Mathematics from the visual world

Description

Professor Michael Starbird of the University of Texas at Austin, presents "a collection of intriguing topics that reveal the rich, wondrous structure of what we see around us. Patterns in nature are the source of our geometrical understanding of the world. Abstracting those patterns leads to concepts from classical geometry ... Extensions of those and other ideas of form have created a beautiful landscape of mathematical ideas, including Euclidean geometry, non-Euclidean geometries, symmetry groups, and graph theory."--Page 1.  Read more... Abstract: Professor Michael Starbird of the University of Texas at Austin, presents "a collection of intriguing topics that reveal the rich, wondrous structure of what we see around us. Patterns in nature are the source of our geometrical understanding of the world. Abstracting those patterns leads to concepts from classical geometry ... Extensions of those and other ideas of form have created a beautiful landscape of mathematical ideas, including Euclidean geometry, non-Euclidean geometries, symmetry groups, and graph theory."--Page 1 Content: Disc 1: Part 1, Lecture 1: Seeing with our eyes, seeing with our minds -- Lecture 2: Congruence, similarity, and Pythagoras -- Lecture 3: The circle -- Lecture 4: Centers of triangles -- Lecture 5: Surprising complexity of simple triangles -- Lecture 6: Clever constructions -- Disc 2: Part 1: Lecture 7: Impossible geometry: squaring the circle -- Lecture 8: Classic conics -- Lecture 9: Amazing areas -- Lecture 10: Guarding art galleries -- Lecture 11: Illusive perspective -- Lesson 12: Planes in space. Disc 3: Part 2: Lecture 13: Cooling towers and hyperboloids -- Lecture 14: A non-Euclidean spherical world -- Lecture 15: Hyperbolic geometry -- Lecture 16: The dark night sky paradox -- Lecture 17: The shape of the universe -- Lecture 18: The fourth dimension -- Disc 4: Part 2: Lecture 19: Patterns of patterns -- Lecture 20: Aperiodic tilings and chaotic order -- Lecture 21: The Mandlebrot and Julia sets -- Lecture 22: Pathways to graphs -- Lecture 23: A rubber-sheet world -- Lecture 24: The shape of geometry.