Archimedes

Archimedes of Syracuse was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the city of Syracuse in Sicily. He lived around 287 to 212 BC and is considered one of the greatest scientists of classical antiquity and one of the greatest mathematicians of all time. His brilliant ideas and discoveries have influenced many areas of science and math even today.

Archimedes made amazing contributions to mathematics. He used clever methods to find the area of shapes like circles and parabolas, and even figured out the volume of a sphere. He also came up with a way to approximate the value of pi, a key number in math. His work laid the groundwork for calculus, a branch of math developed much later.

In addition to his mathematical work, Archimedes applied these ideas to real-world problems. He discovered important principles about levers and buoyancy, which explain how objects move and float. He also designed many useful machines, including a screw pump that moves water and powerful devices to defend his city during wars.

Sadly, Archimedes died during a battle when his city was attacked. Even important Roman leaders wanted him to be safe, but he was killed. centuries later, his brilliant ideas were rediscovered and helped shape the course of science and mathematics through the Renaissance and the Scientific Revolution.

Biography

Archimedes was born around 287 BC in Syracuse, Sicily, a city in Magna Graecia. His father was Phidias, an astronomer, and he may have been related to King Hiero II of Syracuse. Little is known about his personal life, such as whether he married or had children.

Archimedes made many important discoveries in math and science. One famous story tells how he solved a problem for King Hiero II about whether a wreath made for a temple was pure gold or mixed with silver. By noticing how water level changed when he bathed, Archimedes realized he could use water to measure the wreath’s volume. He showed the wreath was not pure gold, proving his method worked.

Archimedes also helped design war machines to defend Syracuse from attacking Romans. These included improved catapults and devices that could drop heavy weights or lift enemy ships out of the water. He is also said to have created other clever machines, though some stories, like using mirrors to set ships on fire, are less certain.

Unfortunately, Archimedes died during the capture of Syracuse by Roman forces. Different stories tell of how he was killed while deeply focused on his math work. Roman leader Marcellus later regretted his death, as he valued Archimedes’ great mind.

Mathematics

Archimedes made important contributions to mathematics, creating new methods to solve problems and proving many geometric facts.

He used a technique called the method of exhaustion to find areas and volumes of shapes. For example, he showed that the area of a circle is the same as the area of a triangle with a base and height equal to the circle’s radius and circumference. He also approximated the value of π (the ratio of a circle’s circumference to its diameter) by comparing circles to polygons with many sides.

Archimedes also developed ways to represent very large numbers. In his work The Sand Reckoner, he described a system to count grains of sand large enough to fill the entire universe, showing that mathematics could handle incredibly big numbers.

Writings

Archimedes shared his work through letters with mathematicians in Alexandria, originally written in Doric Greek.

Surviving works

Measurement of a Circle

This short work includes three ideas. In one idea, Archimedes shows that the value of pi (π) is a little more than 223/71 (about 3.14) but less than 22/7 (about 3.14).

The Sand Reckoner

In this book, Archimedes imagines a number bigger than all the grains of sand in the universe. He talks about the heliocentric theory of the Solar System by Aristarchus of Samos, and tries to measure how far away the Sun seems to be. He uses a special way to count big numbers and finds that the universe might hold about 8×10⁶³ grains of sand.

On the Equilibrium of Planes

This book has two parts. In the first part, Archimedes shows how things balance, like a seesaw. He uses this to find the sizes and balancing points of different shapes such as triangles, parallelograms, and parabolas.

Quadrature of the Parabola

Here, Archimedes proves that the space inside a parabola and a straight line is 4/3 the size of a triangle with the same base and height.

On the Sphere and Cylinder

In this book, Archimedes describes the relationship between a sphere and a shaped cylinder. He finds the volume and surface area of both shapes.

On Spirals

This work introduces what we now call the Archimedean spiral, a curve that spreads out from a center point.

On Conoids and Spheroids

Archimedes calculates the sizes and spaces inside parts of cones, spheres, and shapes like paraboloids.

On Floating Bodies

In this book, Archimedes explains why things float or sink in water. He states that an object in water feels a push up that is equal to the weight of the water it pushes aside. He also looks at how some shapes balance in water, like parts of ships.

Ostomachion

Also called Archimedes' Box, this is a puzzle where 14 pieces can be put together to make a square. It is an early example of a problem in planning and arranging things.

The cattle problem

In this fun challenge, Archimedes asks to count the cattle in the Herd of the Sun by solving many math puzzles together.

The Method of Mechanical Theorems

In this work, Archimedes uses easy ways to understand hard math problems, like finding the size of shapes, before proving them fully.

Apocryphal works

Some books are thought to maybe not be really by Archimedes. One is called the Book of Lemmas, which talks about circles, but experts think someone else might have changed it later.

Lost works

Many of Archimedes' books have not fully survived. Some talk about making spheres, shapes like polyhedra, and spirals. Others might have explained how to find the size of a triangle from its sides, but these are not certain.

Archimedes Palimpsest

In 1906, a old book of prayers was found to have older writing underneath. This writing was by Archimedes and included some of his lost works. The book was sold and studied, and now it is kept by a private owner. It includes some of Archimedes' most important books that we otherwise would not have.

Legacy

Further information: List of things named after Archimedes

Archimedes is often called the father of mathematics and mathematical physics. Historians agree that he was the best mathematician of ancient times. He was famous for his clever inventions and machines. Even though some ancient writers said Archimedes didn’t care much for mechanics, we now know he was very interested in both math and inventions.

During the Renaissance, Archimedes' works were rediscovered and inspired many great thinkers like Leonardo da Vinci and Galileo Galilei. His ideas continued to influence scientists for centuries. Today, Archimedes is remembered not just for his math, but also for his lasting impact on science and culture around the world.