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This tag is used if a reference is needed in a paper or textbook on a specific result.

9 votes
0 answers
196 views

Placing triangles around a central triangle: Optimal Strategy?

This question has gone for a while without an answer on MSE (despite a bounty that came and went) so I am now cross-posting it here, on MO, in the hope that someone may have an idea about how to broac …
Benjamin Dickman's user avatar
9 votes
Accepted

On a paper by Dimitrie Pompéiu and on one (in two parts) by Edmund Landau

Below are both references: links then screenshots. The first reference can be found in full here. In case permissions etcetera should change, below are screenshots of the pages: The second refe …
Benjamin Dickman's user avatar
3 votes
3 answers
375 views

Closed formula for number of ones in a proper factor tree

Edit [2023 Dec 7]: One of my specific wonders, along with that of students, is around when a recursive formula might have – or be expected to have – an explicit or closed formula. What is the mathemat …
Benjamin Dickman's user avatar
7 votes
2 answers
398 views

Quantifying difficulty of integrals versus inverses

Recently, I have been discussing inverses with a tenth grade class and integrals with an eleventh/twelfth grade class, and this has led me to the following wonder: Wonder. Is there a "reasonable" way …
Benjamin Dickman's user avatar
4 votes
1 answer
325 views

Enumerating subsets with no triple appearing together more than once

This question is motivated by a real-world application related to an art project that involves displaying images, but my search hit a dead end after finding the wikipage about Kirkman systems (other r …
Benjamin Dickman's user avatar
2 votes
0 answers
138 views

Integers with exactly three factor pairs whose successors are relatively prime

I am interested in the following problem, and will appreciate pointers around how it can be solved – partially or fully – and/or indicators around whether it is even tractable: Characterize $N \in \m …
Benjamin Dickman's user avatar
18 votes
1 answer
1k views

Distinct integer roots for a degree 7+ polynomial and its derivative

Question: Is there a polynomial $f \in \mathbb{Z}[x]$ with $\deg(f) \geq 7$ such that all roots of $f$ are distinct integers; and all roots of $f'$ are distinct integers? Background: I asked a rel …
Benjamin Dickman's user avatar
20 votes
Accepted

Looking for a paper on transfinite diameter by David Cantor

Hopefully this works: Cantor D.: On an extension of the definition of transfinite diameter and some applications Since you said that you had "been hunting for the following paper for quite a while," …
Benjamin Dickman's user avatar
4 votes
0 answers
228 views

How many arrangements of $n$ points with $k$ edge lengths exist in $d$ dimensions?

[Asking on behalf of a high school mathematics course, but responses written at any level are welcome!] I was recently reading over a nice puzzle called the four points, two distances problem: Fi …
Benjamin Dickman's user avatar
9 votes
1 answer
631 views

De-Nesting Absolute Value Function into Linear Combination of Absolute Value Functions

Context: In formulating problems for secondary school mathematics teachers (and students) about absolute value functions, which we define as functions $\mathbb{R} \rightarrow \mathbb{R}$ that send $x …
Benjamin Dickman's user avatar
5 votes
Accepted

On a theorem of Zhang Jinwen about models of arithmetic

(The final two sections are translated modulo tweaks...) I do not know the answer to your question, but I can try to translate (part of) this paper. There are some terms that are unfamiliar to me ( …
22 votes
Accepted

Anti-Mandelbrot set

Perhaps the key term is tricorn? See Inou's Self-similarity for the tricorn (arXiv pdf) and its references. Sample excerpt:
Benjamin Dickman's user avatar
5 votes
Accepted

Exact reference for Liouville theorem

Is it possible that the Liouville theorem you are thinking of is the boundedness theorem, whereas the result you have in mind is from a different paper of Liouville's? In particular, the paper: Li …
Benjamin Dickman's user avatar
21 votes
5 answers
5k views

What arrangement of unit cubes minimizes surface area?

For each of these two questions, one can assume that the arrangements are polycubes (for which a definition can be found in the excerpt-image below). Question A. How does one arrange $n$ unit cubes t …
Benjamin Dickman's user avatar
10 votes

Origin of the term "generic" in set theory

In trying to trace the history of forcing in an earlier MO question, I came across G.H. Moore's The origins of forcing. I think you can find in Moore's piece an answer to your question, too. On p. 164 …
Benjamin Dickman's user avatar

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