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9 – Conic Sections

  • When you slice freshly baked bread, you may not be thinking about geometry.
    • But geometric shapes and relationships are right in front of you.
    • As you cut the bread, the new shapes are slices of the original loaf.
    • The angle you make the cut determines the shape of the slice.
  • Take a look at these chili peppers. What shapes could you get if you sliced them at different angles?
    • Think of these peppers as right circular cones and your knife as a plane.
    • When you slice a right circular cone with a plane you get a shape called a conic section.
    • So, depending on the angle of the slice, you could cut a circle, an ellipse, a hyperbola, or a parabola.
  • OK, so you can make a nice looking party tray, but really, what’s the big deal if you know you how to cut an ellipse or a parabola from a vegetable?
    • Well, it turns out that these shapes appear everywhere in the real world — far beyond your kitchen.
  • The Hubble Space Telescope would not work without its hyperbolic mirrors.
    • Parabolic dishes are important for receiving communications from satellites and sending data transmissions or broadcasts.
    • And many bridges depend on cables that are in the shape of a parabola.
  • In this unit, you’ll learn all about the special properties of these3 conic shapes, which scientists, astronomers, architects, artists, athletes, and many others find valuable.

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