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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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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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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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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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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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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