The 5 Greatest Contributions of Archimedes

Archimedes is synonymous with the pinnacles of mathematics, physics, and engineering. Born in the 3rd century BC, his life unfolded alongside other great minds like Euclid, marking an era of profound mathematical advancements. Though much of his life story has been lost to time, records suggest that his father was an astronomer and a relative of Hiero II, the Greek tyrant of Syracuse.

Educated possibly by a student of Euclid, Archimedes spent most of his life in Syracuse, with a formative visit to Alexandria in his youth.

During his time, building practical mechanisms was not a common pursuit among scholars, who often admired pure mathematics, as Plato did. However, it was Hiero II who encouraged Archimedes to apply his genius to practical inventions, making his brilliance tangible to many. In this post, we will focus on his theoretical contributions and not delve into his engineering genius.

Like many great minds, Archimedes was deeply absorbed in his intellectual pursuits. His death came at the hands of a Roman soldier, likely because he refused to follow orders while engrossed in solving a mathematical problem.

Below is our top 5 list of great contributions of Archimedes to science.

Eureka! The Principle of Buoyancy

When Hiero II suspected a goldsmith of cheating him by mixing silver into a gold crown, he turned to Archimedes to verify its purity. This task was challenging because the crown could not be damaged. Archimedes pondered the problem until one day, while taking a bath, he noticed that the water level rose as he submerged himself. He realized that this effect could be used to determine the volume of the crown.

According to the famous story, Archimedes was so excited by this discovery that he ran through the streets of Syracuse naked, shouting "Eureka!" This story, although likely embellished over time, highlights Archimedes' contributions to understanding specific gravity and buoyancy. His method laid the groundwork for hydrostatics and demonstrated his remarkable ability to apply theoretical principles to solve practical problems. By using water displacement, Archimedes could determine that the crown had a different density than pure gold, thus proving that it had been adulterated with silver.

The Power of the Lever

While Archimedes wasn't the first to use the lever, he was the first to describe its principle, linking mathematics and physics. His study of the lever reached unprecedented levels of abstraction, considering ideal scales and point objects.

Archimedes formulated the law of the lever, stating that equilibrium is achieved when the arms of a balance are inversely proportional to the weights placed on them. This law's simplicity and significance explain its wide-ranging applications.

Archimedes famously exclaimed, “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.” While obviously improbable, the concept illustrates how a properly designed lever can theoretically move a vastly heavier object with minimal effort.

The Beginnings of Calculus

Beyond his work with geometry, Archimedes was one of the first to use infinitesimal calculations, laying the groundwork for integral calculus, though these ideas weren’t recognized until much later. His method of exhaustion, an early form of integration, involved approximating the area of a shape by inscribing and  circumscribing polygons with an increasing number of sides. By summing the areas of these polygons, he could estimate the area under a curve with remarkable precision.

Archimedes applied these techniques to find the area of a circle, the surface area and volume of a sphere, and the area under parabolas. His work in this domain was so advanced that it would be nearly 2000 years before similar methods were rediscovered and expanded upon.

Approximating Pi

A serious crisis arose in ancient Greek mathematics with the discovery of ineffable numbers, now known as irrational numbers, which cannot be represented by the ratio of integers. This posed significant challenges in comparing curved and rectilinear figures. The method of exhaustion, was a partial solution to this problem.

Archimedes made history by calculating an approximation of 𝜋 and improving the method of exhaustion to determine the volumes and areas of curvilinear geometric figures. His approximation of 𝜋, expressed as 𝜋 ≈ 22/7, was so successful that it was used for centuries and remains suitable for solving various practical problems today.

Volume and Surface Area of the Sphere and Cylinder

Archimedes was most proud of his discovery of the ratio of the volumes of a cylinder and a sphere inscribed within it, which is 3/2. Additionally, he found that the ratio of their surface areas is also 3/2. This discovery was so dear to him that he requested it to be immortalized on his tombstone, asking for a representation of a cylinder and an inscribed sphere to be engraved alongside the mathematical ratios he had discovered.

The contributions of Archimedes span a wide range of fields and have had a profound impact on both ancient and modern science. His work laid the foundation for many principles that are still in use today, cementing his legacy as one of the greatest minds in history.

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