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 Discussion: All Topics Topic: Is a rhombus a kite?

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 Subject: RE: Is an integer rational? (was RE: Is a rhombus a kite?) Author: Mathman Date: Jun 8 2005
On Jun  6 2005, Alan Cooper wrote:

> Has anyone studied or considered why kids naturally tend to do this
> even though they have no difficulty with the idea that a cat is an
> animal? Is it based on something fundamental about how we perceive
> shapes, is it because there is only one named subclass of
> rectangles, or is it just a result of how the material is first
> presented to them?

It depends upon the presentation.  There are other types of rectangle which
still remain rectangles; the Golden rectangle has sides in a determined
proportion other than 1:1, as does one that has no name as far as I know, but is
none the less interesting ...  I came upon it when considering a table designed
by Ikea.  the table top would unfold, rotate 90 degrees, and so be twice the
size.  My question then was what ratio should it be so that the shape of the top
was maintained. As it turns out, it's easy to determine as 1:sqrt(2).  So you
have the set of all rectangles with sides of ratio 1:1 [squares], 1: Phi, and
those with ratio 1: sqrt(2) ...and a few others making up the complete set of
rectangles.

David.