LOGO-L> Total Turtle Trip

Sorry for the delay in replying. A by-election happened and I got stuck

as agent.

I think the problem lies in the transfer of ideas from the mathematics of

mind supported by pen and paper mathematical instruments to

mental mathematics supported by the computer as the medium of

representation.

All that I an saying is that Turtle geometry is the geometry of a virtual

ruler. Specifically, TG has no representation of a compass.

The vocabulary of Logo, as it applies to TG, is solely of turn and move

(left & right, forward & back). The so called 'turtle circle' is the

definition of a regular polygon:

repeat :n (forward :side right 360/:n)

What I an saying is a simple matter of language:

Within the TG subset of Logo vocabulary it is possible to describe a

regular polygon. A description of regular polygon is not a description of

a circle.

To describe a circle we need to add to our vocabulary. The arc primitive

does just this. To the virtual ruler of forward, the arc primitive adds a

virtual compass.

Now, having drawn two figures on the screen that look identical but which

are based on totally different descriptions, then we have food for thought

about what underlying expression might generate such shapes. We can

investigate the nature of the difference by manipulating the inputs to the

procedures. For instance, the polygon 'circle' can be transformed into a

square whilst the arc circle can inflate and deflate.

An a quick comment on a remark of Jeff Richardson's:

It follows from my argument that it is unsound to transfer the concept of

a *tangent* from Euclidean to Turtle geometry. The notion of setting the

turtle heading at 90 units relative to its current heading is, however,

OK.

Many of our problems are related to the use of TG to support extant

mathematics rather than to use Logo to redefine mathematics teaching - and

I don't mean in sociocentric terms.

Michael Doyle (aka Micheal O Duill)

37 Bright Street

SKIPTON BD23 1QQ UK

Tel/fax: +44 (0)1756 794601

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