**What is on the other side of the horizon?****The projective plane as a surface.**

**Visualizing the projective plane on a disc with the boundary identified as the horizon.****The projective plane as a non-euclidean flatland.**

**Some final remarks on the projective plane and visualizing Flatland and Space.:
**

**Curves and Surfaces:**

**
More about proof and what is possible? what is not?**

**A very old problem: In Euclid's geometry,
there are lines that never meet.... but is this true about Flatland? **

**
How can someone in Flatland tell whether 2 lines are parallel? **

**
Question:Given a point P and a line l in Euclid's geometry is there
a unique line through P that is parallel to l? **

*Euclid's answer...
YES!
In the projective plane.... Yes- the parallel line meets the line at a point on the horizon.*

**
Question:Can that be proven from a list of properties (axioms) about the
plane???
**

*Show video:"A
non-euclidean Universe."
*Show orthogonal circles in wingeometry?

**and inversion?
**