September 13th, 2006
Geometer’s Sketchpad is one of my favourite programs but extremely annoying to author in. Here I have created a zipped archive of some of my past Sketchpad efforts for anyone who wants them. I have included a brief description of each file below.
If you don’t have Geometer’s Sketchpad then these will not be very useful to you. You can get hold of a copy from The Curriculum Press in the UK.
An extremely simple file exhibiting the construction of an ellipse defined by two centers and a point. The problem is that the “Locus Constructions” that are revealled don’t tell the whole story; how did I arrive at choosing those two circles to construct the circle with? This requires thought about the definition of an ellipse and the nature of construction.
If you cut a sector from a circle (the bright-red sector) you can join the two radial sides together to form a cone. What is that cone’s volume? How do you maximise the volume of the cone? This sketch allows an exploration of the structure of the problem prior to doing the maths on it. It is a good exploration for construction of graphs at lower levels, or using calculus at higher levels.
A useful sketch for teaching calculus, start with the initial position of the projectile on the ground. Some of the ‘features’ on this sketch are odd and may require some exploration before they make sense!
An example of how to construct a cube using two-point perspective
I believe that this sketch comprises a proof that all quadrilaterals do in fact tessellate. It is an interesting question to whether it does in fact constitute a proof (what is a proof anyway?!) Choose your quadrilateral and click the buttons in order to follow the argument steps.
HexagonalSlideTessellation & HexagonalRotationalTessellation
Dynamic examples of how to distort tessellating hexagons in such a way to ensure that the result also tessellates.
An interesting construction of an egg using four arcs of four circles, it questions students to consider the relationship between mathematics and aesthetics.