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Current time:0:00Total duration:1:27

- 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.