## Notes from Collaboration

I spent two days working intensively with the Fano-Team at the Royal Society last week (7th and 8th November)

Here are some noted from the meetings….

We talked about the 3 Types of geometry….

1. Euclidean Geometry- Drawing

2. Spherical Geometry- Vanishing Point

3. Hyperbolic Geometry- Calibi-Yau

So Calabi-Yau’s occupy Hyberbolic space, and drawing occupies Euclidean Space, Is it possible to draw a Calabi-Yau in hyperbolic space?

We also discussed the 5 Axioms of geometry, which are….

1. “To draw a straight line from any point to any point.”

2. “To produce a finite straight line continuously in a straight line.”

3. “To describe a circle with any centre and distance.”

4. “That all right angles are equal to one another.”

5. The parallel postulate: “That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.”

And this brought us to talking about the book “Flatland: A Romance of Many Dimensions” (1884, Abbott)Â and how we thought there could be more fiction to do with higher dimensions.

I also attended a mathematics seminar at Imperial College on the 7th November 2011….

Attending the mathematics seminar at Imperial was an interesting anthropological experience, I have never been in a situation with other english speaking people where I have understood so little. Aside from my lack of Mathematical genius, It was hard to understand mainly because of the terms used to communicate, I especially like the following terms used at this seminarâ€¦

Super-Potential

Super Connection

Holomorphic Function

Auto-morphisms

Global Super Symmetry

Fermionic Fields

And Orbifold, which I asked one of the mathematicians to explain to me, and his answer was more hands on than I expected….

This believe it or not, is an orbifold!