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Infinite Series

Defining Infinity

Infinite Series

Defining Infinity

10m 31s

Set theory is supposed to be a foundation of all of mathematics. How does it handle infinity?

9m 12s

The Assassin Puzzle

Imagine you have a square-shaped room, and inside there is an assassin and a target. And suppose that any shot that the assassin takes can ricochet off the walls of the room, just like a ball on a billiard table. Is it possible to position a finite number of security guards inside the square so that they block every possible shot from the assassin to the target?

9m 32s

Instant Insanity Puzzle

Imagine you have four cubes, whose faces are colored red, blue, yellow, and green. Can you stack these cubes so that each color appears exactly once on each of the four sides of the stack?

10m 31s

Defining Infinity

Set theory is supposed to be a foundation of all of mathematics. How does it handle infinity?

10m 21s

The Geometry of SET

In the card game SET, what is the maximum number of cards you can deal that might not contain a SET?

10m 7s

What are Numbers Made of?

In the physical world, many seemingly basic things turn out to be built from even more basic things. Molecules are made of atoms, atoms are made of protons, neutrons, and electrons. So what are numbers made of?

7m 17s

Telling Time on a Torus

What shape do you most associate with a standard analog clock? Your reflex answer might be a circle, but a more natural answer is actually a torus. Surprised? Then stick around.

9m 36s

The Mathematics of Diffie-Hellman Key Exchange

Symmetric keys are essential to encrypting messages. How can two people share the same key without someone else getting a hold of it? Upfront asymmetric encryption is one way, but another is Diffie-Hellman key exchange.

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