The Math Club

In this episode, Noah comes to Pete for some help with a really big paint job. After Pete explains just how big (and impossible) the job really is, they have a conversation about surfaces of revolution, and the seeming paradox of Gabriel's Horn.

• Hyundai's 35 meter vuvuzela
• Leave us a voice message with your favorite math joke

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Questions Answered in the Episode: • What is Gabriel's Horn? • How can a shape have infinite surface area but finite volume? • What is a surface of revolution?

Season's Greetings, Math Club! With the holidays on the horizon, a famous song leads Pete and Noah to talk about strategies for adding up long sequences of numbers. Come join the fun, and learn how a young Carl Gauss may (or may not) have done it. And if you're up for a challenge, we even "sum it up" with a special holiday puzzle for you to try.

• Brian Hayes's article in American Scientist

• Submit your puzzle solution here - Google Form

• Submit your puzzle solution here - Twitter

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Questions Answered in the Episode: • What was the method Carl Friedrich Gauss used to quickly sum the numbers one through 100? • What is the general formula used to find the sum of an arithmetic series for the first n integers?

In our last episode, Pete explained to Noah that imaginary numbers aren't so imaginary after all. This time around, he shows Noah how all the other numbers kinda are. So, if you thought there was something less than real about the square root of negative one, wait 'til you hear about the square root of positive two! Buckle up, Math Club, it's time to let our imagination run wild!!

3Blue1Brown's video on visualizing quaternions

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Questions Answered in the Episode: • What is the mathematical definition of an irrational number? • How do quaternions expand upon the complex number system?

Questions Answered in the Episode: • Who coined the term imaginary numbers and why? • What is the geometric interpretation of a complex number?

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

• Leave us a voice message • Email us • Follow us on Twitter Questions Answered in the Episode: • How was the game Prime Climb created? • How can play-based learning improve student engagement and creative sensibility in elementary mathematics?

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

• Leave us a voice message• Email us • Follow us on Twitter Questions Answered in the Episode: • What is the Diffie-Hellman key exchange? • How does modular arithmetic function as the mathematical foundation for modern encryption?