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Aug
20
revised All permutation matrices that convert one Hadamard matrix into another Hadamard matrix.
added 1180 characters in body
Aug
19
revised Interpretation of partial derivatives of vertical coordinate with respect to $x$ and time
added 35 characters in body
Aug
18
comment Combinatorial proof of $a^n - b^n = (a - b)(a^{n – 1} + a^{n – 2}b + \dots + ab^{n – 2} + b^{n – 1})$
I'm uncertain how your question relates to my answer. The last even numbered ball is ball $n$ if $n$ is even and ball $n−1$ if $n$ is odd. The configurations you describe are among the $(a−b)a^{n−1}$ possible configurations where $n$ is even and ball $n$ goes into one of the first $a−b$ boxes. They're among the $(a−b)a^{n−2}b$ possible configurations where $n$ is odd and ball $n−1$ goes into one of the first $a−b$ boxes while ball $n$ goes into one of the last $b$ boxes.
Aug
18
comment What is the origin of “how the Japanese multiply” / line multiplication?
Your question was recently asked again. I don't know the answer, but this post identifies the author of the video you link to. Here's the link to the original video. For some reason, the video doesn't run for me, but it's clearly the same as the video you found.
Aug
17
answered Combinatorial proof of $a^n - b^n = (a - b)(a^{n – 1} + a^{n – 2}b + \dots + ab^{n – 2} + b^{n – 1})$
Aug
15
comment Where does the “Visual Multiplication” technique originate from?
This question has come up on MSE before: here and here.
Aug
15
comment Where does the “Visual Multiplication” technique originate from?
You might be interested in the story told here.
Aug
15
revised Why does solving $\int \frac{v}{9.8-0.0025v^2}\mathrm{d}v=\int1{d}x$ for $v^2$ in terms of $x$ produce 2 completely different answers?
added 1 character in body; edited title
Aug
15
answered Why does solving $\int \frac{v}{9.8-0.0025v^2}\mathrm{d}v=\int1{d}x$ for $v^2$ in terms of $x$ produce 2 completely different answers?
Aug
12
comment Where does the “Visual Multiplication” technique originate from?
I think that the hypothesis that it's a Mayan technique can be ruled out. The MacTutor page on Mayan mathematics is pretty informative, and contains the statement, "We should also note that the Mayans almost certainly did not have methods of multiplication for their numbers and definitely did not use division of numbers." Some Mayan numerals do make use of sets of parallel horizontal lines, which may, at some point, have suggested to somebody a connection with visual multiplication, but I doubt there's anything to it.
Aug
12
answered proof of a theorem in a paper
Aug
12
comment proof of a theorem in a paper
@hardmath: the statement of Theorem 1.1(4) is contained in the same paper and is exactly what you say. To the OP: although the proof of Theorem 1.1 is not given in the paper, it is not hard. The paper contains some examples, which, if studied carefully, should help with the intuition.
Aug
12
revised proof of a theorem in a paper
added reference and link
Aug
10
comment Techniques to find matrix inverses of general classes of matrices?
There are often specialized methods for solving, inverting, and/or finding eigenvalues of matrices with a particular structure. For example, there are specialized techniques for tridiagonal matrices, circulant matrices, and Toeplitz matrices. If you will be dealing with lots of such matrices, it's probably worth learning those techniques.
Aug
10
comment Techniques to find matrix inverses of general classes of matrices?
I don't know whether the two examples you mention are typical of what you need to do, but in both cases, you have to solve a system represented by an augmented matrix $[M|I],$ which is already in row-echelon form. It is not hard to see what the fully-reduced form is going to look like for general $n$ in either of these cases.
Aug
9
answered Algebraically compute $\lim_{x \to 0}\frac{\sin x}{x}$
Aug
9
comment Where does the “Visual Multiplication” technique originate from?
This is a history of math question. It's not asking why the method works.
Aug
9
comment What is the oldest open problem in geometry?
@SteveJessop: the Introduction and History section of that Wikipedia article contain quite a few statements that, to my ear, are very strange. I haven't been following the page, but looking at the Talk page, it appears that some edit warring has been going on. I would recommend that anything in the article that sounds fishy be taken with a grain of salt.
Aug
8
comment What is the oldest open problem in geometry?
@zibadawatimmy: shifts in terminology aside, is there evidence that the Greeks had any notion of Newtonian dynamics? I don't think it's possible to formulate the $n$-body problem without that.
Aug
6
revised All permutation matrices that convert one Hadamard matrix into another Hadamard matrix.
edited body