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 'snake-like' 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 'real-space' 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.