Archimedes’ Force of Imagination: How an Ancient Genius Weighed the World and Calculated Infinity

As Archimedes used to say on Fridays – give me a glass of whiskey, and I’ll turn this whole place upside down!!!

During the two previous sessions, we delved into the timeless geometry of Euclid’s “Elements,” where every theorem is born from postulates and axioms, and today we took a mathematical journey to ancient Syracuse, where under Archimedes’ influence, the science of levers, spirals, and infinity was born!

Once again this semester, within the framework of the mathematical club at the FMCTE faculty of BSPU, three fascinating sessions took place, dedicated to the figure of Archimedes – physicist, mathematician, and inventor, whose name has become synonymous with genius. Participants immersed themselves in a world of science where mathematical discoveries emerged from practical tasks, and abstract ideas were embodied in concrete mechanisms.

The main focus was on Archimedes’ mathematical legacy – from the method of exhaustion and quadrature of the parabola to the elegant spiral that bears his name. Students learned about the famous problem of the golden crown and the discovery of buoyant force, explored the geometric beauty of the arbelos and salinon, and learned to understand how the ancient Greek scientist approached angle trisection using the neusis. Participants learned to see the connection between theoretical mathematics and its practical application – from levers that could “move the Earth” to calculating the volumes of complex solids of revolution.

Another discussion was devoted to the concept of infinity in the ancient understanding, when Archimedes proved that even the number of grains of sand needed to fill the Universe could be calculated. Participants saw how the ancient Greek mathematician operated with enormous numbers long before the appearance of modern notation. Students understood that Archimedes’ law, differential relationships, and geometric properties of Apollonian circles are not just abstract theorems, but living tools of knowledge that have served humanity for twenty-three centuries.

Participants were particularly struck by the realization that Archimedes’ greatest wish was to have a sphere inscribed in a cylinder depicted on his tomb – a symbol of his favorite discovery about the ratio of their volumes. The session not only demonstrated the power of mathematics in understanding the physical world, but also inspired participants to seek beauty in geometric constructions, harmony in proportions, and creativity in solving problems that seemed unsolvable.

Full version:

Citation: Kudinov M. Archimedes’ Power of Imagination: How the Ancient Genius Weighed the World and Calculated Infinity / M. Kudinov. — Zenodo. — 2025. — DOI: 10.5281/zenodo.17566601

Based on materials from the Department of Physics, Mathematics and Teaching Methods