Geometry: An Interactive Journey to Mastery

Course No. 1033
Professor James S. Tanton, Ph.D., Princeton University
The Mathematical Association of America
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Course No. 1033
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Course Overview

Inscribed over the entrance of Plato’s Academy were the words, “Let no one ignorant of geometry enter my doors.” To ancient scholars, geometry was the gateway to gaining a profound knowledge of the world.$1#$ Today, geometry’s core skills of logic and reasoning are essential to success in school, work, and many other aspects of life.

Like other math fields, geometry teaches us how to think. It leads students to uncover new truths based on already established ideas and facts. It requires us to test and examine the conclusions of others. It teaches us to lay out our thinking clearly, describing each step so that others can follow along and verify our results.

This systematic way of thinking is essential in many fields. Drawing conclusions from experimental data is the basis of scientific discovery. Our justice system depends on compelling evidence to render a verdict in a court of law. And we use logical reasoning in everyday conversations to win friends over to our point of view.

In fact, the great Greek scholar Euclid demonstrated just how much you can do with logic. He worked out that basically all of geometry stands on just 10 core principles. You can build the rest using straightforward, logical reasoning.

In short, geometry is among the great intellectual feats of humankind. However, geometry goes far beyond being just an intellectual exercise. Its real-world applications extend to navigation, architecture, engineering, physics, technology, and even art.

  • Botanists use the geometry of triangles to estimate the heights of trees.
  • Astronomers use an understanding of ellipses to describe the orbits of planets.
  • Quantum physicists use the mathematics of rotation to explain aspects of subatomic physics.
  • Architects use principles of symmetry to develop aesthetically pleasing buildings.
  • Engineers use the properties of parabolas to design headlights and satellite dishes.

With its powerful blend of intellectual accomplishment and practical application, it’s no wonder that most schools consider geometry a core subject. Yet as award-winning Professor James Tanton of The Mathematical Association of America shows in Geometry: An Interactive Journey to Mastery, geometry can be an exciting adventure at any age. Those who will benefit from his 36 clear and accessible lectures include

  • high school students currently enrolled in a geometry class;
  • their parents, who seek an outstanding private tutor for their students;
  • home-schooled students and others wishing to study high school geometry on their own;
  • collegestudents who are struggling with math requirements and who need to strengthen their grasp of this fundamental subject; and
  • anyone curious about the intellectual challenge of logic and reasoning that underlies mathematics, the sciences, and our technological world.

Professor Tanton’s excellent teaching style makes the course ideal for those students who have ever believed they’re “not good at math” or have had challenges understanding geometry in the past.

A Different Way to Learn Geometry

Even students who have done well in other math courses such as algebra can sometimes find geometry a challenge. More so than algebra and other equation-based math, geometry places particularly strong focus on making logical inferences from facts and building a story of reasoning. Plus, geometry involves a more visual approach—working with shapes and patterns from the real world.

Many geometry courses begin by teaching the results of geometric thinking—by listing a set of beginning rules first. But how can one build the foundations of a house without first having a sense of what the house should be? Professor Tanton encourages students to start by playing with ideas of the mind (and acts of the hand!) to develop a feel for geometric rules and a context for those rules.

In Geometry: An Interactive Journey to Mastery, Professor Tanton guides students as they build an understanding of geometry from the ground up. With this approach, the instruction focuses on the intellectual play of the subject and its beauty as much as its utility and function. Students begin with elementary building blocks like points, lines, and angles and observe how those basic units interact.

From a clear understanding of the fundamental principles, students use logical reasoning to expand their understanding of geometry. Like building a house brick by brick, each new discovery stands upon the others—without any sudden or confusing jumps.

In the first part of the course, students

  • develop an intuitive context for thinking about terms like point, line, angle, plane, and flat;
  • grasp how to create logical proofs; and
  • uncover the three deep and fundamental assumptions of geometry—the Pythagorean theorem, the parallelism postulate, and the similarity principles.

In the second part, students

  • study common geometric shapes and their properties (such as triangles, polygons, and circles);
  • explore the intersection of geometry and algebra;
  • examine the basics of trigonometry; and
  • learn how to calculate areas.

Once students understand the core principles, they are set loose to play in the third part of the course. Students ponder a range of fascinating and sometimes counterintuitive applications for geometry. They

  • combine two seemingly disparate fields: geometry and probability;
  • dive into the wild world of fractals;
  • investigate conics and their many practical applications;
  • use complex numbers to solve tricky geometry problems; and
  • contemplate spherical and even “taxi-cab” geometry.

Delightful Real-World Examples
A beauty of geometry is its wide variety of fascinating and unexpected applications. Some of the examples students explore in this course include these:

  • Width of a river: You're on a walk and come across a river. Can you estimate how wide it is? See how you can—with no more than a bit of geometry and a baseball cap.
  • Geometry and nature: From the orbits of planets to the shape of your small intestine, geometric shapes appear in some surprising places throughout nature. See how geometry helps us better understand the marvels and mysteries of the world around us.
  • Modern cell phones: Swiping the screen on a cell phone seems to be an ordinary activity. But did you know your phone is actually relying on some clever geometry? Find out exactly what your phone is doing and the mathematics behind it.
  • Works of art: When people think of applications for mathematics, they often mention the fields of science or engineering. But geometry also has its place in the visual arts. See how great artists like M.C. Escher used geometric shapes and principles to create masterpieces.
  • A game of pool: If you're playing pool and want to play a trick shot against the side edge, how do you need to hit the ball? See how you can determine this and more using the reflection principle.

A Teacher of Teachers

Professor Tanton is committed to sharing the delight and beauty of geometry and works with teachers across North America to develop more effective teaching methods for geometry and other math courses.

He is not only a teacher of math, but a teacher of the best ways to teach math. His experience has taught him where students most frequently flounder, which has given him the skills to explain mathematical concepts in a way that removes mental roadblocks to success.

Making each example come to life, Geometry: An Interactive Journey to Mastery engages students in a visual adventure. Professor Tanton uses bright and colorful slides, easy-to-understand whiteboard drawings, and interactive demonstrations to make his explanations crystal clear. And to help students better understand geometric principles, a workbook complete with sample problems and solutions accompanies the course.

Equipped with a firm understanding of geometry, students walk away from the course with the tools and knowledge to continue on to greater challenges in mathematics, school, and life. Your journey into this world of joy and wonder has only begun.

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36 lectures
 |  Average 30 minutes each
  • 1
    Geometry—Ancient Ropes and Modern Phones
    Explore the origins of one of the oldest branches of mathematics. See how geometry not only deals with practical concerns such as mapping, navigation, architecture, and engineering, but also offers an intellectual journey in its own right—inviting big, deep questions. x
  • 2
    Beginnings—Jargon and Undefined Terms
    Lay the basic building blocks of geometry by examining what we mean by the terms point, line, angle, plane, straight, and flat. Then learn the postulates or axioms for how those building blocks interact. Finally, work through your first proof—the vertical angle theorem. x
  • 3
    Angles and Pencil-Turning Mysteries
    Using nothing more than an ordinary pencil, see how three angles in a triangle can add up to 180 degrees. Then compare how the experience of turning a pencil on a flat triangle differs from walking in a triangular shape on the surface of a sphere. With this exercise, Professor Tanton introduces you to the difference between flat and spherical geometry x
  • 4
    Understanding Polygons
    Shapes with straight lines (called polygons) are all around you, from the pattern on your bathroom floor to the structure of everyday objects. But although we may have an intuitive understanding of what these shapes are, how do we define them mathematically? What are their properties? Find out the answers to these questions and more. x
  • 5
    The Pythagorean Theorem
    We commonly define the Pythagorean theorem using the formula a2 + b2 = c2. But Pythagoras himself would have been confused by that. Explore how this famous theorem can be explained using common geometric shapes (no fancy algebra required), and how it’s a critical foundation for the rest of geometry. x
  • 6
    Distance, Midpoints, and Folding Ties
    Learn how watching a fly on his ceiling inspired the mathematician René Descartes to link geometry and algebra. Find out how this powerful connection allows us to use algebra to calculate distances, midpoints, and more. x
  • 7
    The Nature of Parallelism
    Examine how our usual definition of parallelism is impossible to check. Use the fundamental assumptions from the previous lectures to follow in Euclid’s footsteps and create an alternative way of checking if lines are parallel. See how, using this result, it’s possible to compute the circumference of the Earth just by using shadows! x
  • 8
    Proofs and Proof Writing
    The beauty of geometry is that each result logically builds on the others. Mathematicians demonstrate this chain of deduction using proofs. Learn this step-by-step process of logic and see how to construct your own proofs. x
  • 9
    Similarity and Congruence
    Define what it means for polygons to be “similar” or “congruent” by thinking about photocopies. Then use that to prove the third key assumption of geometry—the side-angle-side postulate—which lets you verify when triangles are similar. Thales of Ionia used this principle in 600 B.C.E. to impress the Egyptians by calculating the height of the pyramids. x
  • 10
    Practical Applications of Similarity
    Build on the side-angle-side postulate and derive other ways of testing whether triangles are similar or congruent. Also dive into several practical applications, including a trick botanists use for estimating the heights of trees and a way to measure the width of a river using only a baseball cap. x
  • 11
    Making Use of Linear Equations
    Delve deeper into the connections between algebra and geometry by looking at lines and their equations. Use the three basic assumptions from previous lectures to prove that parallel lines have the same slope and to calculate the shortest distance between a point and a line. x
  • 12
    Equidistance—A Focus on Distance
    You’ve learned how to find the midpoint between two points. But what if you have three points? Or four points? Explore the concept of equidistance and how it reveals even more about the properties of triangles and other shapes. x
  • 13
    A Return to Parallelism
    Continue your study of parallelism by exploring the properties of transversals (lines that intersect two other lines). Prove how corresponding angles are congruent, and see how this fact ties into a particular type of polygon: trapezoids. x
  • 14
    Exploring Special Quadrilaterals
    Classify all different types of four-sided polygons (called quadrilaterals) and learn the surprising characteristics about the diagonals and interior angles of rectangles, rhombuses, trapezoids, and more. Also see how real-life objects—like ironing boards—exhibit these geometric characteristics. x
  • 15
    The Classification of Triangles
    Continue the work of classification with triangles. Find out what mathematicians mean when they use words like scalene, isosceles, equilateral, acute, right, and obtuse. Then, learn how to use the Pythagorean theorem to determine the type of triangle (even if you don’t know the measurements of the angles). x
  • 16
    "Circle-ometry"—On Circular Motion
    How can you figure out the “height” of the sun in the sky without being able to measure it directly with a ruler? Follow the path of ancient Indian scholars to answer this question using “angle of elevation” and a branch of geometry called trigonometry. You learn the basic trig identities (sine, cosine, and tangent) and how physicists use them to describe circular motion. x
  • 17
    Trigonometry through Right Triangles
    The trig identities you explored in the last lecture go beyond circles. Learn how to define all of them just using triangles (expressed in the famous acronym SOHCAHTOA). Then, uncover how trigonometry is practically applied by architects and engineers to measure the heights of buildings. x
  • 18
    What Is the Sine of 1°?
    So far, you’ve seen how to calculate the sine, cosine, and tangents of basic angles (0°, 30°, 45°, 60°, and 90°). What about calculating them for other angles—without a calculator? You’ll use the Pythagorean theorem to come up with formulas for sums and differences of the trig identities, which then allow you to calculate them for other angles. x
  • 19
    The Geometry of a Circle
    Explore the world of circles! Learn the definition of a circle as well as what mathematicians mean when they say things like radius, chord, diameter, secant, tangent, and arc. See how these interact, and use that knowledge to prove the inscribed angle theorem and Thales’ theorem. x
  • 20
    The Equation of a Circle
    In your study of lines, you used the combination of geometry and algebra to determine all kinds of interesting properties and characteristics. Now, you’ll do the same for circles, including deriving the algebraic equation for a circle. x
  • 21
    Understanding Area
    What do we mean when we say “area”? Explore how its definition isn’t quite so straightforward. Then, work out the formula for the area of a triangle and see how to use that formula to derive the area of any other polygon. x
  • 22
    Explorations with Pi
    We say that pi is 3.14159 … but what is pi really? Why does it matter? And what does it have to do with the area of a circle? Explore the answer to these questions and more—including how to define pi for shapes other than circles (such as squares). x
  • 23
    Three-Dimensional Geometry—Solids
    So far, you’ve figured out all kinds of fun properties with two-dimensional shapes. But what if you go up to three dimensions? In this lecture, you classify common 3-D shapes such as cones and cylinders, and learn some surprising definitions. Finally, you study the properties (like volume) of these shapes. x
  • 24
    Introduction to Scale
    If you double the side-lengths of a shape, what happens to its area? If the shape is three-dimensional, what happens to its volume? In this lecture, you explore the concept of scale. You use this idea to re-derive one of our fundamental assumptions of geometry, the Pythagorean theorem, using the areas of any shape drawn on the edges of the right triangle—not just squares. x
  • 25
    Playing with Geometric Probability
    Unite geometry with the world of probability theory. See how connecting these seemingly unrelated fields offers new ways of solving questions of probability—including figuring out the likelihood of having a short wait for the bus at the bus stop. x
  • 26
    Exploring Geometric Constructions
    Let’s say you don’t have a marked ruler to measure lengths or a protractor to measure angles. Can you still draw the basic geometric shapes? Explore how the ancient Greeks were able to construct angles and basic geometric shapes using no more than a straight edge for marking lines and a compass for drawing circles. x
  • 27
    The Reflection Principle
    If you’re playing squash and hit the ball against the wall, at what angle will it bounce back? If you’re playing pool and want to play a trick shot against the side edge, how do you need to hit the ball? Play with these questions and more through an exploration of the reflection principle. x
  • 28
    Tilings, Platonic Solids, and Theorems
    You’ve seen geometric tiling patterns on your bathroom floor and in the works of great artists. But what would happen if you made repeating patterns in 3-D space? In this lecture, discover the five platonic solids! Also, become an artist and create your own beautiful patterns—even using more than one type of shape. x
  • 29
    Folding and Conics
    Use paper-folding to unveil sets of curves: parabolas, ellipses, and hyperbolas. Study their special properties and see how these curves have applications across physics, astronomy, and mechanical engineering. x
  • 30
    The Mathematics of Symmetry
    Human aesthetics seem to be drawn to symmetry. Explore this idea mathematically through the study of mappings, translations, dilations, and rotations—and see how symmetry is applied in modern-day examples such as cell phones. x
  • 31
    The Mathematics of Fractals
    Explore the beautiful and mysterious world of fractals. Learn what they are and how to create them. Examine famous examples such as Sierpinski’s Triangle and the Koch Snowflake. Then, uncover how fractals appear in nature—from the structure of sea sponges to the walls of our small intestines. x
  • 32
    Dido's Problem
    If you have a fixed-length string, what shape can you create with that string to give you the biggest area? Uncover the answer to this question using the legendary story of Dido and the founding of the city of Carthage. x
  • 33
    The Geometry of Braids—Curious Applications
    Wander through the crazy, counterintuitive world of rotations. Use a teacup and string to explore how the mathematics of geometry can describe an interesting result in quantum mechanics. x
  • 34
    The Geometry of Figurate Numbers
    Ponder another surprising appearance of geometry—the mathematics of numbers and number theory. Look into the properties of square and triangular numbers, and use geometry to do some fancy arithmetic without a calculator. x
  • 35
    Complex Numbers in Geometry
    In lecture 6, you saw how 17th-century mathematician René Descartes united geometry and algebra with the invention of the coordinate plane. Now go a step further and explore the power and surprises that come from using the complex number plane. Examine how using complex numbers can help solve several tricky geometry problems. x
  • 36
    Bending the Axioms—New Geometries
    Wrap up the course by looking at several fun and different ways of reimagining geometry. Explore the counterintuitive behaviors of shapes, angles, and lines in spherical geometry, hyperbolic geometry, finite geometry, and even taxi-cab geometry. See how the world of geometry is never a closed-book experience. x

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  • 296-page course workbook
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Your professor

James S. Tanton

About Your Professor

James S. Tanton, Ph.D., Princeton University
The Mathematical Association of America
Dr. James Tanton is the Mathematician in Residence at The Mathematical Association of America (MAA). He earned a Ph.D. in Mathematics from Princeton University. A former high school teacher at St. Mark's School in Southborough and a lifelong educator, he is the recipient of the Beckenbach Book Prize from the MAA, the George Howell Kidder Faculty Prize from St. Mark's School, and a Raytheon Math Hero Award for...
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Geometry: An Interactive Journey to Mastery is rated 4.3 out of 5 by 60.
Rated 5 out of 5 by from Great Courses. Geometry Dr. Tanton;s presentation makes his subject interesting, entertaining and lively. I am enjoying his course on Geometry and recommend it to anyone interested in learning the subject. Personally, The cds and workbook that come with the course. I wish that a program like Great Courses was available when I was in High School and attending College.
Date published: 2019-03-02
Rated 5 out of 5 by from Please do more, Tanton. Working through this course and the Visualization one has added considerable clarity to my understanding of math and geometry, in a fun way, after getting a really horrible math education growing up. To appreciate these courses down deep, you probably have to have been "educated" by being forced to memorize a plethora of impenetrable and meaningless formulas. After that, these courses are treats.
Date published: 2019-02-24
Rated 2 out of 5 by from Not What I Was Looking For... I will preface this by saying I only made it through the first lecture and normally I would not think about reviewing something without having viewed it in its entirety, however, in this case I want to warn folks off in case they are looking for something aimed at an adult audience. This course appears aimed at middle-school level students. If you are an adult student who has perhaps fallen in love with Euclid's Elements and are looking for a philosophical look at Euclidean (and possibly non-Euclidean) geometry, then this is not the course for you.
Date published: 2018-12-09
Rated 5 out of 5 by from Not By the Book, But Fantastic None the Less This course would be the perfect thing to show your child the summer before he starts Geometry in school or for a curious adult to find a gateway drug to mathematics. The mathematics catalog at The Great Courses seems to have established two distinct breeds - the highly curriculum-oriented core material (such as the courses from Bruce Edwards and James Sellers) and the less traditional "for the joy of it" type courses (such as the offerings from Michael Starbird). This course falls squarely in the latter. The disadvantage to such a course is that it will not adequately serve as a guide through your traditional high school or college class. The advantage is that it is an exciting and refreshing look at a subject. It would have been more apt to name this set "Joy of Geometry". This course is so easy to follow and so interesting that it could make a mathophobe fall in love with Geometry. You will gain a big picture understanding of what makes Geometry so fascinating. There is so much value in that. I really REALLY hope that The Great Courses continues to produce courses like this one. If you want, you can fill in the gaps with a more traditional approach later. But it takes a special kind of presentation and passion to coax this much fascinating material out of a topic that we all think we know. I agree with some of the other reviews that the workbook is poor. It is probably not your best option if you are studying for a GED or something like that. For that reason, I am disappointed that The Great Courses appears to have discontinued the previous Geometry course from James Noggle. Granted, the course was 25 years old and there was a new kid in town, but both of these courses have relevance in the same space. Long story short, despite incomplete nature, this course will make you fall in love with Geometry and has something to offer mathematicians at any level. I will certainly be purchasing more courses from Professor Tanton!
Date published: 2018-10-23
Rated 4 out of 5 by from Makes it fun to explore maths again This is a fun course. Professor Tanton has a teaching style that is easy to understand yet very interesting. Love his style the way he gives some real world examples mixed in with the theory. One of the more enjoyable courses I took on Great Courses.
Date published: 2018-08-22
Rated 5 out of 5 by from Be prepared to be fascinated! I just finished this course. Professor Tanton's enthusiasm and passion for geometry is infectious. If you follow along and are careful to master each homework assignment, be warned! You'll find yourself looking for angles and parallel lines with every step you walk and as for circles. Well!! In other words I pretty much agree with the other positive reviews. I found Algebra I and II to be arithmetic on steroids (excellent DVDs taught by James Sellers). Geometry requires more actual learning for me and more conceptual understanding. (I remember this vaguely from high school 50 years ago as well). I took this course because I'm really prepping up to learn calculus but I am now so interested I've become a bit sidetracked! This is a good thing and a tribute to the teacher. There are some mistakes in the workbook - most due to carelessness - and these should have been caught by rechecking and editing. I'm keeping my 5-star rating however because Professor Tanton gets a double A PLUS for how imaginative and beautifully crafted they are. If you work through them carefully, you will not only cement your understanding of the lesson, you will also get an introduction to the next lesson. They encourage independent thinking and analysis and even manage to make the dreaded "word problems" enjoyable and helpful. In the later lessons, by the time I got through some of them successfully I felt like a math goddess! (Please note: I am so not a math goddess!) I ended up Professor Seller's algebra lectures completely blown away by factorials which were entirely new to me. Now I'm equally blown away by fractals and figural numbers. Is there no end to this madness?
Date published: 2018-08-07
Rated 5 out of 5 by from What a Joy Geometry Is! Is there anything more delightful than Geometry? I'm sure there is, but I can't think of what it might be right now. Professor Tanton, I suspect, might have the same feelings about it. He has a wonderful enthusiasm for the subject and presents the subject with a fundamental delight for the visual and logical surprises that it always offers. Some viewers may wish an approach with more "traditional" rigor in the presentation, but this was perfect for an older viewer like me who had recall, however foggy, of the proofs from childhood, and wished, once again, to experience the beauty of it all. Wonderful set of lectures!
Date published: 2018-07-02
Rated 4 out of 5 by from Great Teacher / Great Materials I'm working my way through this course and am almost finished now. I must say that this one of the course from Great Courses that I have thoroughly enjoyed. The instructor is peppy and interesting. He is thoroughly likable and effectively communicates his passion for the subject, breathing life into the subject of geometry. His personality and style of delivery renders this subject even more interesting.
Date published: 2018-06-03
Date published: 2018-01-22
Rated 5 out of 5 by from Puzzle of all times I find the problems are related to the lectures, they just take a little creativity. After solving them one does feel genuine satisfaction. I took Geometry for Dummies, besides doing a miserable job in high school geometry, and I thought it was well done. Its problem was having to endlessly state transitive properties and identities in proofs. The spirit and playfulness as well as the usefulness were not near what they are in Professor Tanton's course. He does proofs like a human. I am writing because the last 12 optional lectures are all gems. I highly recommend. BUT, I CANNOT GET MY HEAD AROUND problem 2 lesson 28. Glue a tetrahedron to an octahedron and get a ? sided figure. He warns you the answer is not 10. The drawing in the explanation might be understood by the Krell's on the "Forbidden Planet" but not me. But isn't that the idea; a course that will challenge anyone. Enjoy. Let me also mention that the professor states take your time. So true. This is not a course where you decide to take 4 lectures a day and finish in 9 days.
Date published: 2017-09-30
Rated 5 out of 5 by from Geometry It is an absolutely fabulous course and definitely one of the finest presentations that I have heard!
Date published: 2017-08-23
Rated 5 out of 5 by from Geometry was never so easy and understandable purchased this course to brush up on basic concepts long forgotten more than 30 years ago, in preparation for an applied physics course. Prof. Tanton's course was interesting, practical and understandable. I really enjoyed they way he presented the concepts with a mix of theory, and everyday practical applications.
Date published: 2017-07-15
Rated 5 out of 5 by from Unorthodox, but Brilliant... I have been teaching high school mathematics (for over 20 years) mostly from a "traditional" perspective so I'm always looking for fresh, new explanations. This DVD set more than exceeded my expectations. I have used the ideas in this course, both in teaching geometry and trigonometry. You may want to look at Michael Starbird's Mathematics from a Visual World first (which I also own). If you want a more conceptual understanding of this timeless topic, then I highly recommend this course.
Date published: 2017-07-06
Rated 5 out of 5 by from Geometry as a tool for everyday life! My professional formation is Law but I used to like Maths because its challenger character always and trying my power of concentration and my ability to solve problems. Professor James S Tanton´s course makes a point when he brings Maths to the real world. The first part of any lecture is theoretical, explaining the origins and the fundamentals of the mathematical object of study (lines, points, polygons, etc.). The second part is devoted to the solution of maths problems. But the most interesting is the last part of the lesson: how you can use what you did learn. The abstraction of the beginning becomes the reality and all the beauty of the Maths appears before us. If we watch our world carefully, we will perceive the relations, the links, the interactions of the objects, the full reality written in absolute perfects laws. This is Mathematics. This is our real life. Highly recommended course.
Date published: 2017-06-03
Rated 1 out of 5 by from Numerous errors are frustrating Nothing is more frustrating than poor presentation and poor editing in a math class. I counted at least 18 errors in 24 lessons in either the questions or the solutions or both. Sometimes they were just math errors and sometimes they were major omissions (find c where c isn't shown in the illustration). I spent hours trying to track down why my answer didn't match the solution only to find the solution was wrong. Didn't anyone else ever try to answer the questions? And Professor Tanton presentations were often peppered with him correcting himself - something that could have been edited out easily. For an expensive course like this one would think a little bit of editing would be justified. I've taken some good and some really excellent courses here at GC but this one stunk.
Date published: 2017-05-28
Rated 5 out of 5 by from What a treat! I always suspected that I would have enjoyed geometry in school, had I not had a teacher who ate doughnuts and read the newspaper during class instead of teaching her students. So I bought this class to see what I missed. I expected knowing geometry to be useful, but this course has convinced me that the subject is downright FUN! Dr. Tanton has a relaxed, friendly, and engaging style, and his enthusiasm is contageous. He describes concepts in such a way that they make perfect sense, his frequent visual demonstrations are a great help, and he includes practical applications of geometry that make it clear just how handy it is to understand geometric principles. Be sure to make use of the workbook, as it includes challenging problem sets that are very effective in driving home the concepts Dr. Tanton teaches. Dr. Tanton makes math a joy, and although I haven't finished his geometry course yet, I'm already excited about taking another course from him (and am hoping that the Great Courses will produce many more)!
Date published: 2017-05-06
Rated 5 out of 5 by from The world needs more professors like Dr. Tanton The road to understanding is being able to visualize a problem. This is what Dr. Tanton does in this course, encourage the listener to visualize a problem. Too often, people/students can produce correct mathematics but, the mathematics produced don't solve the stated problem and, this is because, the understanding/visualization of the problem is incorrect. The negative reviews for this course, give me the impression that some people don't realize there is a big difference between learning and understanding. Prof. Tanton's presentation is geared towards understanding by visualization. Superb.
Date published: 2017-04-01
Rated 5 out of 5 by from Very good and wonderfully entertaining This video was great. The subject was well-presented and Tanton clearly loves the subject and is a splendid presenter.
Date published: 2017-02-18
Rated 1 out of 5 by from Horrible Course for the Beginner to Geometry! I never take the time to write reviews in general, good or bad, but this course is absolutely not for you if you are new to Geometry and need to learn it for school. Just a little bit on my background and why I bought the course. I've been teaching music in the private sector for over 20 years and have decided to go into teaching music in the public schools. As a result, I need to take the Praxis 1 core exams for teachers which includes hight school math. I hadn't taken math for 29 years and my high school math history only included basic math and Algebra 1 (I never took Geometry!). So to review, I bought the "Mastering the Fundamentals of Mathematics" and "Algebra 1" offered through The Great Courses done by Professor James A. Sellers. These courses were exceptional! He not only explained the material, but also how to solve the problems in the video so when I went to the workbooks, I completely understood how to approach the problems and work through them. Unfortunately, the "Geometry: An Interactive Journey to Mastery" is done by a different professor James S. Tanton. It is painfully obvious that Professor Tanton has very little experience teaching at the high school level. If you only watch the videos for his presentations, then you will not notice what my complaint is. However, if you then try to do the examples in the workbook, which is a necessary part of the learning process, then you will understand what I am saying. After trying to do the examples in the workbook, I am convinced that the workbook was either done by a different person or Professor Tanton is oblivious to the learning process of students new to Geometry and can't structure appropriate questions for the material of his own presentations. When you look at the questions in the workbook after watching the lesson, 90% of the material of the problems, were never covered in the lesson whatsoever! On the plus side, his presentations in the video are thoughtfully and creatively done. So if you are just passively interested in watching the videos for fun then go for it. However, if you are getting this to try to help you learn for the SAT, GRE or Praxis I Core Test, then I would avoid it and look to another source.
Date published: 2017-01-29
Rated 1 out of 5 by from Jooom, Brooom.... I just purchased this course and his Power of Math Visualization as a set. I understood that they were high school level courses, and bought them to encourage some young friends towards STEM. I have only looked a the first few lessons and have a headache. He is doing the circuit of a triangle, or some other polygon, with his marker: jooom, jooom,..., brooom, .... Whew! Are these annoying sound effects carried throughout this course and the visualization course? If so, my inclination is to return them. I should note that I have purchased close to 100 Great Courses and have thoroughly enjoyed the Great majority. When I have had complaints, it has typically been strange vocalization or mis-pronounciation of words. I am not ready to rate or recommend this course. Rather am just sharing my first impression and hoping for reassurance that it will get better. My major concern is with the Presentation.
Date published: 2016-10-24
Rated 5 out of 5 by from Great course Geometry in an interesting entertaining style. A great course.
Date published: 2016-07-29
Rated 5 out of 5 by from Not Plain Geometry With Gou Daa (Good Day) Professor Tanton starts each interesting lecture. He begins with the basics of plane geometry: line segments, angles, triangles, polygons. He progresses to the geometry of linear equations, circles, ellipses, parabolas, triangular measurement, area, and understanding pi. At the midpoint of the course--Lecture 19--the material becomes increasingly interesting and complex. Dr.Tanton presents the geometry of fractals, complex numbers, geometric progression and figurate numbers. He concludes with spherical geometry illustrating how the axioms of plane geometry do not apply in three-dimensional space. Dr. Tanton has a winning presentation style. He is able to simplify complex problems, then expand complexity for student understanding. This is not a typical geometry course. Anyone looking for the standard geometry course studied in high school will either be disappointed, or like me, enchanted. This course does not stop at plane geometry, but prepares one for understanding discrete mathematics and calculus.
Date published: 2016-07-17
Rated 5 out of 5 by from Have fun learning on your schedule! The best thing for any age. I am retired 12 years now. I love this education when I want it, no class and no schedule. Take it with you. You do not need to go to it.
Date published: 2016-01-21
Rated 5 out of 5 by from A great course The course content was excellent. It was presented in a way that I found easy to follow. Lectures are always enjoyable when you can tell that the presenter really enjoys his topic. I liked his sense of humour.
Date published: 2016-01-14
Rated 5 out of 5 by from Unique I came to this course as a teacher wanting to improve my understanding and teaching of Geometry. Prof Tanton presented Geometry in a way i had never seen before and gave me plenty of examples I can take away and use. For example, his introduction to Trigonometry in Lecture 16 is brilliant; in all the years i've done maths, attended lectures and read books, I have never come across this material before. His style is easy to follow, he starts with some of the basic tenets of Geometry and carefully proves them. He then links some of the basic ideas to more complicated ideas, for example, in lecture 2 he uses Euclid to talk about the problem of circular reasoning and how that led to David Hilbert's work in the early 1900's. All his lectures use visual material to help you understand each concept. Virtually every concept is shown in a variety of ways and I liked this. There are a few reviews which were critical that some of the material was too easy and not reflective of the title of the course - "An Interactive Journey to Mastery". However, i disagree, i think he went from the basic ideas and proofs to the more complicated and mostly used a visual and interactive approach. For example, lecture 24 goes through some proofs of Pythagoras theorem but he then extends this to investigate whether the theorem holds for other shapes besides the "square of a side" with interesting results. Later lectures cover more difficult material, i enjoyed the lecture on Chaos and Fractals, Also, Dido's problem was interesting. Even his linking of Geometry to Complex Numbers is something i have not seen before. I also liked his investigation of whether "pI" exists for other shapes besides circles, A few areas I think he can improve on is a more detailed linking of Geometry with Philosophy - as in Prof Grabiner's series "Mathematics, Philosophy and the Real World." Also, he does need better visual aids for his explanations of Hyperbolic Geometry. Overall, an interesting, useful and worthwhile course for any one interested in High School Geometry with investigations into more complicated and interesting questions.
Date published: 2015-10-14
Rated 5 out of 5 by from Fun Introduction to Geometry Somehow geometry never really clicked in school. I was always much more comfortable with numbers and albegra. Prof Tanton makes geometry fun and entertaining and at the same time gets across the serious point of the subject. If you dive in, follow along with the reasoning in the lectures and tackle some of the questions, you will come away with a genuine understanding of geometry and have a lot of intellectual fun along the way. One minor quibble, there do seem to be a few typos in the answers to the questions, so be careful when checking your solution against the course book.
Date published: 2015-07-19
Rated 4 out of 5 by from My review of "Geometry: An Interactive Journey to Mastery" by James Tanton: Professor Tanton is very dynamic and engaging, and he does a really good job of keeping the material fun. I like that he goes into more "sacred geometry" in the latter lectures. One improvement is that I would've liked to have seen him cover deductive reasoning in more detail.
Date published: 2015-07-15
Rated 5 out of 5 by from Best course of geometry This course is extremely interesting! I have never written a review before, but felt that i had to do it now, after watching a part of the course. The professor is engaging, the content is interesting. I am over average interested in math and uses much of my free time learning new concepts, tricks and facts, and I felt that this course, though I have only seen part of it, has been very helpful learning those things. Look forward to learning the mathematical salute, and then learn it to all your friends:) I promise you, they will get c onfused. This course is a MUST for everyone who enjoys the great courses!
Date published: 2015-05-26
Rated 5 out of 5 by from Extremely Helpful I am doing duel preparation for actuarial exams and GMAT testing. It's been a long time since I've studied mathematics at the level I was seeing in the sample questions. I really needed to revisit Geometry to start building my skills from the ground up. This course was amazing. The only downside is that if you're on a time crunch,o this course can be a bit long winded, but thats the only qualm I could even mount when being highly critical of the course.... perhaps his Australian accent could be an issue for some, but that's just nit picking. The course is fantastic, prof does a wonderful job, kudos to putting together a great course. As a notation, i've also studied some free courses online and when comparing the free ones and the great courses which obviously involves a fee, I can say that the big difference is the depth the great courses offers is superior along with the method of how its conveyed. Free courses usually have a youtube video of poor to moderate quality with someone sketching material that is sometimes not legible. Then you're left with questions and a chat room full of people who may be leading you in the right direction or not. You won't leave this course with any questions, trust me.
Date published: 2015-01-18
Rated 5 out of 5 by from Geometry: An interactive Journey to Mastery The Professor was very knowledge and his booklet was outstanding. I strongly recommend the lesson to all high school students taking or plan to take the course.
Date published: 2015-01-17
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