Traditionally, a “conic section” is a curve where a plane and a two-way-infinite cone intersect. You can see this in the following image (courtesy of Pbroks13 from Wikipedia):
The three different types, as numbered in the picture, are:
- The parabola;
- The ellipse (including the circle as a special case);
- The hyperbola.
I was relaxing in bed in a hotel on vacation when I suddenly noticed a hyperbola on the wall. No, the hotel didn’t hire an analytic geometer to paint their walls. It was a hyperbola of light. I quickly realized that by moving the lamp around, I could project all three conic sections onto the wall. Here are the pictures: (If you have a laptop, be sure you angle the screen so you can differentiate the subtle shades of light)
Lamps and Conic Sections?? What’s Going On??
It’s very simple how this works. The lamp-shade constrains the light into a two-way cone shape. The wall is a plane. We can’t very easily move a wall, so we have to move the lamp instead. To make the two halves of the cone equal, it’s best if the lamp shade has a cylindrical shape like the one I used. Otherwise the hyperbola will be deformed (the parabola and ellipse will still work fine).
Bet you never thought you’d read about the analytic geometry of lampshades!
FURTHER READING
The Inverse Graphing Calculator
The Equation of a Line Segment
Three Applications of Higher Math