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Jan
3
comment Reference to an atlas of curves and surfaces?
@bubba oh, yes, I get that. The point of asking for an atlas is to collect all the equations and their properties in one place so that one might more easily do as you suggest.
Jan
3
comment Reference to an atlas of curves and surfaces?
@bubba sure but from where? Where do you get the 3D printer designs?
Dec
28
comment Factorial and exponential dual identities
Nice! Can you relate this theorem to the ordinary and exponential generating function in my comments to the OP: $g(x)=\int_0^{\infty} e^{−u}G(xu) du$? Also, can you give any meaning/interpretation to the master theorem here?
Dec
11
comment Determining the number of zeros in the upper half plane
If only there were an easy way to visualize complex functions. It's basically like having to see 4-dimensions, where 2 are the independent variable and another 2 dependent. Sadly hand graphing calculators won't do it. (computer algebra packages might help). I'm only suggesting this as visualization, not analytic solution for the exact answers.
Nov
18
comment Combinatorics Identity about Catalan numbers.
Do you want an algebraic proof or a combinatorial one?
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
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
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
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
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
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
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?