Beginnings—Jargon and Undefined Terms
Episode 2 of Geometry

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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.
Zero The Math Hero - Geometry Tutor
This is a 12 video playlist
Similarity and Congruence
Episode 9 of Geometry
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 Joy of Primes
Episode 3 of The Joy of Mathematics
A number is prime if it is evenly divisible by only itself and one: for example, 2, 3, 5, 7, 11. Professor Benjamin proves that there are an infinite number of primes and shows how they are the building blocks of our number system.
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.
What Is the Sine of 1°?
Episode 18 of Geometry
So far, you've seen how to calculate the sine, cosine, and tangents of basic angles (0deg, 30deg, 45deg, 60deg, and 90deg). 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…
Practical Applications of Similarity
Episode 10 of Geometry
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.
The Geometry of a Circle
Episode 19 of Geometry
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.
The Classification of Triangles
Episode 15 of Geometry
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).
The Pythagorean Theorem
Episode 5 of Geometry
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.
Proofs and Proof Writing
Episode 8 of Geometry
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.
Circle-ometry—On Circular Motion
Episode 16 of Geometry
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…