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.

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.

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!

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.

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.

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.

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.

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.

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.

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.