Robot Rob needs help?

Question

Give instructions telling robot Rob how to move and turn so that his path is regular octagon that has sides of length 3 meters. Draw a sketch to indicate Rob's route and explain the reasoning you use to determine Rob's angles of turning. 

Answer 1

In the late 1960’s, Seymour Papert and a team at MIT developed “Turtle Graphics” and the Logo Programming Language to teach kids how to program.  A programmable “turtle” was placed on the floor and given instructions.

Go to:

   http://www.logointerpreter.com/

 

Select “Editor” and enter the following (incomplete) program as new logo commands.  Execute it (the rocket blasting off).  Then complete it so you can explain it (and why you chose this angle) and give instructions to Rob.  Be sure to complete the program.

 

Forward 100

Left 45

Forward 100

Left 45

Forward 100

Left 45

Forward 100

Left 45

Forward 100

Left 45

Forward 100

Left 45

Forward 100

 

Answer 2

First, center the octagon so that the top and bottom sides are parallel. Then label the point to the left of the top side as A, and continuing labelling the points to H.

 

Since we have a regular octagon, the interior angles will all be 135^o. which is a property of a regular octagon. The angle from the perpendicular will be 45^o.

 

We will use compass points to define the directions.

 

So, start at A and proceed due East to point B

At B, turn 45^o South-south east to point C

At C, proceed due South to point D

At D, turn 45^o South-south west to point E

At E, proceed due West to point F

At F, turn 45^o North-north west to point G

At G, proceed due North to point H

At H, turn 45^o North-north east to point A