Thursday, February 20, 2020

From Arts Bathsheba
20 Feb 2020

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

Ford and scattering

6 and 13 Feb 2020 

K.V Shajesh

Rayleigh scattering off Ford circles

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.

Thursday, November 14, 2019


21 November and
and 5 December 2019

Thushari Jayasekera

Symmetry in Materials Physics

← click to view details.

Tuesday, November 12, 2019

Geometry and numbers

From Fine Art America
14 Nov 2019

Don Redmond

Polygonal numbers as differences of squares

Sunday, October 27, 2019


31 October and 7 November 2019

Jerzy Kocik 

Lattices, spinors, and classification of Apollonian disk packings.  Here are the first 21 irreducible classes of lattices.

More on "geometric Apolloniana".
(Simply "", 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


10 and 17 October 2019

K.V. Shajesh 

How does quantum vacuum energy gravitate?