Matrices and vectors
with Emily.
| Mini-topic | Description |
| * Guide the robot | Introduction of vectors |
| *coming soon: What are vectors? | Formal definition of vectors |
1. Guide the robot.
Mentor:
Let
us imagine ourselves on a remote planet, where our spaceship crashed during
a science mission. Luckily, nobody was seriously hurt, but we can't repair
the ship here. Our small crew has to install a radio beacon to call for the
rescue mission from Earth.
The planet is full of known and unknown dangers, so we decided to send a robot on. Our new automatic robot did not survive the crash. We will have to use an older robot; a person has to guide it by radio. You are the chief engineer of the ship, so it is up to you to guide the robot. The lives of the crew and the invaluable scientific data depend on you.
You can
use a radar to see the robot's movement. On the radar screen, you will see
the robot as a blue circle, the place for the beacon as a green circle, and
dangerous places the robot should avoid as squares. The robot only goes straight,
but it can turn to change direction. To guide the next move, decide where
it will end. Then count the steps the robot would have to make if it could
only move by the grid lines: left-right, or up-down. Then enter the numbers
in the windows on your radio transmitter below the radar. The first window
is for left-right; it says: "X=..." For the robot, "-" in front of the number
means "left," and no sign means "right." The second window is for up-down;
it says: "Y=..." There "-" means "down" and no sign means up.
The robot has a small radar of its own that tells if the given path crosses any dangerous zones. In this case, the robot will refuse to go. It will also send the message: "IMPOSSIBLE! Try again" to you screen. It is good the robot tries to save itself: we only have one robot, and if it it fails, one of the crew will have to go on the life-threatening mission.
Mentor: Now, every step our robot can make mathematicians call "a vector." If you played the game, you already know quite a lot about vectors. The next section will help you put this knowledge in words.
2. What are vectors?
| © Copyright 1998 by Maria Droujkova and Dmitri Droujkov. All rights reserved. No part of these materials should ever be used in any situation that involves compulsory teaching. See also copyright notes and student rights. |