3blue1brownGreatest Common Tiling
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Tags: greatest-common-divisorcoprime
In this blog post I cover Bezout’s identity, how to compute Bezout coefficients, and how they can be used to quickly settle a question about all the common divisors between two numbers.
My aim was to make the mathematical content relatively light, but framed within a concrete story, which should make it accessible from high-school level onwards. I also included some questions throughout the text, for readers who want to check their understanding, or curious to be pushed into directions that go slightly beyond what is covered in the post itself.
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Well motivated and clearly explained! :clap:
The article is well written, easy to understand and follow, and complete. The topic is relatively easy, but probably good for high school audience. Story part is fun, but in general not much interesting.
Note: When the page loads, it asks for login info in a pop-up modal. I can close the modal, but its annoying.
Really really great, perfect if you have struggled to understand gcds and bezout’s, with a neat proof that is not normally seen directly like that👍
Nice and simple motivation. I liked the chatbot interaction. It gives the explanation a relaxed and natural feel. Also, the summary at the end is very concise and gives a nice recap.
Small correction: “use equation (1) to bring down the 26 to 0 in equation (2)” seems like it should be “use equation (2) to bring down the 26 to 0 in equation (1)”, if I understand correctly.
Eh, framing it around “how to fix the output of whatever ChatGPT is telling me” is sketchy at best. If you set it up as “This is why you shouldn’t ask LLM chatbot math questions”, it might have worked? But fixing LLM output for such an elementary problem is equivalent to doing it yourself. So, going back to ChatGPT severla times is… useless and boring.
Nice introduction to Bezout’s identity and also illustrating how to compute the solutions. Also nice exercises at the end on how we can extend this more use cases as well.
Maybe working with slightly larger numbers (4-5 digits) might help to illustrate the power here as it becomes more difficult to check and gives a better illustration of how it might help.
Well motivated, though the use of Bezout’s Lemma over standard Euclidean Algorithm is not very clear.
Clearly written.
relatable original problem