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Hoensch, Ulrich A. – College Mathematics Journal, 2009
We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to…
Descriptors: Equations (Mathematics), Calculus, Geometric Concepts, Mathematics Instruction

Spaulding, Raymond E. – Mathematics Teacher, 1974
Descriptors: Geometric Concepts, Mathematical Enrichment, Networks, Problem Solving

DeTemple, Duane; Robertson, Jack M. – Mathematics Teacher, 1974
Descriptors: Experiential Learning, Geometric Concepts, Instruction, Mathematical Concepts

Wallrabenstein, Hartmut – Educational Studies in Mathematics, 1973
Descriptors: Curriculum, Elementary School Mathematics, Evaluation, Geometric Concepts

Andrews, Peter – American Mathematical Monthly, 1988
Given is a proof on the classification of surfaces that involves some simple graph theory. It could serve as an introduction to some methods of modern differential topology. (MNS)
Descriptors: College Mathematics, Geometric Concepts, Graphs, Higher Education

Galtier, Jean – Educational Studies in Mathematics, 1973
Outlines a guided discovery activity for ascertaining the conditions which allow for the correct tracing of networks. (JP)
Descriptors: Discovery Learning, Experiential Learning, Geometric Concepts, Instruction