oragami project

[Nage...@aol.com]

Hi, I teach geometry at an all-girls high school in Toledo, Ohio and am working on lesson plan ideas for the 2002-2003 school year and would like to do a project on oragami.  My class is a 9th grade geometry class.  Has anyone done a successful project they would be willing to share?

Bonnie Nagel
St. Ursula Academy

[Walter Whiteley]

I am not sure what scale a 'project' has to be, or what geometry
content you want to connect to.

For example, There is a nice project to do around
'angle bisectors' of triangles (and exterior triangles).

Take a rectangle (or square) of paper.  Fold over one
corner into a triangle (any triangle - a different one for
each student).  Now in that triangle, fold each pair
of edges onto one another - generating 3 lines.
They meet in a point.  Why?  Well I already gave it away,
but it gives a different sense to this construction.

Now go to the other part of the paper.
Take the two edges which extend edges of the triangle,
and the other side of the third side (the fold) of the triangle.
Fold each pair of these edges onto the other.  Those three
lines meet in a point.  Why?

There are other possible pairs of edges of the paper (and the fold)
to be folded.  Look at all those lines and see which triples
of lines meet in a point.

I have a Geometer's SketchPad sketch of this as well,
to explore the implicit incircles, excircles, etc.

Another more extensive project is finding ways to fold
a loose piece of paper (ragged edges) so that one has
each of the 'types' of quadrilaterals.  Some are easy
(rhombus), some are hard (parallelogram) ... .

Walter Whiteley
York University Toronto Ontario