Skip to content
Triangle Geometry
I am considering studying how meaning arises in triangle
geometry. There is a lot that one can do with a triangle, but then again,
there is only so much you can do with a triangle.
Or so it seems. But there are about 200 Wikipedia articles:
Furthermore, there is a list of 65,000 triangle centers (or notable points)
starting with incenter, centroid, circumcenter, orthocenter, nine-point
center, and so on...
Thus is it possible to study how this conceptual language evolves from the
most basic concepts.
As a precalculus teacher in San Diego, and then a tutor in Chicago, I
taught my students fundamental principles such as "Every right triangle is
half of a rectangle" or "Every triangle is the sum of two right
triangles." These can be used to prove, for example, that the area of a
triangle is 1/2 base times height. They also formulate pictorial thinking
(such as drawing an altitude) which is very much in the spirit of Jere's
Relational Symmetry Paradigm.
Cognitively, I think there are four basic ways to think of triangles - in
terms of three paths, three intersecting lines, three angles or sweeping
out an oriented area. Pairs of these ways make for six Mobius
transformations which arise in the Wondrous Wisdom theory of emotion, see
"A Geometry of Moods"
Triangles are also key in Buckminster Fuller's .
Circumcenter. — Size (width at maximum)
In-circle. — Shape
Want to print your doc?
This is not the way.
This is not the way.
Try clicking the ⋯ next to your doc name or using a keyboard shortcut (
CtrlP
) instead.