1. Euclidean geometry.

Axioms.

• fifth axiom

Constructions with a ruler and a compas.

• nobody can trisect angles wit a ruler and a compas

2. Golden section and Fibonacci numbers

• How are these three objects related
• 

3. Symmetries, Tilings

• Which is more symmetric:
• or ?
• How symmetric is ?

4. Fractals

• What is a fractals? Here are a couple of examples.

Here are two more of them (Kerry Mitchell, 1997):

Mona Lisa

Nite

5. Pespective

• 
• 

6. Polyhedra

• Intarsia Polyhedra, Fra Giovanni c.1520

7. Conic sections

8. Hyperbolic geometry

• another world:

• another art (Escher, Circle Limit 3).

9. Topology

• what is the shape of this world