Maximizing Triangle Area

In the February 1954 issue of Mathematics Teacher, Paul C. Clifford describes an optimization problem from his trigonometry class. Of all isosceles triangles ABC with sides AB and BC of length 12, which one has the maximal area? Clifford told his class that an exact solution to the question required calculus. One student, … Continue Reading ››

Constructing Rectangles with Constant Perimeter and Constant Area

In the fall of 2023, I taught a geometry methods course at City College here in New York. While my goal was to make use of Web Sketchpad throughout the semester, I knew that the most effective use of the software required activities that coupled it with hands-on modeling. Two such opportunities arose … Continue Reading ››

Constructing Daisy Designs

With nothing but a compass, students can construct a lovely daisy design consisting of seven interlocking circles, all of the same size.

I was delighted to see that the U.S. postal service chose to feature … Continue Reading ››

The Mysteries of Polygon Flats

What do you get when you cross geometry with the classic murder mystery game Clue? Why, the Mysteries of Polygon Flats, of course!

In my prior post, I offered examples of how Web Sketchpad can help students classify special quadrilaterals like squares, rectangles, kites, parallelograms, … Continue Reading ››

Ah geometry, how you suffer from a lack of attention in the elementary grades! Rare is the curriculum that doesn't stuff geometry into its final chapter, waiting patiently in line behind number and operation.

But the one geometry topic that does command attention is classifying two-dimensional shapes into … Continue Reading ››

Teaching with Web Sketchpad

This past semester, I taught a geometry course for teachers at City College here in New York. As you might expect, Sketchpad figured heavily in the course contents. But unlike other semesters when desktop Sketchpad was my tool of choice, this time, I took the plunge and limited myself to Web Sketchpad.

A Transformations Approach to Complex Numbers

This post, inspired by the work of Al Cuoco, uses Web Sketchpad to explore a transformations approach to complex numbers.

Special Quadrilaterals and Their Diagonals

Given two segments and their midpoints, what quadrilaterals can you build using the segments as the diagonals of the quadrilateral?

The Origami-Math Connection

This post examines the connections between origami and geometry in the context of a new book written by Daniel Scher and Marc Kirschenbaum.

Hats Off to This Aperiodic Tiling

This post examines the role of social media in promoting the discovery of an aperiodic monotile.