant that the volume of a hemisphere must be2⁄3πr3, and since a sphere’s volume is twice the volume of a hemisphere, the volume of a sphere is:

V = 4⁄3πr3

Archimedes also proved that the surface area of a sphere is 4πr2.

Archimedes saw this proof as his greatest mathematical achievement, and gave instructions that it should be remembered on his gravestone as a sphere within a cylinder.

Death and Legacy

Archimedes died during the conquest of Syracuse in 212 BC when he was killed by a Roman soldier.

He was buried in a tomb on which was carved a sphere within a cylinder. This was his wish, because he believed his greatest achievement was finding the formula for the volume of a sphere.


Give me somewhere to stand and I will move the earth.

Be silent unless you can say something that is more useful than your silence.

Mathematics reveals its secret only to those who approach it with pure love, for its own beauty.