All Questions
Tagged with visualization nt.number-theory
8 questions
0
votes
0
answers
100
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Possible shifts in finite elementary cellular automata
I investigated the long term behaviour of a pair of black cells ■■ on a circle of $N$ cells under the action of each of Wolfram's rules $R$. For each combination $(R,N)$ I determined the first ...
- 9,720
6
votes
3
answers
681
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When is $2\varphi(n) > n$ – and how to prove it?
When coloring the squares of the Ulam spiral not only by black and white (for being prime or non-prime) but by shades of grey representing the normalized totient function $\varphi(n)/n$
and ...
- 9,720
5
votes
1
answer
503
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Explaining patterns in modular multiplication graphs
Let the multiplication graph $n/m$ be the graph with $m$ points distributed evenly on a circle and a line between two points $a$, $b$ when $an \equiv b\operatorname{mod} m$.
These graphs often look ...
- 9,720
1
vote
1
answer
378
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Why is $n_{n^2-1}$ the smallest graph that clearly shows the structure of multiplication by $n$?
Initially, I wanted to ask this question as a puzzle.
Consider a regular $m$-gon. Let $0$ be the lower corner and count the corners clockwise.
Let $n_m$ be the multiplication-by-$n$-graph of $...
- 9,720
12
votes
2
answers
1k
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How to visualize finiteness of class number?
As the question title asks for, how do others "visualize" the finiteness of class number with algebro-geometric insight? I just think of it as a result in algebraic number theory and not one in ...
3
votes
0
answers
238
views
Visualization of hidden structures in numbers
[Please allow me a note: The way desribed below allows to depict functions $f:X^2 \rightarrow Y$ completely in two dimensions (without hiding or omitting any information). This allows for depicting ...
- 9,720
36
votes
2
answers
3k
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How to visualize Dirichlet’s unit theorem?
As the question title asks for, how do others "visualize" Dirichlet’s unit theorem? I just think of it as a result in algebraic number theory and not one in algebraic geometry. Bonus points for ...
14
votes
1
answer
2k
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How to visualize the Frobenius endomorphism?
As the question title asks for, how do others "visualize" the Frobenius endomorphism? I asked some people in real life and they said they didn't know and that I could go and ask on MO and possibly get ...