Discoveries of Archimedes
Archimedes is one of the most famous scientists not only of his era. Some of his discoveries and inventions were successfully applied by his contemporaries, while others were appreciated by humanity only hundreds or sometimes even thousands of years later.
No other “great Greek” has as many myths and legends as Archimedes. What is true and what is not? What did Archimedes actually invent and discover, and what stories are pure fiction?
Who Was Archimedes
If very briefly, Archimedes’ biography is as follows… He was born in Sicily, in the city of Syracuse, studied in the scientific center of the ancient world—Alexandria (where the largest library of antiquity was located). Then he returned to Syracuse, where he pursued science for the sake of science.
Unlike other great scientists of antiquity, Archimedes did not establish his own school and did not have many followers. However, he left behind numerous scientific works, inventions, and discoveries. Some of them were used immediately, while others were appreciated only centuries after Archimedes’ death.
He died during the siege of Syracuse by the Romans in their Second War with Carthage.
But in addition to scientific discoveries, many legends are known about Archimedes—probably more than about any other scientist of antiquity.
Great Discoveries of Archimedes
Archimedes’ Number
Archimedes’ most famous discovery in mathematics is the number pi. In fact, it was not quite the same pi number we know today; it was an approximation—22/7.
Scientists already knew about the relationship between a circle’s circumference and its diameter, so what did Archimedes discover?
He created a method for calculating “pi” that was used by scientists until the 17th century!
The essence of the method was to describe a polygon around a circle and inscribe another polygon inside it. By increasing the number of vertices of the polygon, it would become “almost like a circle.” Then, the areas of the inner and outer polygons were calculated.
The area of the circle was less than that of the outer polygon and greater than that of the inner polygon.
The great scientist stopped at a 96-sided polygon. The number he obtained differed from the modern value of pi by only 0.04%. Before pi was given its modern name in the 18th century, it was often called “Archimedes’ number.”
Mathematical Analysis
Yes, the very “higher mathematics” that university students struggle with. Archimedes invented integrals! Or almost did.
One of Archimedes’ great achievements was developing a method for calculating areas of curved figures. Seeking to determine areas and volumes of complex shapes, he used the “method of exhaustion,” well known to Greek scientists.
Archimedes utilized the concept of infinitesimally small quantities and infinite series to compute the areas of curved figures.
This is the foundation of what we now call integral calculus, which only formally appeared in the 17th century in the works of mathematician Leibniz.
The Lever Invention
Of course, Archimedes did not invent the lever. Simple levers were likely known to humanity since the Stone Age.
So what did Archimedes discover? He developed the theory of levers—that is, he explained how to calculate forces and moments in advance.
In his work “On the Equilibrium of Planes,” he stated that objects of equal mass balance at equal distances, while objects of different masses balance at distances inversely proportional to their mass.
For example, a 1 kg weight and a 2 kg weight will be in equilibrium if the smaller weight’s arm is 2 meters long and the larger one’s arm is 1 meter long.
It seems simple, but before Archimedes, no one had formalized it.
Archimedes’ Principle
People had long known that ships could float; the Greeks were excellent sailors, which allowed them to spread their influence throughout the Mediterranean. So what did Archimedes discover?
Archimedes’ principle states that an object submerged in a fluid experiences a buoyant force equal to the weight of the fluid displaced by the object.
In simple terms, for a ship to stay afloat, its weight must be less than the weight of the water it displaces. Looking at the formula makes it clearer what Archimedes discovered.
Fa=ρgV
Here, ρ is the fluid density, g is the gravitational constant, and V is the volume of displaced fluid.
He established that “buoyancy” depends on volume. That is, you can make a ship of any mass, and it will not sink as long as it is large enough to displace a sufficient volume of water. Archimedes proved the relationship between the volume of displaced fluid and the force acting on the submerged object.
This is why ships are now measured in displacement, as it is the key indicator—the weight of water displaced by the ship’s hull.
Archimedes presented his principle in a work titled “On Floating Bodies,” roughly as follows:
If any body heavier than a liquid is immersed in it, it will sink until its weight equals the weight of the displaced liquid.
Archimedes’ Screw
Archimedes probably invented the screw, which was used by his contemporaries to lift water from wells. The invention consisted of a tube with a spiral inside.
This invention is still used today for pumping liquids, moving bulk materials, and as a propulsion system in highly specialized screw-driven vehicles.
What else did Archimedes discover and what else is he famous for beyond what is described above? A lot.
He was the first to prove that the angle of incidence equals the angle of reflection, that the heights of a triangle intersect at one point, that the surface area of a sphere is four times its largest cross-section, and that the volumes of a cone, sphere, and cylinder are in the ratio 1:2:3…
And much more… But some stories about Archimedes are simply fiction.
