Archimedes

Archimedes of Syracuse was an ancient Greek mathematician, physicist, engineer and astronomer whose contributions place him among the most influential scientific thinkers of classical antiquity. Although the biographical details of his life remain scarce, his surviving works reveal a mind of exceptional originality. His discoveries in geometry, mechanics and hydrostatics shaped the development of mathematics and the physical sciences for centuries.
Archimedes is credited with anticipating core elements of calculus through his use of the method of exhaustion and principles similar to those later formalised in integral calculus. By applying these methods, he produced rigorous demonstrations of results concerning the area of a circle, the surface area and volume of a sphere, the shape and measurement of an ellipse, and volumes generated by rotating parabolas and hyperbolas. He also explored the properties of spirals and devised a numerical system capable of expressing extraordinarily large quantities. His work stands out for its precision and mathematical creativity, often surpassing that of his contemporaries.

Mathematical Achievements

Archimedes’ mathematical mastery was built on a profound understanding of geometry. Among his many achievements, several remain central to modern study:

• Measurement of geometrical figures: He developed accurate methods for calculating areas and volumes, including those of spheres, ellipses, parabolic segments and spirals.
• Archimedean spiral: His study of this spiral contributed to later advances in polar geometry and mechanical design.
• Approximation of π: Through bounding techniques involving polygons, he produced one of the earliest reliable approximations of the value of π.
• Large-number notation: He introduced an innovative method for representing very large numbers, particularly in his exploration of the scale of the universe.

His mathematical works demonstrate a systematic approach that blended logical proof with empirical insight, a methodology that influenced scientific reasoning in subsequent eras.

Contributions to Physics and Engineering

Archimedes was one of the earliest figures to apply mathematical reasoning to physical problems. His investigations into mechanics and hydrostatics laid foundations for the scientific understanding of equilibrium and buoyancy.

• Law of the lever: He formulated the principle of leverage, explaining how forces and distances operate in mechanical systems.
• Centre of mass: By examining the balance of objects, he helped establish the concept of the centre of mass, now fundamental to physics and engineering.
• Archimedes’ principle: His studies on floating bodies led to the articulation of the law of buoyancy, explaining why objects float or sink according to the weight of displaced fluid.

In addition to theoretical advances, Archimedes devised machines ranging from practical tools to complex defensive technologies. These included the screw pump used for irrigation, block-and-tackle systems to move heavy loads and innovative war machinery used in the defence of Syracuse.

Astronomy and Scientific Instruments

Archimedes applied observation and mathematical reasoning to astronomy. He estimated the apparent diameter of the Sun and produced early measurements relating to celestial distances. Ancient accounts also attribute to him a mechanical device resembling a planetarium, capable of modelling the motions of known heavenly bodies. Such an instrument may have been a precursor to more sophisticated mechanisms of the Hellenistic world.

Life and Historical Context

Archimedes was born around 287 BC in Syracuse, a Greek city on the island of Sicily. His father, Phidias, is believed to have been an astronomer, though little else is known about him. Syracuse at the time was a flourishing centre of Hellenistic culture, and Archimedes maintained intellectual connections with scholars in Alexandria, one of the foremost centres of learning in the ancient world. Some of his surviving works are addressed to figures associated with the Alexandrian scholarly tradition.
Ancient writers offered varying accounts of Archimedes’ origins and associations. Some claimed he was related to King Hiero II of Syracuse, while others implied more modest beginnings. Details of his personal life, including whether he married or travelled widely, remain unknown.
Archimedes’ death occurred during the Roman siege of Syracuse between 213 and 212 BC. Despite explicit Roman orders that he should be spared, he was killed by a soldier. Later Roman authors described visiting his tomb, which traditionally bore a carving of a sphere and a cylinder—figures representing one of his favourite mathematical discoveries.

The Wreath Problem and the Legacy of Hydrostatics

One of the most enduring stories connected with Archimedes concerns the golden wreath made for King Hiero II. According to later accounts, the king suspected that the goldsmith had adulterated the gold with silver. Archimedes reportedly devised a solution by observing the water displaced when immersed bodies sink into a bath, leading to the famous exclamation “Eureka”. Whether or not the tale is historically accurate, it reflects his association with the principle of buoyancy and his ability to apply mathematics to practical problems.
Alternative ancient accounts describe the investigation using submerged balances rather than the bathtub image, aligning more closely with the principles he articulated in his work on floating bodies. Regardless of the precise details, the story illustrates his approach to experimentation and his systematic study of hydrostatics.

Engineering for Syracuse

Archimedes’ engineering skills were particularly valued in Syracuse. Ancient sources describe his role in designing mechanisms for lifting and launching heavy objects, including the construction of large ships such as the Syracusia. Various writers attribute to him devices ranging from windlasses to pulley systems that demonstrated mechanical advantage. Some accounts suggest he could move a ship single-handedly using such instruments, an anecdote often associated with his remark on leverage: “Give me a place to stand and I will move the Earth.”

Defence of the City

During the Roman siege, Archimedes is credited with overseeing the construction and operation of defensive machines that slowed the Roman advance. These reportedly included improved catapults, cranes capable of lifting or overturning ships and other mechanical devices designed to exploit the city’s coastal fortifications. Although details vary across ancient historians, his reputation as a master engineer was firmly established through these accounts.

Transmission and Later Influence

Archimedes’ writings were not widely circulated in antiquity. Scholars in Alexandria preserved and commented on his works, and early compilations in the Byzantine world helped maintain the transmission of his texts. In the Middle Ages his work was translated into Arabic and later into Latin, influencing the study of mathematics and physics during the Renaissance and the scientific revolution.