## Today was the first edition of Geometry Cafe’…

Today was the first edition of Geometry Cafe’ – a little lunchtime group to discuss various geometrical bits and bobs. I spoke, mostly about areas and volumes of various standard solids and plane figures.

For example, I went through a cute proof of the formula for the volume of a sphere, more or less rigorous, and without any calculus. The main tool is Cavalieri’s Principle.

Although the group wasn’t too well attended (more lecturers than students in the audience), I think I will continue it. There were several suggestions of topics, including Platonic Solids, some important plane curves, conic sections, knots and braids, non-Euclidean Geometry….

## Henselianity in the language of rings, with Franziska Jahnke

I would like to write about a new paper ([AJ15]) which Franziska Jahnke and I have written and put on the arXiv. It’s called Henselianity in the language of rings. In it we investigate the relationship between the following four properties of a field $K$:

(h) $K$ is henselian, i.e. $K$ admits a nontrivial henselian valuation,

(eh) $K$ is elementarily henselian, i.e. every $L\equiv K$ is henselian,

(def) $K$ admits a definable nontrivial henselian valuation, and

($\emptyset$-def) $K$ admits a $\emptyset$-definable nontrivial henselian valuation.

## Puzzle corner: Sylvy’s puzzle #5

Cross-reference to puzzle page on my website

Here is my next puzzle! Sorry that it’s been greatly delayed.

I mentioned previously the problem of constructing the midpoint of a given circle, using only ruler and compass. One student solved it nearly immediately (congratulations!), so here I offer a more general problem.

#### Sylvy’s puzzle #5

Given a parabola in the plane, construct its vertex using straightedge-and-compass construction (sometimes called ruler-and-compass’ construction).

## Still mostly maths

Originally, I had intended this blog to be a tool I would use to help teach an introductory course on Statistics, but that plan changed when I switched to using UCLan’s own system (Blackboard’) for managing course materials. So this blog has a new purpose: it will be a random, unplanned, haphazard collection of bits and bobs that pique my interest…. but it will always be mostly maths’.

## Hello! A new semester at UCLan

Hello! I have decided to write a blog to accompany my teaching this semester at UCLan. I will be teaching MA1861 Introductory Statistics, and I hope that this blog will provide a forum for additional discussion and explanation of topics contained in the course and some beyond it…

This blog will also host discussions of other topics (mostly mathsy) which take my fancy.

The next post, to be written shortly, will give a provisional course outline.

Edit: a slight change of purpose. There will be a blog on the blackboard space’ for MA1861 (at http://portal.uclan.ac.uk) for official course content. Instead, this blog will contain various mathematical-bits and sundry logical-bobs; some related to teaching and others not. But nothing that is not written on the blackboard space for MA1861 will be required reading for that module. Inevitably there will be some cross-posting.