27 Feb 2020
Kalpa Madhawa
Quaternionic eigenvalues
Thursday, February 27, 2020
Thursday, February 20, 2020
From Arts Bathsheba |
Duston Wetzel
On gyroid
Gyroid was discovered by our own Alan Schoen and is enjoing an increasing general popularity in sience and in in general math culture
Tuesday, February 4, 2020
Saturday, January 18, 2020
Math from physics
23 and 30 Jan 2020
Philip Feinsilver
Eigenvectors from eigenvalues
>> Relevant paper on Arxiv
>> Quanta Magazine on this subject
<< see the original image
Philip's presentation (NEW)
plus this page.
Philip Feinsilver
Eigenvectors from eigenvalues
>> Relevant paper on Arxiv
>> Quanta Magazine on this subject
<< see the original image
Philip's presentation (NEW)
plus this page.
Thursday, November 14, 2019
Symmetry
21 November and
and 5 December 2019
Thushari Jayasekera
Symmetry in Materials Physics
← click to view details.
Tuesday, November 12, 2019
Sunday, October 27, 2019
Apolloniana
Jerzy Kocik
Lattices, spinors, and classification of Apollonian disk packings. Here are the first 21 irreducible classes of lattices.
More on "geometric Apolloniana".
(Simply "tinyURL.com/jkocik", if you need to retype it)
Here is Don's derivation of parametrization of \(x\), \(y\), \(z\), and \(w\) satisfying $$x^2+y^2=zw$$ by three parameters \(\alpha\), \(\beta\), and \(\gamma\): $$ \begin{array}{rl} x=&\beta\gamma-\alpha^2\\ y=&\beta\gamma+\alpha^2-2\alpha\gamma-\alpha\beta \qquad\quad(1)\\ z=& -\alpha^2 -(\beta-\alpha)^2\\ w=&-\gamma^2-(\gamma-\alpha)^2\\ \end{array}$$ This would suggest the following parametrization of spinors: $$\mathbf a=\begin{bmatrix}\alpha\\\alpha\!-\!\beta\end{bmatrix},\quad \mathbf b=\begin{bmatrix}-\gamma\\ -\gamma\!+\!\alpha\end{bmatrix}$$ with \(x=\mathbf b\times\mathbf a\), \(y=\mathbf a\cdot\mathbf b\), \(z=-\|\mathbf a\|^2\), and \(w=-\|\mathbf b\|^2\). Another arrangement: $$\mathbf a=\begin{bmatrix}\alpha\\\alpha\!-\!\beta\end{bmatrix},\quad \mathbf b=\begin{bmatrix}\gamma\!-\!\alpha\\ -\gamma\end{bmatrix}$$ with \(x=\mathbf a\cdot\mathbf b\), \(y=\mathbf a\times\mathbf b\), \(z=-\|\mathbf a\|^2\), and \(w=-\|\mathbf b\|^2\).
Question: Does \(2^2 + 8^2 = 4\cdot 17\) admit a representation by some \(\alpha\), \(\beta\), and \(\gamma\) of Eq. (1)?
Wednesday, October 9, 2019
Sunday, September 22, 2019
Numbers
Fordon James, "Primary spaces" |
Don Redmond
On representing integers as sums of four squares
Here are Don's notes on this subject
Wednesday, September 18, 2019
Wednesday, September 4, 2019
Periodic Table
5 and 12 September 2019
Punit Kohli
Periodic Table: patterns of elements
Here is the paper Mike has mentioned:
(Click here)
Title: How the modified Bertrand theorem explains regularities of the periodic table I. From conformal invariance to Hopf mapping
Authors: Arkady L. Kholodenko, Louis H. Kauffman
Also: a popular podcast "Battle of elements".
Punit Kohli
Periodic Table: patterns of elements
Here is the paper Mike has mentioned:
(Click here)
Title: How the modified Bertrand theorem explains regularities of the periodic table I. From conformal invariance to Hopf mapping
Authors: Arkady L. Kholodenko, Louis H. Kauffman
Also: a popular podcast "Battle of elements".
Thursday, August 29, 2019
Spider-web
29 August 2019
Jerzy (Jurek) Kocik
Unexpected fractal -- a case of experimental mathematics
The question of the three dimensional case is addressed here:
Jerzy (Jurek) Kocik
Unexpected fractal -- a case of experimental mathematics
The question of the three dimensional case is addressed here:
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