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

Potpourri Seminar

2 p.m. Thursdays

From Arts Bathsheba |

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

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.**

Eigenvectors from eigenvalues

>> Relevant paper on Arxiv

>> Quanta Magazine on this subject

<< see the original image

21 November and

and 5 December 2019

Symmetry in Materials Physics

← click to view details.

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

More on "

(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 \(w=-\|\mathbf b\|^2\).

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