The Geometry of Figurate Numbers
Episode 34 of Geometry

The Great Courses
Show More

If you are a student or a professor:

Watch now

If you are a librarian or a professor:

Related videos

The Joy of Numbers
Episode 2 of The Joy of Mathematics
How do you add all the numbers from 1 to 100--instantly? What makes a square number square and a triangular number triangular? Why do the rules of arithmetic really work, and how do you calculate in bases other than 10?
The Joy of Fibonacci Numbers
Episode 5 of The Joy of Mathematics
The Fibonacci numbers follow the simple pattern 1, 1, 2, 3, 5, 8, etc., in which each number is the sum of the two preceding numbers. Fibonacci numbers have many beautiful and unexpected properties, and show up in nature, art, and poetry.
The Joy of Geometry
Episode 11 of The Joy of Mathematics
Geometry is based on a handful of definitions and axioms involving points, lines, and angles. These lead to important conclusions about the properties of polygons. This lecture uses geometric reasoning to derive the Pythagorean theorem and other interesting results.
Complex Numbers in Geometry
Episode 35 of 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…
The Equation of a Circle
Episode 20 of Geometry
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.
Divide and Conquer
Episode 4 of Secrets of Mental Math
Turn now to the last fundamental operation of arithmetic: division. Explore a variety of shortcuts for dividing by one- and two-digit numbers; learn how to convert fractions such as 1/7 and 3/16 into decimals; and discover methods for determining when a large number is divisible by numbers such as 3,…
Advanced Multiplication
Episode 11 of Secrets of Mental Math
Professor Benjamin shows you how to do enormous multiplication problems in your head, such as squaring three-digit and four-digit numbers; cubing two-digit numbers, and multiplying two-digit and three-digit numbers. While you may not frequently encounter these large problems, knowing how to mentally solve them cements your knowledge of basic mental…
The Joy of the Imaginary Number i
Episode 14 of The Joy of Mathematics
Could the apparently nonsensical number the square root of -1 be of any use? Very much so, as this lecture shows. Such imaginary and complex numbers play an indispensable role in physics and other fields, and are easier to understand than they appear.
The Joy of Higher Algebra
Episode 7 of The Joy of Mathematics
This lecture shows how to solve quadratic (second-degree) equations from the technique of completing the square and the quadratic formula. The quadratic formula reveals the connection between Fibonacci numbers and the golden ratio.
Bending the Axioms—New Geometries
Episode 36 of Geometry
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.
The Joy of Mathematical Magic
Episode 24 of The Joy of Mathematics
Closing the course with a magician's flair, Professor Benjamin shows a trick for producing anyone's phone number, how to create a magic square based on your birthday, how to play "mathematical survivor," a technique for computing cube roots in your head, and a card trick to ponder.
Three-Dimensional Geometry—Solids
Episode 23 of Geometry
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.