In this episode, Noah's having trouble with an old game from his childhood until Pete saves the day by tackling the twisty turns of topology. From donuts to coffee cups, and spheres to tori (or, as Noah calls them: toruses), come explore the interesting world of continuous deformations. It's time to get into shape!

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Questions Answered in the Episode: • What is the difference between topology and geometry? • How do you calculate the Euler characteristic of a shape?

In this episode, Pete and Noah are joined by Dan Finkel, founder of Math for Love and co-creator of the award winning game, Prime Climb. Listen in as they talk about Dan's work making math fun and accessible by tapping into children's natural desire to play. And because we know you love to play, too, Dan will also challenge you with a puzzle.

Math for Love

Dan's TED Talk - 5 ways to share math with kids

Submit your puzzle answer

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Today's match-up answers the age-old question of what happens when an unstoppable brain meets an unbreakable cipher. In the red corner, weighing in at 2,193 digits…. Noah's deviously encrypted message! And in the blue corner.... The Commissioner of Codebreaking…. The Foreman of Frequency Analysis…. Pete's decoding skills! Only one will leave the ring victorious. Who will it be? Tune in and find out! The match is about to begin... DING DING DING!

• Encrypted passage to decode

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Questions Answered in the Episode: • How do you use frequency analysis to break a substitution cipher? • How can math help with decryption?

Surprise!!! Pete needs some more time with the codebreaking challenge, so this week we're giving you a previously unaired bonus episode from The Math Club's earliest days (six months ago). Also, Alexa finally grows too big for her britches.

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Questions Answered in the Episode: • How did Archimedes approximate the value of pi? • Why is the ratio of a circle's circumference to its diameter constant regardless of the circle's size?

Yesterday's episode explored the Diffie-Hellman Key Exchange algorithm, including a section in which Pete and Noah came up with a valid generator for a modulus of 23. The rules about what makes a generator valid can be a bit tricky without visuals, so we made this video bonus to help illustrate what's going on here.

If you use the internet, you rely on mathematical algorithms to securely transmit your private data over public networks. In this episode, Noah describes an encryption scheme he made up in high school, which leads to a discussion about how computers securely exchange encryption keys today. It all ends up with Noah getting Pete to put his money where his math is, by accepting an interesting decoding challenge.

• Encrypted passage to decode

• Diffie and Hellman's original paper: New Directions in Cryptography

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Pete's out with a broken leg, so Noah and Alexa use math to investigate the mathematics of his skateboarding accident. Listen in as they talk about angular momentum, the acceleration of falling bodies, and pounds of force generated upon impact.

Free Fall with Air Resistance Calculator

Force of Impact Car Crash Calculator

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Questions Answered in the Episode: • How do you calculate the distance traveled on a skateboard half-pipe? • How does the conservation of angular momentum affect a skateboarder's speed?

Math always seems so objective, with little room for debate. In other fields there are sometimes huge disagreements among experts. But what about math? In this episode, Pete and Noah discuss the age-old argument of where math came from... was it a discovery or was it an invention? Join us as we dive into the debate.

Here's a place where you can share your thoughts about our previous seven topics Were they more invention or more discovery? https://bit.ly/mathclubpodcast-ep8

Roger Penrose Video

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Questions Answered in the Episode: • Is mathematics a human invention or a universal discovery?• How can mathematics be viewed as a combination of both invention and discovery?

Infinity. Most kids first learn about this neverending concept when double and triple jinx don't seem to do enough anymore. There are infinity pools, the Infnity Engine, and even an Inifinity War. But how does infinity differ from the counting numbers and the familiar rules that govern them? In this episode, Pete and Noah use the paradox of Hilbert's Grand Hotel to explore infinity and discuss some of its interesting quirks.

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Questions Answered in the Episode: • What is Hilbert's Paradox of the Grand Hotel and how does it demonstrate the properties of infinite sets? • What is the difference between countable and uncountable infinity in mathematics?

Yesterday's episode dove into the numbers around a positive test result that is 99% accurate, when 1 in 100 people have a specific condition. The result was a bit surprising and counterintuitive, and this video bonus helps to show why it comes out the way it does.