Mathematics from the Visual World

Course No. 1447
Professor Michael Starbird, Ph.D.
The University of Texas at Austin
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Course No. 1447
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Course Overview

Geometry has long been recognized not only as a fascinating skill, but as a gateway to the highest realms of human thought. Mathematics from the Visual World, taught by distinguished Professor Michael Starbird, introduces you to the terms, concepts, and astonishing power of geometry, including topology, conic sections, non-Euclidian geometry, congruence, and much more. In 24 richly illustrated lectures, you discover the important role this profound mathematical field plays in everything from algebra and calculus to cosmology and chemistry to art and architecture. This delightful, invigorating, and enlightening journey will allow you to master one of the most glorious inventions of the human mind.

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.

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:

  • In exploring the surprisingly diverse ways of defining the center of a triangle, you learn that one type of center, and the associated circle that inscribes the triangle with that center, led to a breakthrough in skin-grafting techniques for surgeons.
  • The unusual shape of art galleries, with many nooks and crannies, raises the question of how many security cameras suffice to protect the room. You learn creative strategies for attacking this problem and reaching a solution.
  • The shape of the universe itself is subject to simple geometric analysis. The observations themselves may be tricky, but Dr. Starbird shows that distinguishing among three possible geometries is relatively straightforward once we have the data.

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.

Famous Problems

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:

  • 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? A geometrical argument by 19th-century German astronomer Heinrich Wilhelm Olbers proved that the universe cannot be infinite in size, infinitely old, and compositionally the same in all directions. Otherwise, the night sky would be ablaze with light—which it isn't.
  • Königsberg bridges: Walkers in 18th-century Königsberg in Prussia amused themselves by seeing if they could cross all seven bridges in the central city without passing over the same bridge twice. Mathematician Leonhard Euler showed there is no solution, laying the foundation for the field of graph theory.

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.

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24 lectures
 |  Average 30 minutes each
  • 1
    Seeing with Our Eyes, Seeing with Our Minds
    Shapes, patterns, and forms have intrigued humans for millennia. You start your exploration of the world of geometry by examining the contributions of the ancient Greek mathematician Euclid, who wrote the most famous textbook in any subject for all time: the Elements. x
  • 2
    Congruence, Similarity, and Pythagoras
    What geometrical objects qualify as being the same? This lecture explores the concepts of congruence and similarity, which Professor Starbird uses to give two proofs of the Pythagorean theorem, including one discovered by Leonardo da Vinci. x
  • 3
    The Circle
    You investigate basic features of the circle, including its radius, diameter, circumference, and the famous constant pi. On the practical side, you learn that a belt that is snuggly encircling the Earth can be comfortably loosened by adding just a few feet to the circumference, and that manhole covers need not be circular. x
  • 4
    Centers of Triangles
    Delving into the hidden complexity of triangles, you discover the many ways of defining the center. There are the incenter, circumcenter, and orthocenter, to name just a few. Every triangle has circles naturally associated with it, which recently inspired an innovative technique for grafting skin. x
  • 5
    Surprising Complexity of Simple Triangles
    This lecture looks at three theorems about triangles that illustrate different strategies of proofs. The nine-point circle proof takes simple geometric properties and extends them to explain an amazing relationship. Napoleon's theorem can be proved with a process called tessellation. And the proof of Morley's Miracle proceeds backward! x
  • 6
    Clever Constructions
    Every student of Euclidean geometry learns how to construct basic geometric figures using a straightedge and a compass. You see how these methods reveal a connection between the construction of the golden rectangle and the regular pentagon. A surprisingly deep question is, Which of the other regular polygons can also be constructed? x
  • 7
    Impossible Geometry—Squaring the Circle
    You investigate three famous construction problems that were posed in antiquity and remained unsolved until the 1800s. Using a straightedge and a compass, is it possible to (1) double a cube, (2) trisect every angle, or (3) construct a square with the same area as a given circle? x
  • 8
    Classic Conics
    A plane passing through a right circular cone produces one of four classic shapes depending on the angle at which it intersects the cone. These "conic sections" are a circle, ellipse, parabola, or hyperbola. They arise frequently in physics; for example, the orbits of the planets are ellipses. x
  • 9
    Amazing Areas
    Professor Starbird starts with formulas for simple polygons such as a rectangle, a parallelogram, and a triangle. Then he shows how to deduce the area formulas for a circle and an ellipse. Finally, he demonstrates ingenious methods developed recently to compute the areas of various curved figures. x
  • 10
    Guarding Art Galleries
    How many security cameras are needed in an art gallery that has many nooks and crannies? You examine a clever proof that illustrates two effective strategies for analyzing the problem: divide and conquer, and seek essential ideas. The proof delivers an "aha" moment when the pieces fall into place. x
  • 11
    Illusive Perspective
    The challenge of depicting three dimensions on a two-dimensional plane leads you to an exploration of map projections, in which various strategies are used to render a globe on a flat surface. Artistic perspective is another technique for dealing with three dimensions on two. x
  • 12
    Planes in Space
    You investigate the method devised by the ancient Greek mathematician Archimedes for determining the volume of a sphere. Then you explore some surprising features of the two-dimensional plane that are revealed by projecting shapes into a third dimension. x
  • 13
    Cooling Towers and Hyperboloids
    Challenging you to imagine what a cube that is spinning on two opposite corners looks like, Professor Starbird uses this exercise to introduce a proof of Brianchon's theorem, in which you discover the fascinating properties of the architectural shape common to nuclear reactor cooling towers. x
  • 14
    A Non-Euclidean Spherical World
    The most controversial of Euclid's axioms was his parallel postulate, which mathematicians sought in vain to prove from Euclid's other axioms. Two millennia later, this problem led to the breakthrough of non-Euclidean geometries. One of these is spherical geometry, which you study in this lecture. x
  • 15
    Hyperbolic Geometry
    You explore hyperbolic non-Euclidean geometry, which has the property that for any point not on a given line there are infinitely many lines through the point that are all parallel to the line. A model for hyperbolic geometry called the Poincaré disk was the source for artistic work by x
  • 16
    The Dark Night Sky Paradox
    The dark night sky is proof that the universe is not infinitely expansive, infinitely old, and isotropic. You see how geometry is used to prove this and other features of the universe, including the size of the Earth and the nature of planetary orbits. x
  • 17
    The Shape of the Universe
    Is the universe best described as having spherical, hyperbolic, or Euclidean geometry? Another way of asking this question is, Does the universe have positive, negative, or zero curvature? You examine the possible observations that would help determine the true shape of the universe. x
  • 18
    The Fourth Dimension
    Higher-dimensional geometry is a rich domain with truly surprising insights. This lecture uses thought experiments in the first, second, and third dimensions to help you reason by analogy into the fourth dimension. Once you have this skill, there's no obstacle to going to even higher dimensions. x
  • 19
    Patterns of Patterns
    One of the most fundamental features of decorative designs is symmetry, seen in the repeated patterns on floor tiles, carpets, wall coverings, building ornamentation, screensavers, and paintings. You learn that different patterns have different ways of repeating. x
  • 20
    Aperiodic Tilings and Chaotic Order
    This lecture investigates Penrose and pinwheel tilings as illustrations of symmetry that is, paradoxically, at once orderly and chaotic. Such examples of aperiodic geometry have an uncanny ability to describe the real physical world and also lead to a new aesthetic sense. x
  • 21
    The Mandelbrot and Julia Sets
    Fractals have caught the popular imagination due to their beautiful complexity, and apparent symmetry and self-similarity. But how are they made? In this lecture, you see how infinitely intricate images arise naturally from repeating a simple process infinitely many times. Examples include Mandelbrot and Julia sets. x
  • 22
    Pathways to Graphs
    You focus on three famous geometric problems that relate to graph theory: the Königsberg bridge problem, the traveling salesman problem, and the four-color problem. Although easy to state, each leads into a fascinating thicket of mathematical ideas that can be explored with graphs. x
  • 23
    A Rubber-Sheet World
    Topology deals with shapes that retain their identity after twisting and stretching. For example, a coffee cup and a doughnut are topologically equivalent because each can be continuously deformed to produce the other. You look at surprising transformations that can occur in the topological realm. x
  • 24
    The Shape of Geometry
    Professor Starbird concludes by stepping back to survey the big picture of the geometrical questions explored during these lectures. From Euclid to fractals, the evolution of geometrical ideas over thousands of years is a model for how concepts spring from one another in marvelous profusion and grow in unexpected directions. x

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What's Included

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Video DVD
DVD Includes:
  • 24 lectures on 4 DVDs
  • 120-page printed course guidebook

What Does The Course Guidebook Include?

Video DVD
Course Guidebook Details:
  • 120-page printed course guidebook
  • Suggested readings
  • Questions to consider
  • Timeline

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Your professor

Michael Starbird

About Your Professor

Michael Starbird, Ph.D.
The University of Texas at Austin
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,...
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Reviews

Mathematics from the Visual World is rated 4.3 out of 5 by 31.
Rated 4 out of 5 by from Entertaining Math In the early part of the course, it was fun to work out the proofs myself. As the course progressed, the math came to be beyond my scope for solving, but interesting as new information. Professor Starbird has a good way of holding your attention.
Date published: 2013-08-22
Rated 5 out of 5 by from Wakes me up! This lecturer sneaks up on your brain, and presents complex ideas in a very accessible way. For example, he had someone (his wife?) make a patchwork representing a hyperbolic surface with straight lines. It looks too ordinary to be 'maths', but there it is!
Date published: 2013-01-30
Rated 5 out of 5 by from Fun, Interesting, and Valuable This is a great course not just for review of rusty math skills from years ago, but for getting a clear and visual approach that high school and college did not provide. There were also some new topics and perspectives that I really appreciated. Professor Starbird is just wonderful with his enthusiasm and use of supportive visuals. I would buy another of his courses in a moment. I did find the background fake looking window, red brick and plant distracting and irritating. I think this would be improved by having a background of chalkboard, whiteboard, or any other means to display supporting material that the professor would like to bring in. That irritation was not enough to bring down my rating though - I loved the course and professor - 5 stars all the way.
Date published: 2011-08-05
Rated 4 out of 5 by from Restructure your thinking This course advances your thinking beyond the 3D Euclidian geometry your intuition tells you about. If you want to better understand Stephen Hawking's books and TTC courses about String Theory, this will certainly get you started. What's more, it will get you to think more creatively about practical geometries in your daily encounters (Attention carpenters and auto mechanics). If you had trouble with other TTC math courses, start with this one and go back to the others. I found it high-school basic, yet I learned something new in each lecture. So if I learned 24 new things, that was good enough reason to take the course. Good investment of my time. And I think Professor Starbird has an engaging dry humor.
Date published: 2011-05-08
Rated 5 out of 5 by from Absolutely love it 1) What's most useful for me is that it effects my way of thinking about things and objects I see in everyday life. 2) Professor Starbird not only explained why the theorems discussed are the way they are, how to apply them but also provides historical perspective.
Date published: 2011-04-10
Rated 4 out of 5 by from Impressive, but . . . Professor Starbird’s course seems geared for already-competent mathematicians and people with real aptitude for geometry: I assume those folks will find much in this course to like. In contrast, my comments are directed at those, like me, who don't readily understand math and geometry. Without doubt, this course is mathematically significant and presents interesting observations--from which I was happy to absorb some of the high points. However, I usually couldn’t follow proofs for the various conclusions, which soon caused me to lose interest in such “details” (and this course is full of such details). I saw enough general interest to keep me watching, but my interest ebbed and flowed and I often could maintain only passive attention. I see why Professor Starbird is so widely acclaimed. He speaks enthusiastically, without seeming to need a script, and his mastery of the subject is obvious. Yet, he did not make everything as plain to me as I needed. That, of course, says something (unfortunate) about me, but it also suggests the instruction will be too advanced (or abstract or perhaps under-explained) for many students. For example, Starbird sometimes assumes the student already understands vital mathematical predicates, when in fact I (for one) often didn’t understand. At times he just moves over things too fast. So, if you come expecting the concepts to be made very simple (for the novice), you might be disappointed. It’s understandable that mathphiles (and perhaps many others) would rate this course 5 stars--it’s full of impressive content. However, I couldn’t follow much of it or stay very engaged, and was therefore disappointed. Nevertheless, based on the course’s general impressiveness, I give it 4 stars, which, though, is generous relative to how much I actually learned.
Date published: 2011-03-18
Rated 2 out of 5 by from too many mistakes We sent this series back after the first 6 lectures because my husband, who was a math major, found so many mistakes in the professor's lectures, including glaring mistakes in formulas. I was enjoying the course, but then I didn't know what was inaccurate.
Date published: 2011-03-01
Rated 4 out of 5 by from Another success from Michael Starbird Well, another successful course by Michael Starbird; does he want to become the Bob Greenberg of TTC Mathematics courses or what? He's well on his way, if not there already, though will never be able to equal the production of good old Bob. Michael's colleague Ed Burger looked to have been taking that title for himself recently, but Starbird has been impressively steady in producing a course every other year, for the past decade. I can't help but see the similarities between the presentations of Starbird and Dave Letterman; entertaining for educated folk, while still playing the role of teacher for those who want to learn. Well, so okay, now...by the way...Michael does have some obvious drawbacks to his lectures. He doesn't read the teleprompter all that well at times, most times, but what he does say, seems thought provoking and true. So no matter how he presents the examples, some better than others, one can rely on them to be useful for those who want to learn and study the subject. So regardless of the clarity, the message will get through...if not immediately, then eventually. Yes, these lectures can be somewhat dense and abstract, as is the trend in recent TTC courses, it seems to me. Yet the point is that the course wasn't designed for a one-time viewing. Multiple viewings are best, and required, is one wants to learn and absorb the material. So although Michael can rush at times, or spend too much time on abstract examples, while not fully describing others, one can use this course as an archive for which to learn, relearn, and refer to when necessary, again and again. After all, that should make the buyer think they are getting their money's worth.
Date published: 2010-11-07
Rated 5 out of 5 by from Opens a new view of mathematics Professor Starbird has taken the abstract science of number, quantity and space and shows by way of interesting and novel illustrations, how this applies to our world of everyday visual experiences.
Date published: 2010-03-31
Rated 4 out of 5 by from Good content; Less talk... As a high school math teacher, I've incorporated some of the lectures into my classroom. The topics and life-applications are good. I did find Prof. Starbird a bit long-winded (I sometimes wish he would get to the graphics sooner). Beyond that, it is a good set but a little above my students' heads at times. Nevertheless, the material can be distilled and simplified enough to make it understandable to someone who is not mathematically inclined.
Date published: 2010-01-12
Rated 5 out of 5 by from Enjoyable I have a treadmill and I watch these DVDs while walking. Therefore I appreciate the visually-oriented ones. It keeps me from getting bored while I exercize. This is one of the best teachers in the Teaching Company series.
Date published: 2009-10-10
Rated 2 out of 5 by from Mathematics from the visual world I purchased this course as a part of a two course set and was convinced of its worth by the overall description of the course which was, in my opinion written by a vastly over enthused individual that I certainly was not able to agree with in the first three disks that I suffered through. I must admit that I did not go any further because I was too upset with what I considered a useless expenditure of my hard earned money. I returned the courses and am expecting my money back shortly. I have purchased 51 different courses from the Teaching Company and have been completely satisfied and a constant supporter. I continue to extol the wonders I feel for the wonderful help that the courses have been to me in the manuscripts I am writing for two more books of a trilogy to add to the one I have already published.
Date published: 2009-07-07
Rated 5 out of 5 by from I now understand 4 Dimensions! The first 6 lectures were about high school geometry and were a little slow. However, Prof Starbird did go through some proofs I’d never seen before which I enjoyed. The lectures then took a turn into Spiral and Hyperbolic geometries. The lectures then covered all sorts of complex notions like: 4 dimensional space and the shape of the Universe. Finally fractal shapes were investigated. Prof Starbird is a great teacher, he takes you through stuff you think might be beyond your ability to understand, but with clever examples, pictures, animations and explanations you find the “penny drops”. I particularly liked his attempt to demonstrate 4 dimensional space. I still don’t fully understand it, but it's now within my reach. Also, he explains the Mandelbrot set in detail (which i 've never seen before). Although the first 6 lectures are a little slow the rest of the series is fascinating. Prof Starbird, as most great teachers do, takes you through step by step and connects the dots, by the end you've travelled on quite a journey and learnt a great deal. Also he has motivated me to learn more.
Date published: 2009-07-06
Rated 5 out of 5 by from I think i understand 4 Dimensional space I was unsure whether to get these lectures as I do not really enjoy geometry but I thought I might learn something. The first 6 lectures were about high school geometry and Prof Starbird did go through some proofs I’d never seen before and I enjoyed. The lectures then took a turn to go into Spiral and Hyperbolic geometries, which I had never seen before. The lectures then covered all sorts of abstract notions like, 4 dimensional shapes and the shape of the Universe. Finally fractal shapes were investigated. Prof Starbird is a great teacher, he takes you through stuff you think might be beyond your ability to understand, but with clever examples, pictures, animations and explanations you find the “penny drops”. I particularly liked his attempt to visualise 4 dimensional space. I still don’t quite understand it, but its now within my reach. Although the first 6 lectures are a little slow the rest of the series is fascinating. Prof Starbird, as most great teachers do, has motivated me to learn more. As such I’ve found a free 20 minute talk on hyperbolic space on TED.com by Margaret Werthiem which uses crochet (of all things) to model hyperbolic space. Overall, this lecture series is well worthwhile.
Date published: 2009-06-22
Rated 2 out of 5 by from what's the point? Starbird, who I like, blasts through the first 6 lectures with an apologetic tone--all this is so "technical" or "complicated"or whatever--but he does not give enough time to let us soak in the technicalities or the complexities, because? Because he does not think we are here for that real "hard" stuff? I don't know. So what's the point of lecturing us on some really good geometry without giving us the time and figures--plates--to see how it happens? The point is there is no point; it makes the subject seem superficial and that is not why I came.
Date published: 2009-06-01
Rated 5 out of 5 by from As Advertised, and More If you're a geometry fan, this course is a real home run. Now, geometry really isn't at the top of my list, but I have several courses from Prof. Starbird, and I was sure that whatever he had to say was worth listening to. I wasn't wrong. This is a lively, fast-paced tour of geometry and real-life things we've either seen or know about. To be honest, I haven't done any real geometry in 50 years, and I was frankly expecting a sit-back-and-watch kind of course, without an awful lot of brainpower required. To my (pleasant) surprise, I was wrong. This course is chock full of detail that you may not fully absorb in a view-only first pass, but it's there whenever you want to come back to it. Unless you're already well-versed in geometry, I suspect you'll get a lot of insight and appreciation you don't have now. The first half of the course is a little tedious. There are a lot of geometric proofs and constructs, and Prof. Starbird goes through them fairly quickly. If you really want to get a lot out of them, you'll probably need to take notes and work along with him, and this will mean really exercising your DVD remote. The second half of the course is easier, and has a lot of really interesting stuff. I really enjoyed the lecture on visualizing a fourth dimension. I'd never seen it presented this way before, and by the time Prof. Starbird was done, I pretty well had the picture. And, I got a benefit I wasn't expecting - in one lecture (I forget which one), Prof. Starbird shows how the Lorentz Factor in special relativity is calculated. Yes, I know it's pretty simple, especially after you know how, but I had been hung up on this thing since Prof. Wolfson's Einstein/Quantum course. No more. As to fractals (lesson 21), even though I've been through the Prof. Strogatz' Chaos course, I got an even deeper understanding of these things. It's a very nice presentation, and if you're willing to muscle your way through complex numbers, really informative. As with all TTC science and math courses, I recommend you read about the lecture in your course booklet before and after watching the lecture. For your first time, you'll probably just want to be a spectator. You can always go through it again, taking notes. If this is your first course from Prof. Starbird, you'll find him a lively and enthusiastic instructor and in addition to all you'll learn, you're sure to be entertained as well.
Date published: 2009-04-23
Rated 5 out of 5 by from Great Achievements Dr. Michael Starbird’s course on “Mathematics in the Visual World” is another one of his great achievements. He also did the “Calculus Made Clear” DVD that was excellent. You don’t need to have excelled in math to gain a lot from his DVDs. However, they are designed for the non-mathematician. They are designed for everyone who can gain an edge in this specialized field. His courses are not boring. The one I’m referring to now, the “Mathematics in the Visual World,” is not just about measuring triangles and angles. He extends the concept into the fourth dimension and talks about the art of fractals. It expanded my knowledge. It expanded my mind even though I’m only an Algebra person in my life. Not to mention it, I wonder how he would be able to expand my knowledge on that level of math as well. I wish he would also do a course in Algebra I and II.
Date published: 2009-03-03
Rated 4 out of 5 by from A bit misleading TTC does a great job promoting Starbird's newest lecture series, focusing on the "visual" aspect. However the series itself falls short by half. If you loved high school geometry in the most basic sense, you will love this course. The first part is just that: topics like geometric proofs, angles in parallelograms, etc. Nothing new, very retro. Even some "novel" material, such as "Guarding Art Galleries" proved to be basic geometry (how to devise a straight path - ie a security camera - in an oddly angle room). The course picks up more in the second half, where the "artistic" comes in ("Patterns of patterns", Mandelbrot, "Rubber sheet world." But you need to either skip to that part or have tons of patience to wade thru the high school part. I wonder why Starbird felt inclined to devote so much time to the basics; you do not need it to understand the more "beautiful" parts. I would recommend this course as long as its limitations are understood.
Date published: 2009-02-21
Rated 5 out of 5 by from Wonderful Course - Wonderful Teacher Professor Starbird is truly a “star” teacher! Please bring out more courses by him. Few teachers have the ability, like him, to make an incredibly dry subject (and yet very important subject) interesting and meaningful. He has that talent. In this course, he also brings in interesting history and personal anecdotes (such as the one about his daughters helping him to measure the height of the Eiffel Tower when visiting Paris). This makes the mathematical theories more fascinating and his teaching entertaining. As a consequence, we understand the subject matter. We also very much enjoyed his course on probability. Thank you. PPBNJ
Date published: 2009-02-15
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