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Results tagged with gm.general-mathematics
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user 6094
Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
51
votes
Fascinating moments: equivalent mathematical discoveries
Consider $n$ evenly spaced points on a circle representing $\mathbb{Z}^n$.
Two sets of points
with the same multiset of distances between them (measured by the shortest distance around
the circle) are …
1
vote
smallest square containing k non-overlapping equal rectangles at any orientation
Just a note to indicate why this question might not
be straightforward, now that it's been bumped to the homepage.
For $k=2$ rectangles of size $a \times b = 1 \times 6$,
the diagonal packing is bette …
- 151k
13
votes
17 camels trick
This does not quite match your criteria, but feels similar.
It is a method for multiplying two decimals, say $13 \times 27$.
Form two columns headed by $13$ and $27$.
Halve $13$ and discard any remain …
0
votes
Are there any undergraduate-friendly research areas in algebra?
One option is to focus on an elementary but unsolved problem, and let
exploring that problem lead you to learn relevant techniques.
(1) For example, tight bounds on the number of "edge guards" to cove …
1
vote
math circles video lectures for school children?
This may not be exactly what you seek, but it hits your 3rd class, "a bird's eye view of the world of mathematics": The Museum of Mathematics Encounters videos, available at this link.
(so …
21
votes
Accepted
Relation between math and piano music
There is a Masters thesis by Lauren Halsey entitled,
"An examination of rhythmic practices and influences in the keyboard works of György Ligeti"
(UNCG link), which addresses your question:
"...th …
- 151k
22
votes
How to improve writing mathematics?
Halmos, Paul R. "How to Write Mathematics." L'Enseignement Mathématique 16.2 (1970): 123-152.
(PDF download.)
Idiosyncratic, but a classic. I especially enjoyed the section, "Think about the al …
2
votes
Card game / options pricing / Brownian bridge question
Perhaps the delightful paper, How to lose as little as possible,
by Vittorio Addona, Stan Wagon, and Herbert Wilf, is related to your question? If not, you
lose little by scanning it. From their Abs …
- 151k
2
votes
What are examples of problems we know how to solve for primes (or prime powers), but not for...
Convex Equipartitions of volume and surface area.
We show that, for any prime power $p^k$ and any convex body $K$ (...) in $\mathbb{R}^d$, there exists a partition of $K$ into $p^k$ convex sets with …
14
votes
What are possible applications of deep learning to research mathematics?
This predates deep learning, but we should not forget that there has already been
some progress in graph theory by recognizing patterns
(OP: "patterns in the data")
and forming conjectures.
Hansen, P …
14
votes
What are possible applications of deep learning to research mathematics?
Adam Wagner has a new paper on arXiv (29 Apr 2021), "Constructions in combinatorics via neural networks," whose
Abstract is:
"We demonstrate how by using a reinforcement learning algorithm, the deep …
13
votes
Anything special (historical?) about surface $x\cdot y\cdot z\ +\ x+y+z=0$?
Just wanted to see what it looks like...
Now added origin and axes $\pm 1$ in each coordinate.
- 151k
34
votes
Books on music theory intended for mathematicians
There is the book by Tymoczko from which his lecture was no doubt drawn:
Tymoczko, Dmitri. A geometry of music: Harmony and counterpoint in the extended common practice. Oxford University Press, 2 …
40
votes
Short papers for undergraduate course on reading scholarly math
I think this is a delightful paper:
Hull, Thomas C. "Solving cubics with creases: The work of Beloch and Lill." The American Mathematical Monthly 118, no. 4 (2011): 307-315.
(PDF download.)
It …