The Math Club

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.

In this episode, Noah's certain that he has a disease because he tested positive on a test that's 99% accurate. Does that mean he almost certainly has the disease? Pete's not so sure, and brings up a statistics concept to help shed some light on the numbers.

• Our online simulator that you can play with • Submit your puzzle answer here

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Lots of us have played with a Rubik's Cube at one time or another, but did you know this simple little toy is chock full of math? Join Pete and Noah as they talk about billions of combinations, set theory, and the maximum number of moves required to solve the cube. *Skateboard not required.

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Questions Answered in the Episode: • How many possible combinations and valid configurations are there for a Rubik's cube? • How does group theory and the study of symmetries apply to solving a Rubik's cube?

You've heard about two-factor authentication, but have you heard about two-factor numbers? Of course you have! They're called primes, and in this episode Pete and Noah discuss what they are, how we find them, and some of the more interesting (and as-yet unproven) conjectures about them. Pete even speculates about how primes might make their Broadway debut!

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Questions Answered in the Episode: • What is the fundamental theorem of arithmetic and why does it exclude the number 1 from being prime? • How did Euclid prove that there are infinitely many prime numbers?

In this episode, Pete and Noah provide opposing viewpoints on how to respond to a classic mathematical paradox.

• Game Theory and Strategy - Textbook used in Pete's Game Theory course • Are you a one boxer or a two boxer? - Use this link to let us know what you'd decide after listening to the episode.

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Questions Answered in the Episode: • What is Newcomb's Paradox? • How does Newcomb's Paradox illustrate the conflict between the dominance principle and expected utility?

In this episode, Pete and Noah discuss right triangles, pythagorean triples, and why the Scarecrow's brain might not be all it was cracked up to be.

• Pythagorean Theorem water demo • 3Blue1Brown • Plimpton 322 • Leave us a voice message • Email us • Follow us on Twitter

Questions Answered in the Episode: • What is the relationship between Pythagorean triples and the Pythagorean theorem? • How can you calculate a Pythagorean triple using a mathematical formula?