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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?
Nov
10
comment Determining if Graphs are Isomorphic.
Wait, are these two separate problems, 2 graphs in qn 1 and 2 graphs in question 2?
Nov
10
comment Determining if Graphs are Isomorphic.
@wbrugato also, I'm pretty sure that, even if the number of edges is fixed, there's no way they could be acyclic (it would imply tree implying 7 edges and degree 1 for at least 2 vertices)
Nov
10
comment Determining if Graphs are Isomorphic.
@lhf Are two graphs isomorphic if they exhibit the same degree of nonexistence?
Nov
9
revised Assumptions needed for proof of the Pythagorean Theorem from examples
slight rewording
Nov
9
comment Is it possible to formulate category theory without set theory?
Russell's paradox happens in CT, too. And independently, you can take CT as a base formalization and embed set theory in it (similar to the usual reverse situation to bootstrap people into understanding of category theory by starting off stating CT in terms of sets of objects, morphism, etc.)
Nov
7
awarded  Benefactor
Nov
7
comment Assumptions needed for proof of the Pythagorean Theorem from examples
@SammyBlack Understood. It may very well be that to establish the form of the relation among the sides that you've already gotten the constants and proven PT. And if you knew the form were $d a^2 + e b^2 = f c^2$ only one instance would set the coeffs to 1. I realize my "any other assumptions" is a bit broad, but are there any restrictions on form that leave a non-trivial interpolation?