- Judah L Schwartz
In the left hand panel you can build any shape triangle, quadrilateral or pentagon The right hand panel shows the distribution of side lengths and angles in your polygon. Looking at the right hand panel - how can you identify each of the following kinds of triangle [ scalene - isosceles - equilateral - acute - obtuse - right ] Looking at the right hand panel - how can you identify each of the following kinds of quadrilateral [ square - parallelogram - rhombus - kite - trapezoid - right angle trapezoid - quad that can be inscribed in a circle - quad in which a circle can be inscribed] How can you detect non-convex quads? Looking at the right hand panel - how can you identify [ regular pentagons - cyclic pentagons - degenerate pentagons that look like quads - degenerate pentagons that look like triangles ] How can you detect non-convex pentagons? If this applet permitted the construction of a hexagon, what would the right hand panel look like? What other problems could/would you set for your students based on this applet?
GOING FURTHER - Why does it make sense to compare segment lengths to the perimeter if the polygon? Why does it make sense to compare the angles to [n - 2] pi where n is the number of sides? What would be an appropriate measure of the area of the polygon? What is the area of an n-sided regular polygon as a function of its perimeter and the number of sides? Can you think of how you might generalize this way of represnting polygons in the plane to representing polyhedra in three dimensions?