TTC - Mathematics from the Visual World [reduced]

TTC - Mathematics from the Visual World [reduced]

TTC - Mathematics from the Visual World
MKV | AVC 657kbps | English | 632x480 | 29.97fps | 24x30 mins | AAC stereo 112kbps | 2.1 GB
Genre: Video Training

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:
Conic sections: Euclid and other ancient mathematicians investigated conic sections-the shapes produced by the intersection of a plane and a cone. Two thousand years later, Galileo, Kepler, and Newton discovered that these shapes describe the paths followed by free-falling objects in a gravitational field.
Non-Euclidean geometry: Euclidean geometry is simple and intuitive, and it appears to govern the world around us. But a nagging problem with Euclid's concept of parallel lines led to the discovery of new geometries in the 1800s. These non-Euclidean geometries accurately reflect phenomena in physics and other disciplines.
Topology: Under what conditions can a coffee cup and a doughnut be considered the same? When they are analyzed in topology-the branch of mathematics that deals with shapes that retain their identity after twisting and stretching. Topology captures fundamental geometric properties of objects, giving us a new perspective on reality.
24 Lectures:
01 Seeing with Our Eyes, Seeing with Our Minds
02 Congruence, Similarity, and Pythagoras
03 The Circle
04 Centers of Triangles
05 Surprising Complexity of Simple Triangles
06 Clever Constructions
07 Impossible Geometry-Squaring the Circle
08 Classic Conics
09 Amazing Areas
10 Guarding Art Galleries
11 Illusive Perspective
12 Planes in Space
13 Cooling Towers and Hyperboloids
14 A Non-Euclidean Spherical World
15 Hyperbolic Geometry
16 The Dark Night Sky Paradox
17 The Shape of the Universe
18 The Fourth Dimension
19 Patterns of Patterns
20 Aperiodic Tilings and Chaotic Order
21 The Mandelbrot and Julia Sets
22 Pathways to Graphs
23 A Rubber-Sheet World
24 The Shape of Geometry

TTC - Mathematics from the Visual World [reduced]
TTC - Mathematics from the Visual World [reduced]
TTC - Mathematics from the Visual World [reduced]
TTC - Mathematics from the Visual World [reduced]



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