Stretching Arrows

Lesson 4 of 12 · 7 min · Free, no account needed

What you will learn

Multiplying an arrow by a number k is a scalar multiple: k(x, y) = (kx, ky).
k bigger than 1 stretches, k between 0 and 1 shrinks, a negative k turns the arrow around.
All the multiples of one arrow lie on one line through the start.

Your hero walks with the move (2, 1). Now it sprints at double speed.
Where does the sprint arrow end? Tap your bet.
Stretch the arrow with k. Reach each flag.
Slide k. Watch both parts of the arrow change together.
Which flags can the hero reach just by changing speed?
Tap all of them, then Check.
k(2, 1) = (2k, k): x is always twice y. (3, 2), (-2, 1) and (1, 3) break that rule.
That is a scalar multiple.
Multiplying an arrow by a number is a scalar multiple: k(x, y) = (kx, ky).
k bigger than 1 stretches, k between 0 and 1 shrinks, negative k turns it around.
The number k is called a scalar: it only scales.
Which k makes the dashed arrow?
No flags now. Read each dashed arrow and set k.
Give your hero three gears.
Run is faster, creep is slower, back goes the other way. Pick a k for each.
Run needs k > 1, creep 0 < k < 1, back k < 0.
Game: blind dash. Land on each pad.
Set k and Dash. You only see the arrow after you land.
AI learns by stepping downhill on an error bowl.
The slope arrow g points uphill. Each step moves by -lr times g. Pick the learning rate lr that lands at the bottom in one step.
What is the second part of -2 · (3, -2)?
k(x, y) = (kx, ky), so -2 · (3, -2) = (-6, 4).
k times an arrow stretches, shrinks or flips it.
Your hero's card. Tap each gear.

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