TURTLE GEOMETRY MICROWORLD 2
In
last issue Chris Gregory looked at how the Turtle can be used to explore
the ideas of perimeter and area. In this issue he introduces another approach
to exploring area called snakes.
Issue 3 of GO shows that one way the Turtle can be used to explore the
idea of area is to draw shapes on square paper. The area of the shape
is represented by the the number of 'surrounded' squares. Summing elemental
squares is a powerful mathematical method familiar to many classroom activities
on area. A snake is a way of creating shapes from the basic elemental
square.
• Square Left and Square Right
The procedure for a square can use the RT command. Ask the children if
they think it would make any difference if they used the LT command. They
can explore this problem using the Turtle. The square is the same except
for its position relative to the Turtle.
TO SQR
REPEAT 4 [FD 10 RT9O]
END 

TO SQL
REPEAT 4 [FD 10 LT 90]
END 
• Introducing Snake
TO SR
SQR
FD 10
END 


TO SL
SQL
FD 10
END 
The square right and left procedures can be used to create two more basic
procedures SR and SL.
in their turn these two programs can be used to create the basic snake
procedures: SNR and SNL.
TO SNR :N
REPEAT :N [SR]
END 

TO SNL :N
REPEAT :N [SL]
END 
• Making Shapes with Snakes
The 'snakelike' path the Turtle takes creates a shape. The area of the
shape is the sum of the variables used in the SNR and SNL procedures.

SNL 1 LT 90
SNR 2 LT 90 SNL 1 LT 90
SNR 3 LT 90 SNL 2 LT 90
SNR 4 LT 90 SNL 3 LT 90
SNR 5 LT 90 SNL 4 LT 90
_______________________
Area 15 plus 10
= 25 units 
The UNCOIL program shows how a square can be drawn using
snakes. Those familiar with LOGO recursion will recognise the possibilities.
(Recursion will be dealt with in a later issue of GO).

SNR 4 RT 90 SNL 2 RT 90
SNR 4 RT 180 SNR 4 RT 90 SNL 2 RT 90
SNR 4 RT 180 SNR 4 RT 90 SNL 2 RT 90
SNR 4 RT 180 SNR 4 RT 90 SNL 2 RT 90
etc. 
A snake program for drawing a square or an oblong.

SNL 5 LT 90
SNR 1 LT 90
SNR 2 RT 90
SNL 2 RT 90
SNR 2 RT 180
SNR 2 RT 90
SNL 1 LT 90
SNR 2 RT 90
SNL 1 RT 90
SNL 1 LT 90
SNR 1 RT 90
SNL 1 RT 90
SNR 1 LT 90
SNR 3
____________
Area 25 units 
It is possible to draw complex shapes using snakes.
Even the Turtle's high accuracy will limit the complexity of possible
shapes drawn by a snake. However, although the 'realspace' nature of
a floor Turtle drawing is lost it is certainly valuable to use snakes
as a means of 'filling space' on the computer screen. It is interesting
to see the effect of changing the basic size of the snake.
• Snake Rule
Never draw over a square twice.
