Main content

## Pixar in a Box

### Unit 11: Lesson 1

Modeling grass with parabolas- Start here!
- Introduction to parabolic arcs
- 1. String art
- String art construction
- 2. Midpoint formula
- Midpoint formula
- 3. Parabolic arcs
- Parabolic curve matching
- 4. Modeling grass
- Design challenge: Modeling grass
- 5. Animating grass
- Design challenge: Animating grass
- Getting to know Tony DeRose
- Hands-on activity

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# 3. Parabolic arcs

Are we really creating parabolic curves using this construction? Let's gain some insight first.

## Video transcript

(lamp and ball boinging) - Congratulations. You're now an expert on midpoints. (arrow whooshes) Now let's take the next step. I've been claiming that the curves created with the string art construction are parabolas. But how do we know that's actually true? Well, it's actually a little bit hard to prove that rigorously but we can get some intuition in the following exercise. Now you may have seen parabolic arcs as graphs of quadratic equations like this one, for instance. So here I have a green curve that's the graph of a quadratic function. And so it's a parabola. And I have a blue curve generated through the string art construction. It's my job in this exercise, it'll be your job in the exercise, to see if you can reposition the points so that the blue curve sits exactly on top of the green curve. So for instance, I'm gonna try moving this point, say down here. And this point over here. Over there. So the blue curve is getting a little bit closer, but it's not exactly on top of the green curve yet. And in fact I'm gonna ask you to try it in the next exercise.