Cartesian Product of Two Sets Visually! @MathVisualProofs

Uploaded August 2025 | Updated September 2026, 2 weeks ago

In this video, we show a visualization of the Cartesian product of two (finite) sets. From this visual, we can immediately get the product principle, a rule often investigated in probability, statistics, and combinatorics.

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#logic #settheory #cartesianproduct #cartesianproducts #setsrelationsandfunctions #sets #setconnectives #crossproduct #venndiagram #visualproof #math #manim #discretemathematics #statistics #descartes #combinatorics #productprinciple #productrule #multiplication #multiplicationprinciple

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$Chaos in a Heptagon! In this short, we show what happens when iterating the procedure of choosing a heptagon vertex at random and moving 0.692 of the distance from the current dot to the chosen point. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you want to know more about the Chaos game, see the following links: https://en.wikipedia.org/wiki/Chaos_game https://mathworld.wolfram.com/ChaosGa... https://math.bu.edu/DYSYS/chaos-game/... https://youtu.be/kbKtFN71Lfs https://youtu.be/IGlGvSXkRGI https://youtube.com/shorts/yDHkNDrHfIw #chaos #chaosgame #heptagon #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractal #fractals To learn more about animating with manim, check out: https://manim.community$

$Mediant Inequality from Slopes This is a short, animated visual proof demonstrating what one might call the mediant inequality. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! For an alternate visual proof of this fact, see: https://youtu.be/RKeBuWL1B4A https://youtube.com/shorts/cI92ZID95g4 https://youtu.be/pODylgdI3p8 For the wide format of this video, see: https://youtu.be/AuxqpiDTCyU?si=kLa0Un4L8ADM6a_q This animation is based on a visual proof by Li Changming from the January 1988 issue of Mathematics Teacher (https://www.jstor.org/stable/27965677 - page 63). #math #inequality #numbertheory #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #fractions #mediant #mathematics #fareyfractions #farey #mathshorts #mathvideo To learn more about animating with manim, check out: https://manim.community$

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