![]() It can be used as an education tool, as it can help you teach mathematics in a clean and intuitive working environment. Paul Kunkel email to reach me, the word geometry must appear in the body of the message.The Geometer's Sketchpad is a powerful application designed to help users learn and improve their knowledge when it comes to geometric shapes, trigonometric functions, and other mathematical concepts. Another is a geometric construction of six trigonometric function graphs. One is a unit circle with six trigonometric functions of an acute angle modeled as lengths of line segments, and three identities presented by applying the Pythagorean Theorem. Trigonometry - These are some useful images for understanding several trigonometry concepts. An iterated parameter was used to translate his BASIC code into something that Sketchpad could deal with. Spiral - These spiral constructions were inspired and guided by the book Mathographics, by Robert Dixon. If the iterations could be carried out infinitely, it would be a two-color map, with no adjacent regions having the same color. Custom tools and iterations were used to create this sketch in only a few minutes. One line in the wrong place, and I blew a week of work. Shells - As a child, I once tried to draw a similar design on Dads drafting table. I did some variations on that idea and came up with some striking images. Images.gsp - One of the beta releases of version 4 had a file showing how to make a family of ellipses by using the parameterized colors. ![]() Custom tools were created to calculate determinants of square matrices up to dimension 5. Polynomial functions are fit to free points on the coordinate grid. Linear_Algebra - This idea came from Rick Nungester. Kaleidoscope.gsp - As with a real kaleidoscope, these beautiful patterns are created by simple reflections of colorful, nondescript objects. Inequality.gsp - One, two, or three linear inequalities are graphed on the Cartesian plane. Graphs can be plotted on the custom coordinate system, but it is also convenient for printing a blank grid for hand plotting. It offers a lot of options for the grid and tick mark spacing, index numbers, and colors. It is intended to help people customize graphs that are being prepared for printed material. Graph_Paper - This replaces the version 3 Graph file that used to appear here. Here you can adjust the cone and the plane and see the changes in the intersecting curve. OthersĬonic Sections.gsp - You know how it works. It makes an interesting and effective demonstration. It was sent to me by Nick Jackiw after a GSP Summer Institute. ![]() These are a few files that were created to model the tools included in the Perspective_Tools file.ģD_Chaos_Game - This last one is not mine. This is actually a file from the perspective series, but all of the geometric construction has been hidden in order to create a more useful physics demonstration. The three dimensions are shown in perspective view. ![]() Maxwell2 - Maxwells equation relating electric and magnetic waves is shown with a model of both waves travelling along the same axis and changing in orthogonal directions. Interference - Youngs slit experiments for light wave interference are simulated. It also has a geometric representation of a voltage calculation and two movable equipotential curves. Watch the effects on the field when the charges and positions of the points are changed. Physicsĭoppler - An animated sketch models the Doppler effect and sonic booms.Į-field - Point charges create an electric field. A point representing an initial condition can be dragged across the field and the curve through that point is drawn. In this sketch, the size and density of the field can be changed. A curve can be approximated by simply drawing along the grain. Slope_field - This is something that gets a lot of use in differential equations classes. Integral - Several concepts are modeled here, including Riemann Sums, Simpsons Rule, and the antiderivative. If you are using the file for that purpose, let me recommend that you change most of the line weights to medium or thick. Many of these sketches (particularly the physics files) are suitable for classroom demonstrations. This will degrade the resolution of the curve, but it will also allow the animation to run faster. Select any loci you see on the screen (including graphs). If your computer is not driving the animation fast enough, try this fix. It has been brought to my attention that many of my animated sketches are unreasonably slow because I tend to set the locus samples very high. The GSP4 files seem to be behaving well in GSP5, the current software version, so most of them have been retained without changing the format. Here are some more that are not attached to any particular lesson. Many of the Whistler Alley Mathematics topics include Geometers Sketchpad files.
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