The Continuing Adventures of Myrtle the Turtle

  • Published January 29, 1990
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Geometry Microworld Part II by Chris Gregory Senior Lecturer in Mathematics at Bradford and Ilkley Community College

Geometry Microworld Part I was published by Valiant Technology in May 1986. Against a background story of Myrtle the Turtle travelling back in time and helping to invent geometry the Microworld presents a series of interesting Turtle activities. The next few issues of GO will publish Geometry Microworld Part II.

The Story So Far:

 
Myrtle the Turtle has travelled back in time and has taught Grub the caveman to measure and Ded-Loth the Egyptian to mark out his fields. She had decided to visit the Pyramids but they were not there…
  Myrtle was disappointed and was about to return to the time machine when she heard a strange voice.”Myrtle, how nice to see you. I’ve been expecting you. How are you?”Myrtle turned and saw a beautiful woman.She was standing in the desert surrounded by light. “Who are you?” Myrtle asked..
“I am Sesheta, the Goddess of Construction and Civil Engineering.””A G-G-G-Goddess, I’ve never met a G-G-G-Goddess before.”

“It’s alright Myrtle, we don’t bite,” Sesheta thought for a moment. “Well some of us do, but I don’t. I am here to build the pyramids and I need your help.”

“I wish I could help but all I can do is draw” Myrtle said.

“Drawing is a very important job, Myrtle. Can you draw squares and triangles?”

Myrtle nodded.

“Then you can help build the Pyramids by drawing the designs in the sand.”

Myrtle quivered with excitement. Sesheta explained how to mark out a square and the triangular sides of the Pyramid and Myrtle worked hard for the rest of the day. That evening Sesheta said goodbye. Myrtle trundled across the sand towards the flashing lights of the time machine.

Polygons and Polyhedra

The activities focus on regular polygons – shapes in which all sides and angles are equal, and polyhedra – three-dimensional shapes, the faces of which are polygons. These activities are suitable for introducing procedures, using variables as inputs and the ‘top down’ approach to programming (breaking a large task into several smaller, more manageable tasks).

Draw the plans for the Pyramid

It will be useful if you can make a model of a pyramid.

Program the Turtle to draw an equilateral triangle and a square to represent the construction plan. Before writing the program, the children should examine the model. They should discuss the shapes needed and their relative sizes.

Some children may be ready to write the program using procedures. Others will prefer to use direct commands. If this is the case, encourage them to record the commands. It will help gain an overall understanding of what they are telling the Turtle to do.

Children who are ready to write their instructions in programs will be able to save them on disk. Where appropriate the Logo procedural approach to geometry can be used. This method creates shapes by description rather than algebraic formula or obscure drawing techniques. For example, SQUARE indicates that a square has four equal sides and four angles of 90 degrees.

These activities may be attempted by young children who have little or no formal understanding of measuring in degrees. Seymour Papert cites examples of children who regarded angular inputs as codes which determined how much the Turtle turned.

 

TO TRIPENDOWN
FD 30
RT 120
FD 30
RT 120
FD 30
RT 120
PENUP
END
TO SQUAREPENDOWN
FD 30
RT 90
FD 30
RT 90
FD 30
RT 90
FD 30
RT 90
PENUP
END
Or using the REPEAT facility:TO TRIPENDOWN
REPEAT 3 [FD 30 RT 120] PENUP
END
TO SQUAREPENDOWN
REPEAT 4 [FD 30 RT 90] PENUP
END

Draw Different Sized Triangles and Squares

When children can draw a triangle and square, ask them to draw the shapes with different sizes. Again, some children will use the direct drive method. Other children may alter the value of the FORWARD command inside a procedure. A more elegant and versatile method is to use a procedure with a variable input.

It is interesting to note if the children appreciate which value must remain unchanged (angle) and which must alter (sides).

The variable is a powerful and fundamental mathematical concept and should be introduced with caution. Logo programs and the Turtle offer a medium through which children may become familiar with the idea.

 
TO TRI: SIDE
REPEAT 3 [FD: SIDE RT 120] END
TO SQUARE: SIDE
REPEAT 4 [FD: SIDE RT 90] END
Different sized polygons can now be drawn with specific input
TRI 30
TRI 50 etc.
SQUARE 30
SQUARE 50 etc.

Further Activities

Exploration of some aspects of the history of practical geometry can be interesting in itself, and can offer an appreciation of why such ideas as ratio, and the properties of triangle received so much attention. Selected material, including some of the actual techniques used in e.g. surveying or navigation can add another dimension to the work.

Different sized polygons can now be drawn with specific input.

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