lato's Academy in Athens was the think tank of the ancient world and bore this motto over its door: "Let no one ignorant of geometry enter here." Ever since, geometry has been recognized as not only a useful and fascinating skill, but also as a gateway to the highest realms of human thought.
Mathematics from the Visual World, taught by veteran Teaching Company Professor Michael Starbird of The University of Texas at Austin, takes Plato's dictum to heart and introduces you to the terms, concepts, and astonishing power of geometry.
In 24 richly illustrated lectures, you learn that geometry is everywhere. It is the key to scientific disciplines from cosmology to chemistry. It is central to art and architecture. It provides deep insights into algebra, calculus, and other mathematical fields. And it is stunning to contemplate in its beauty.
From the simplicity of the golden rectangle to the infinitely complex realm of fractals, no other area of mathematics is so richly endowed with interesting examples as geometry, which appeals to both the intellect and the eye.
Geometry is also amply stocked with famous problems, some with life-or-death implications. Take the Delian Problem: Legend has it that in ancient Athens the citizens consulted the oracle at Delos for advice on how to stop a deadly plague. The oracle replied that the plague would end if the Athenians doubled the size of their cube-shaped altar to the god Apollo. So the Athenians doubled each side. But the plague continued unabated. The oracle had meant that they should double the altar's volume, not its linear dimensions.
Doubling the cube in this way is a classic problem from antiquity, which Professor Starbird proves is impossible to solve with the traditional tools of a straightedge and compass. Here are some other famous problems that you investigate in Mathematics from the Visual World:
- How large is the Earth? The problem of measuring the Earth was solved around 200 B.C. by the Greek mathematician Eratosthenes. All he needed were observations of the shadow cast by the sun at two particular locations on a special date—plus a bit of geometry.
- Why is it dark at night? In the 19th century, astronomer Heinrich Wilhelm Olbers used geometrical reasoning to prove that the universe cannot be infinite in size, infinitely old, and compositionally the same in all directions. Otherwise the night sky would not be dark.
- Königsberg bridges: In the 18th century, Leonhard Euler invented a new branch of mathematics by solving a geometrical puzzle for walkers in Königsberg, Prussia: Is there a way to cross all seven bridges in the central city without passing over the same bridge twice?
A Delightful, Enlightening, and Invigorating Journey
A specialist in geometry and topology, Dr. Starbird has won most of the major teaching awards at The University of Texas at Austin, plus a prestigious statewide teaching award and the national teaching award from the Mathematical Association of America. He believes there is no excuse for a dull course on mathematics, a philosophy he pursues throughout Mathematics from the Visual World.
An old story recounts that King Ptolemy of Egypt asked Euclid, the father of geometry, whether there was a simpler way to understand the axioms, theorems, and proofs of the subject. Euclid's famous answer was, "There is no royal road to geometry." However, now there is Professor Starbird's road, which is a delightful, enlightening, and invigorating journey through one of the most glorious inventions of the human mind.