Department of Mathemtaics Education
Taking Some Mystery Out of the Nine Point Circle with GSP
This paper examines the nine point circle as the common circumcircle of three special triangles of any given triangle -- the triangle formed by the midpoints of the segments from the orthocenter to the vertices, the medial triangle, and the orthic triangle.
Mathematics Education Web Course Development on a Shoestring
This paper was published as Chapter 4 in Wilson, P. S. (Ed.) (1993). Research Ideas for the Classroom: High School Mathematics. New York: MacMillan.
The book was part of the National Council of Teacher of Mathematics Research Interpretation Project, directed by Sigrid Wagner.
The bibliographic reference for the published version is
Wilson, J. W., Fernandez, M. L., & Hadaway, N. (1993). Mathematical problem solving. In P. S. Wilson (Ed.), Research Ideas for the Classroom: High School Mathematics (pp. 57-78). New York: MacMillan.
Multiple-Application Medium for the Study of Polygonal Numbers
This article is an expanded version of the paper presented at the 1994 International Symposium on Mathematics/Science Education and Technology, San Diego, CA, and published as: Abramovich, S., Fujii, T., & Wilson, J. (1994). Exploring and Visualizing Properties of Polygonal Numbers in a Multiple-Application Computer-Enhanced Environment. In G.H. Marks (Ed.), Proceedings of the 1994 International Symposium on Mathematics/Science Education and Technology. Charlottesville, VA: AACE.
What is the ratio of areas of the two squares?
This is a discussion of some exploration and extensions of this problem.
This paper examines sets of equations that have graphs crossing the x-axis only at 2 and 5. For a preview on one family of such graphs, click here.
Problem Solving with Heron's Formula.
This is a paper on the development and demonstration of Heron's formula for the area of a triangle given the lengths of its three sides. Problems and explorations are included for using Heron's formula.
An Investigation with Parametric Equations.
This paper examines the movement of triangles when one vertex is moved along the x-asis and another is moved along the y-axis. We trace trace the movement of the thrid vertex.
Extended Concurrencies of the Triangle
Paper presented at the 1996 MAA Annual Meeting, Orlando, Florida.
Envelopes of
Lines and Circles.
This paper was constructed for a presentation/demonstration to Elbert County High School Mu Alpha Theta club on March 18, 1997. The paper examines the curves formed by sets of lines or circles that move along some defined paths.
Trisecting the
Area of a Triangle.
This is an investigation of the constructions required to dive the area of a triangle into three regions of equal area, under different initial conditions.
When two relations are multiplied, points (x,y) on either will appear on the product graph. Characteristics of the graph are described to tell whether a relation is factorable.
What is the locus of the orthocenter when one side of a triangle is fixed and the third vertex is moved along some path?
Find two linear functions f(x) and g(x) such that the product h(x) = f(x).g(x) is tangent to each of the original lines.
Exploration of a Triangle Ratios Problem.
Given a triangle ABC and an interior point M. Extend a segment from each vertex through M to its intersecion with the opposite side creating segments AD, BE, and CF. The exploration will evaluate some ratios of segments within the triangle.