Counting in Babylon Babylon had in all probability the earliest written language. At the same time, an elegant system elementary modern physics pdf weights and measures kept the peace in the marketplace. Their method of counting was in some ways better than our present one! We look at some ancient math tables, and ideas about Pythagoras’ theorem 1,000 years before Pythagoras.

Early Greek Science: Thales to Plato In the ancient port city of Miletus, there took place a “discovery of nature”: philosophers tried to understand natural phenomena without invoking the supernatural. The Greeks imported basic geometric ideas from Egypt, and developed them further. Motion in the Heavens: Stars, Sun, Moon, Planets A brief review for moderns of facts familiar to almost everybody in the ancient world: how the Sun, Moon and planets move through the sky over the course of time. Aristotle A brief look at the beginnings of science and philosophy in Athens: Plato’s Academy and Aristotle’s Lyceum. On to Aristotle’s science: causes in living things and inanimate matter, Aristotle’s elements, and laws of motion. Aristarchus gave a completely correct view of the solar system, anticipating Copernicus by 2,000 years or so. Science flourished for centuries in Alexandria, Egypt: Euclid, Apollonius, Hypatia and others lived there, Archimedes studied there.

Basic Ideas in Greek Mathematics Nailing down the square root of 2. Zeno’s paradoxes: Achilles and the tortoise. Proving an arrow can never move – analyzing motion, the beginning of calculus. How Archimedes calculated Pi to impressive accuracy, squared the circle, and did an integral to find the area of a sphere. How the Greeks Used Geometry to Understand the Stars The universe is like an onion of crystal spheres: Plato, Eudoxus, Aristotle.

More earthly ideas: Eudoxus and Aristarchus. Understanding planetary motion in terms of cycles and epicycles: Hipparchus and Ptolemy. Galileo and the Telescope Copernicus challenged Ptolemy’s worldview. Galileo saw mountains on the Moon, and estimated their height – the first indication that the Moon was Earthlike, not a perfect ethereal sphere at all. Life of Galileo A few facts and anecdotes to try to give something of the flavor of Galileo’s life and times, plus references to books for those who would like a more complete picture. We explore some of the consequences.