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## Pixar in a Box

### Course: Pixar in a Box>Unit 11

Lesson 1: Modeling grass with parabolas

# 2. Midpoint formula

Explore how midpoints are used to describe the "string art construction.".

## Want to join the conversation?

• So, the more strings, the curvier the parabolic arc?
• If by "more curvy" you mean "smoother" (the points where it changes direction are less visible to the naked eye), then I believe you are correct. Increasing the frequency of shifts will distribute the changes over smaller and smaller intervals, making each change less apparent.
• At , he starts talking about creating the second order midpoints. The way he talks about it, is computing the midpoints between each subsection. Would we not get the same result, if rather than using each subsection, we actually construct each 1/4 point, between the end points?

For example, you get the midpoint of on the segment AB by taking (A+B)/2. What he is suggesting is to then go to the next order you calculate the midpoint on each subsection so subsection A((A+B)/2) and B((A+B)/2).

But are these also not the "quarter points (1 and 3)" on segment AB.

So rather than going midpoint [2,1] = (A+(A+B)/2)/2 we could go midpoint [2,1] = (A+B)/4...

Expanding the first formula, we end up with (A+(A+B)/2)/2 = (A+A/2+B/2)/2 = (3A/2+B/2)/2 = 3A/4+B/4...

It may appear that I have either made a mistake, or am not sure of what I was understanding intuitively... (A+B)/4 = A/4+B/4...
• You are absolutely correct. If you calculate a midpoint, then the midpoints between the end points and that first midpoint the you get a "quarter point" and a "three quarter point", which can be calculated directly with the equation you suggest. Later, you'll see we can use the equation `(1 - t)A + tB` and plugging in values of t from 0 to 1, to get a point any proportion along the line AB.

The reason he explained it this way was to show that just by using the midpoint formula repeatedly, you can get multiple, evenly spaced points along a line.
• so great! but i'm not understand very much.
but I think it so amazing. in your country have a lot of amazing subject. i'm from viet nam but in viet nam, we don't study a lot about computer. :( but student in Vietnam love it.
in grade 8 to 12, last year we have computer lesson. but at that subject, we study only about word, exel or paint. it so boring.
and now, in my country, Vietnam, we don't have computer lesson for grade 8 -> 12. Minister of Education and Training think we have to study more for math and English, so...of cause, they cut computer lesson of timetable in school. it so sad! How to we have a basic knowledge about computer for our future? it so important!!
• use khan alot
play around with whatever devices you have access to
try taking online courses
• So anyone can do KA even if they are in 12 grade do you think that I should try it out?
• Yes definitely! Even adults can learn from and get a lot from this site.
• at what does sub mean when he says b sub x and b sub y?
• It's short for subscript, which means writing the letter smaller and lower down. "b sub x" means you write `b` followed by a smaller, lower `x`. In this case, this refers to the x-coordinate or point b.
(1 vote)
• at , What does he mean when he says "A sub X and Y" and "B sub X and Y"?
• One way of understanding "Ax" would be to read and think of it as "x coordinate of A".
So, Ax and Ay are the x and y coordinates of A.
Equivalently, A has the coordinates (Ax, Ay).
• I don't understand what the letters are! It's too complicated!
(1 vote)
• The letters are called "variables". They're used to represent a number, when that number is unknown.