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 ››

While most numbers lead anonymous lives away from the mathematical spotlight, e^{iπ } occupies hallowed ground. Douglas Hofstadter writes that when he first saw the statement e^{iπ} = −1, “. . . perhaps at age 12 or so, it seemed truly magical, almost other-worldly.”

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.

This post presents virtual dances based on geometric transformations. As a penguin travels around a polygon, you, as a frog, must match its movements, but with the added challenge of dancing as a reflection, rotation, or dilation of the penguin’s path.

In geometry, we learn that if we erect squares on the legs of a right triangle, the sum of their areas is equal to the area of the square on the triangle's hypotenuse. This is visual way to conceptualize the Pythagorean Theorem. But now consider the image below that shows a bust of … Continue Reading ››