Geometry: An Interactive Journey to Mastery

Experience an intuitive and fun approach to learning the subject of geometry in this course taught by an award-winning educator.
Geometry: An Interactive Journey to Mastery is rated 4.4 out of 5 by 72.
  • y_2021, m_10, d_22, h_19
  • bvseo_bulk, prod_bvrr, vn_bulk_3.0.19
  • cp_1, bvpage1
  • co_hasreviews, tv_6, tr_66
  • loc_en_CA, sid_1033, prod, sort_[SortEntry(order=SUBMISSION_TIME, direction=DESCENDING)]
  • clientName_teachco
  • bvseo_sdk, p_sdk, 3.2.1
  • CLOUD, getAggregateRating, 85.07ms
Rated 5 out of 5 by from My Favorite Instructor so far! Thank you, The Teaching Company, and thank you, Dr. Tanton, for this excellent course! I always struggled in math in school and studied business and computer technology in college to avoid math because I just couldn't do it, no matter what discipline. I am now in my mid-fifties and retired, and I joined The Great Courses Plus to help fill my time learning the sciences that I loved but never got to enjoy in school. As such, I knew that I needed to try to learn some math to help with my Physics studies, and it has been a very positive experience so far. Dr. Tanton's Geometry and Visual Mathematics are my absolute favorites so far. Dr. Tanton is so pleasant through this whole course, and his innovative and unique presentation style really helped me grasp Geometry, finally, after all this time! I also loved his stories, humor, accent and the fun demonstrations! I would truly love for Dr. Tanton to teach a course in non-Euclidean Geometry (or other Advanced Mathematics), and I sincerely hope Wondrium and Dr. Tanton will consider offering such courses. Thank you!
Date published: 2021-06-20
Rated 5 out of 5 by from Geometry: An Interactive Journey to Mastery Dr. Tanton clearly explains every step in solving each geometric puzzle he presents. He's very entertaining. I enjoyed how he presented geometric examples to real world concepts.
Date published: 2021-06-04
Rated 5 out of 5 by from Prof Tanton is a Great Edutainor I've gone through a few of Prof. Tanton's courses and I've loved every single one. He's fun, high energy, and he has great examples. I didn't really need to take this course - I'm already pretty decent with my geometry - but I wanted to :) Plus, I actually did learn more than I expected to - so it was well worth it.
Date published: 2021-05-20
Rated 5 out of 5 by from This is absolutely brilliant! This lecture is so great that I am having a hard time of stopping watching it. The professor explained the concepts so well and so creative. Love it! When the professor mentions some mathematician's names, it will be even better if the names can appear on the screen.
Date published: 2021-03-30
Rated 5 out of 5 by from Excellent Presentation I am a retired engineer who studied Geometry in the late sixties. Professor Tanton worked through this subject in a most creative and logical way. He sort of followed Euclid's Elements and then expanded on them. His detailed explanation of Astronomy and semi circles leading to right angles and Trigonometric functions was the best I have ever heard. He made this course logical and enjoyable. I would sincerely recommend this course to any high school student or anyone who really wants to understand Geometry.
Date published: 2021-03-16
Rated 5 out of 5 by from You didn't know that Geometery could be this cool! Coming from a high school geometry nerd, this was a great course. Fascinating and creative new ways to look at "plain" geometry.
Date published: 2021-03-07
Rated 5 out of 5 by from Great Course Prof T gets the old wheels in my head moving, and to quote a lady "in a most enjoyable way".
Date published: 2020-12-29
Rated 5 out of 5 by from wonderful I am a retired physician who enjoyed mathematics as a youth. This course was a delightful refresher for the principles and concepts in geometry. Professor Tanton is one of the most enthusiastic and exciting teachers I have ever had. This is clearly a course in which a text and additional reading/study is required but not necessary. Highly recommend this course.
Date published: 2020-12-04
  • y_2021, m_10, d_22, h_19
  • bvseo_bulk, prod_bvrr, vn_bulk_3.0.19
  • cp_1, bvpage1
  • co_hasreviews, tv_6, tr_66
  • loc_en_CA, sid_1033, prod, sort_[SortEntry(order=SUBMISSION_TIME, direction=DESCENDING)]
  • clientName_teachco
  • bvseo_sdk, p_sdk, 3.2.1
  • CLOUD, getReviews, 4.01ms


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 knowledge. Its core skills of logic and reasoning are essential to success in school, work, and many other aspects of life. Yet sometimes students, even if they have done well in other math courses, can find geometry a challenge. Now, in the 36 innovative lectures of Geometry: An Interactive Journey to Mastery, Professor James Tanton of The Mathematical Association of America shows students a different and more creative approach to geometry than that usually taught in high schools. Like building a house brick by brick, students learn to use logical reasoning to uncover fundamental principles of geometry, and then use them in fascinating applications."


James Tanton
James Tanton

Our complex society demands not only mastery of quantitative skills, but also the confidence to ask new questions, to explore, wonder, flail, to rely on ones wits, and to innovate. Let's teach joyous and successful thinking.


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 excellence in math teaching. Professor Tanton is the author of a number of books on mathematics including Solve This: Math Activities for Students and Clubs, The Encyclopedia of Mathematics, and Mathematics Galore! Professor Tanton founded the St. Mark's Institute of Mathematics, an outreach program promoting joyful and effective mathematics education. He also conducts the professional development program for Math for America in Washington, D.C.

By This Professor

The Power of Mathematical Visualization
Geometry: An Interactive Journey to Mastery
Geometry: An Interactive Journey to Mastery


Geometry-Ancient Ropes and Modern Phones

01: 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.

33 min
Beginnings-Jargon and Undefined Terms

02: 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.

28 min
Angles and Pencil-Turning Mysteries

03: 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

28 min
Understanding Polygons

04: 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.

31 min
The Pythagorean Theorem

05: 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.

29 min
Distance, Midpoints, and Folding Ties

06: Distance, Midpoints, and Folding Ties

Learn how watching a fly on his ceiling inspired the mathematician Rene Descartes to link geometry and algebra. Find out how this powerful connection allows us to use algebra to calculate distances, midpoints, and more.

29 min
The Nature of Parallelism

07: 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!

35 min
Proofs and Proof Writing

08: 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.

29 min
Similarity and Congruence

09: 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.

34 min
Practical Applications of Similarity

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.

31 min
Making Use of Linear Equations

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.

29 min
Equidistance-A Focus on Distance

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.

33 min
A Return to Parallelism

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.

31 min
Exploring Special Quadrilaterals

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.

30 min
The Classification of Triangles

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).

30 min
Circle-ometry-On Circular Motion

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.

32 min
Trigonometry through Right Triangles

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.

28 min
What Is the Sine of 1?

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.

32 min
The Geometry of a Circle

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.

29 min
The Equation of a Circle

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.

33 min
Understanding Area

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.

28 min
Explorations with Pi

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).

31 min
Three-Dimensional Geometry-Solids

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.

32 min
Introduction to Scale

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.

30 min
Playing with Geometric Probability

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.

30 min
Exploring Geometric Constructions

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.

29 min
The Reflection Principle

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.

31 min
Tilings, Platonic Solids, and Theorems

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.

32 min
Folding and Conics

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.

29 min
The Mathematics of Symmetry

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.

28 min
The Mathematics of Fractals

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.

30 min
Dido's Problem

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.

31 min
The Geometry of Braids-Curious Applications

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.

29 min
The Geometry of Figurate Numbers

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.

32 min
Complex Numbers in Geometry

35: Complex Numbers in Geometry

In lecture 6, you saw how 17th-century mathematician Rene 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.

32 min
Bending the Axioms-New Geometries

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.

32 min