Introduction to conics and the parabola.

1. Today ... I am Samurai!
Watch, as I wield my great
and mighty swuhord!
Photo source: Miyamoto Musashi

2. Conic Sections
Photo source
... and another good resource

3. You'll need a piece of paper ...
A campsite is located in a large, flat clearing near a straight river. The camper
is at point A and the tent is at point B. The tent catches fire, and fortunately
the camper already has a bucket in hand. At what point P on the river should
the camper fill the bucket with water to make the shortest possible path to
douse the fire?
Heron of Alexandria (a Hero of mathematics)

4. What else can we learn from a piece of paper ...