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 Nov 16 comment Assumptions needed for proof of the Pythagorean Theorem from examples @DamkerngT The proof of PT via Heron's formula is an interesting alternate proof by nontraditional means. And I am looking for an alternate proof of PT, but very different. I know it seems like a strange thing to look for, a proof using finite examples, because most proofs try to avoid instances. Nov 15 comment Determinant tridiagonal matrix How did you get the linear recurrence? (in case the values on the diagonals change) Nov 15 comment Where to learn how numbers work? @A.P. Thanks for the edits. Yes I was aware of the reading difficulty. I don't know how a screen reader really works, but at least the LaTeX itself is fairly readable (which is close to how I would write it without screen formatting without LaTeX. Nov 15 revised Where to learn how numbers work? added note about binary Nov 15 reviewed Approve A variation of Borel Cantelli Lemma Nov 15 answered Where to learn how numbers work? Nov 15 comment Where to learn how numbers work? Are you asking about fibonacci or exponentiation or addition or what? fib is just defined that way, there's no justification to be had. The single algorithm you gave for exponentiation by repeated squaring is not obvious but does have a justification. The way you asked the question is too broad "How does it all work?" You need to specify for us to have a reasonable chance to answer. Nov 15 comment Where to learn how numbers work? You don't know why what is correct? Nov 15 reviewed Approve Where to learn how numbers work? Nov 15 comment Assumptions needed for proof of the Pythagorean Theorem from examples ... In other words, I am not looking for a simple proof of PT, rather a constrained proof, one where you use instances of PT and some other facts (this is what I'm looking for). Nov 15 comment Assumptions needed for proof of the Pythagorean Theorem from examples @robjohn As you note there are many proofs of PT. Some of them rely on different things, things that are independent, but eventually lead to the same thing, PT. I am trying to explore a different path. Yes, I realize (as I have noted in comments) that some of the tiling proofs of the individual items are extremely close to a full general proof of PT. But frankly one of the PT proofs are extremely close to the more general 'the sum of areas on similar shapes on the legs equals the area of a similar shape on the hypotenuse' but intellectually it is a difficult leap to discover. Nov 14 revised Assumptions needed for proof of the Pythagorean Theorem from examples added picture Nov 13 comment Generating Pythagorean Triples from Others via Dissections Forget dissection for the moment, do you have any visualization for the matrix multiplication (relevant to the geometry of a triangle)? Nov 12 comment Solve a matrix product without computing the inverse Do you need to do this by hand, or do you need an algorithm, or do you want to prove a statement about how to do this? (sure the last two are similar but the last one is more work) Nov 12 awarded Talkative Nov 11 reviewed Approve Assymptotic approximation of $\int x^n \log xdx$ Nov 11 reviewed Reject Compass-and-straightedge construction of the square root of a given line? Nov 11 revised Assumptions needed for proof of the Pythagorean Theorem from examples slight rework Nov 11 revised How many ways can $32$ cards be distributed so that three players receive $10$ cards each? latex Nov 10 comment Assumptions needed for proof of the Pythagorean Theorem from examples Also, would take 3 instances if the form were as given in my comment and edited question. Is it that simple? Also, is there any quick intuition that would make someone guess that the relation is some combination of areas?