[ Back ] [ Up ] [ Next ] [Timeline]

Grade 8:  The Learning Equation Math

33.02 Topology

The student will:

• represent, analyse, and describe regions and colouring problems.

topology - "regions  study".   Topology is the mathematical study of properties of objects which are preserved through deformations, twistings, and stretchings. (Tearing, however, is not allowed.) A Circle is topologically equivalent to an Ellipse (into which it can be deformed by stretching). Ellipse: Source:  Ellipse--from Eric Weisstein's World of Mathematics source:  Mathmania Tour Topology, precisely, is the branch of mathematics that deals with the properties of geometric configurations that are unaltered by elastic deformations.   It is easy to see why Space Rollercoasters were fun. One of the best things about them was that the tubes were flexible. Since the tubes were flexible, they could change shape as you slid through them! Going on the same Space Rollercoaster twice was like going on two different ones. You never really knew which direction you would be turning next because the tube was moving, curving and stretching as you passed through it.   arc - part of a curve region - areas completely or partly enclosed by arcs vertex - point of intersection of the sides of a polygon or arcs of a region vertices - plural of vertex.  There are 5 vertices joined by arcs in this example. degree of a vertex - the number of arcs that meet at a vertex.  The degree of this vertex is 3. odd vertex - when an odd number of arcs meet at a vertex even vertex - when an even number of arcs meet at a vertex network - consist of vertices that are all joined by arcs traversable - a network that  can be traced in one continuous path by moving along every arc exactly once.  Traversable networks can have no more than two odd vertices.

Math Forum: Leonard Euler and the Bridges of Konigsberg

Beyond Numbers - coloring maps

Ideas, Concepts, and Definitions - 4 color  maps

Mathematical Surfaces

Fancy Knots and Links

Tangle Calculator

Java Applet: Curvature Flow

• describe, analyse, and solve network problems.

Key Terms:

network, vertex, arc, region, degree of a vertex, odd vertex, traversable

Prerequisite Skills:

• Trace a path, using oral and written instructions, and write instructions for a given path.

• Develop charts to record and reveal patterns.

• Use a variety of methods to solve problems with multiple solutions.

[ Back ] [ Up ] [ Next ] [Timeline]

Comments to:  Jim Reed

Started September, 1998. Copyright © 1999, 2000

visitors since September 3, 2000