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Younglings are always asking when we'll use polynomials in real life. This video shows not only how polynomials give rise to beautiful patterns, but also how these patterns can be used to create other patterns that we might be after. Here's the proof that a non-zero degree-d polynomial has at most d roots: It's a proof with simple steps. And the video also talks about other number systems which is a very cool topic! If you haven't seen any of this before and especially if you like proving things I STRONGLY suggest watching it. --- Paper links: The paper central to our story: The paper using viral loads and Kirkman triples to solve pooled RT-PCR testing: The paper using the Chinese Remainder Theorem to create disjunct matrices: The paper using the method of conditional probabilities to create codes and disjunct matrices: --- Applications of Error-Correcting Codes: Link to the topic of secret sharing schemes (Shamir's Scheme is closest to coding theory): Fingerprint-enabled vault application taken from Essential Coding Theory (Chapter 21 in Jan 31 2022 draft): --- Dobble links: “The Mind-Bending Math Behind Spot It!, the Beloved Family Card Game“ by Lina Rodrigues McRobbie: “How to make the card game Dobble (and the Maths behind it!)“ by MirKat Maths: ^ Includes a worksheet to try out things yourself! “Dobble / Spot it: the maths behind the cards“ by local meadows: And a video by Stand-up Maths, with some additional links in it: --- 0:00 Introduction 3:55 The pattern in question 7:02 The pattern not in question 9:09 Finding the pattern not in question 12:13 Finding the pattern in question 15:01 Conclusion --- Thanks to Grant Sanderson and the SoME2 organizers for the motivation to create such videos, to the manim community for the amazing software, and to my friends who first told me of this use of polynomials and who gave me feedback on the video.
