The joy of sets of sets

The simplest construct in mathematics is probably a finite set of sets. Unlike a simple set alone, it has natural algebraic, geometric, analytic and order structures built in. In the finite case, there is lot of overlap but still, there is a rich variety of structure. Algebraic structure An example of a an algebraic structure is to have the symmetric … ….

On Numbers and Graphs

We have calculated with graphs from the very beginning: Humans computed with pebbles like in this scene of the `Clan of the Cave Baer` (1986)) or with line graphs when writing with tally sticks (see this lecture). In all of these cases, the addition of graphs is the disjoint union which serves a nice monoid like the natural numbers. It … ….

Branko Grünbaum

Branko Grünbaum (1929-2018) passed away last September. Here is the obituary from the university of Washington. One of his master pieces is the book “Tilings and patterns”, written with G.C. Shephard. The well illustrated book is considered the bible on Tilings. Here is a page from that book: Links: Personal website at Washington. featuring an other picture. Wikipedia entry … ….