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Plato'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. Seemingly simple geometric ideas such as the Pythagorean theorem turn out to have profound implications in unexpected places, including our modern conception of space and time.
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.
Consider these intriguing applications of geometry:
Intellect and Eye
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. All of geometry's many applications make use of the bedrock concepts of axioms, theorems, and proofs. In Mathematics from the Visual World, you discover that these traditional techniques are not ends in themselves but tools for gaining new insights such as these:
On a more everyday level, you may be interested to know that the age-old problem of how to cut a square cake so that each piece has the same quantity of icing is easily solved.
Geometry is also richly endowed 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. However, in the 17th century Isaac Newton showed that the construction can be done if one is allowed to make two marks on the straightedge. Dr. Starbird explains how this clever trick works.
Here are some other famous problems that you investigate in Mathematics from the Visual World:
A Delightful, Enlightening, and Invigorating Journey
A specialist in geometry and topology, Dr. Starbird is not only Professor of Mathematics at The University of Texas at Austin but also University Distinguished Teaching Professor. He has won an impressive array of teaching awards, including most of the major teaching awards at UT, a prestigious statewide teaching award, and the national teaching award from the Mathematical Association of America.
Professor Starbird believes that there is no excuse for a dull course on mathematics, a philosophy he pursues throughout Mathematics from the Visual World. In Lecture 1 he says, "To me, the satisfying aspect of a great proof occurs when the proof reveals some underlying, often surprising connection or relationship from which we see some truth that we previously could not fathom. When we see such a proof, we might say, 'Aha, that's why it's true.'" Although they don't always come easily, you have many such "aha" moments in this course.
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.
Dr. Michael Starbird is Professor of Mathematics and University Distinguished Teaching Professor at The University of Texas at Austin, where he has been teaching since 1974. He received his B.A. from Pomona College in 1970 and his Ph.D. in Mathematics from the University of Wisconsin-Madison in 1974. Professor Starbird's textbook, The Heart of Mathematics: An Invitation to Effective Thinking, coauthored with Edward B. Burger, won a 2001 Robert W. Hamilton Book Award. Professors Starbird and Burger also collaborated on Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas, published in 2005. Professor Starbird has won many teaching awards, including the Mathematical Association of America's 2007 Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics, which is the association's most prestigious teaching award. It is awarded nationally to 3 people from its membership of 27,000. Professor Starbird is interested in bringing authentic understanding of significant ideas in mathematics to people who are not necessarily mathematically oriented. He has developed and taught an acclaimed class that presents higher-level mathematics to liberal arts students.