More Articles/Papers/Talks

Please note that although these articles have been roughly classified into two broad categories of Mathematics Education and Mathematics there is sometimes considerable overlap between the two categories. They have also not been arranged in chronological or any other specific order.

The articles below may be used for non-profit, educational

purposes only, provided that their source/origin is properly referenced at all times.

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GENERALIZING VAN AUBEL USING DUALITY (pdf file) (Presents a summary of some dual generalizations of Van Aubel's theorem, namely, the centers of the squares on the opposite sides of any quadrilateral lie on perpendicular lines and that the segments connecting them are congruent).

A DUAL TO KOSNITA'S THEOREM (Provides a dual to Kosnita's theorem and uses a generalization of the Fermat-Torriceli point to establish the result, as well as Kosnita's theorem).

DUAL OF SHARP RESULT (pdf file) (A side-angle dual to a problem in the Sharp Competition in the Mathematical Digest is formulated and proved).

OVERLAPPING CIRCLES (pdf file) (Uses Ceva's theorem and power lines to prove Haruki's theorem).

MATHEMATICAL TREASURE HUNTING (pdf file) (The power of transformation geometry is illustrated in not only the solution of an interesting, classical problem, but also in leading to a further generalization involving a spiral similarity).

PLACE-KICKING LOCUS IN RUGBY (pdf file) (Examines the "best position" for a place kick in rugby and shows that the locus is a hyperbola).

GENERALIZATION OF AN IMTS PROBLEM (pdf file) (A generalization of an International Mathematical Talent Search problem which involves ratios of areas).

GAME, MATH, AND LUCK! (pdf file) (Provides a simple mathematical model, using probability, of the point scoring system in tennis).

EXPLORING LOCI ON SKETCHPAD (pdf file) (Three examples are given, including the classic approach to a parabola as the locus of all points equidistant from a point and a line).

PROBLEMPOSING VARIATIONS ON FERMAT'S LAST THEOREM (pdf file) (Some variations on Fermat's Last Theorem are posed).

AN INTERESTING DUALITY IN GEOMETRY (pdf file) (The side-angle duality in Euclidean geometry is briefly discussed in relation to quadrilaterals).

THE AFFINE INVARIANCE & LINE SYMMETRIES OF THE CONICS (pdf file) (Please note converted from a fax) (This paper proves the affine invariance of the conics and derives formulae for the axes of symmetry of the conics using transformation geometry).

A SKETCHPAD DISCOVERY INVOLVING TRIANGLES AND QUADRILATERALS (pdf) (An interesting further extension of a familiar high school geometry result).

CONJECTURE & PROOF WITH SKETCHPAD: A CASE STUDY (pdf) (Another investigation suitable for high school geometry).

ALL PARABOLAS SIMILAR? NEVER! (pdf) (Provides a heuristic description of the author's surprising (re)discovery that all parabola are similar, i.e. any parabola can be enlarged or reduced to map onto any other).

[A zipped Sketchpad sketch which uses enlargements to illustrate the similarity of all parabola can be downloaded from ]

A MATHEMATICAL LOOK AT VOTING POWER (pdf) (An introduction to the Banzhaf method as a way of quantifying "voting power" in any voting body).