Pixar in a Box
- Start here!
- Weighted average of two points
- Weighted averages
- 2. Where is the touching point?
- Exploring the parabola construction
- 3. Compute the touching point
- Calculating the touching point
- 4. How can we prove this?
- Touching point
- Bonus: Completing the proof
Where does the string touch the parabola? See if you can come up with your hypothesis!
Want to join the conversation?
- what would the touching place be for(4 votes)
- The touching place is to see at what point on the parabola, the straight line is tangent with the parabola. For the computer, this is useful to know whether or not to place a pixel (color) at that exact location.(7 votes)
- I have a question about the next exercise 'Exploring the parabola construction'. What do they mean when they indicate a line like this: AQ|AB = QB|AB (in the normal question, these are written underneath each other)?
Thanks in advance.(3 votes)
- AQ / AB means the ratio of the length of AQ : AB. In other words it's a fraction - you divide the length of AQ by the length of AB.(3 votes)
- When do i get to make a cartoon(1 vote)
- how do you get the weight(1 vote)
- The weight, the t value from the previous lesson, is whatever you need it to be. It's the variable in the equation. The only rule is that it has to be between 0 and 1. When you plug every possible value for t into the ultimate formula that will be constructed, then you'll get all of the possible touching points. Graphing all of those points (or an evenly-distributed finite set of them, at any rate) will create the parabolic arc.
In short, you don't "get" the weight. You provide the weight.(2 votes)
- We're ready for step two in our search for the elusive formula of how to compute a point exactly on a parabola. To gain some intuition, let's go back to the interactive that we used to kick this all off. So here's my string art construction with a bunch of lines. And now, let me cycle through the lines one at a time, highlighted here in magenta. So there's one of them, here's another one, here's another one. And each of these magenta lines can be described by some fraction T that names that point on the line. As I wiggle the magenta line back and forth, notice that it continues to touch the parabola in exactly one place. Well if I can develop a formula for where that place is, that's the formula I'm looking for. We can see that even more clearly in this version of the interactive that you'll be using in a moment to solve a couple of exercises. So in this version, I can use this perimeter T to name which string art line I'm talking about. And notice that each of the string art lines touches the parabola in exactly one place. In the next exercise, you'll be asked to come up with a hypothesis for where that place is. And the hypothesis, as a hint, has something to do with the ratios of these subsegments that are being created. And we've color coded those subsegments to give you an even more of a hint. So see if you can figure out what that special relationship is.