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In this session, we’ll examine the implications of breaking the 5th postulate by constructing and exploring hyperbolic geometry, using Poincaré’s disk model of the hyperbolic plane.

The resulting hyperbolic geometry can be made particularly vivid by Henri Poincaré’s remarkable disk model, which allows that geometry to be visualized-and, in Sketchpad, manipulated-within the Euclidean plane. Lobachevsky, Bolyai, and Gauss all independently conceived a geometry in which the 5th postulate is “broken” by allowing many lines-rather than just one-to be defined as parallel to a given line through a point not on that line. The study of hyperbolic geometry-and non-euclidean geometries in general- dates to the 19th century’s failed attempts to prove that Euclid’s fifth postulate (the parallel postulate) could be derived from the other four postulates. Classroom-tested activities are accompanied by presentation sketches and detailed teacher notes, which provide suggestions for use by teachers as a demonstration tool or for use by students in a computer lab or on laptops.The Geometer’s Sketchpad: Non-Euclidean Geometry & The Poincaré Disk Nicholas Jackiw KCP Technologies, Inc. Teachers can use it daily to illustrate and illuminate mathematical ideas.

Sketchpad is the optimal tool for interactive whiteboards. And high school students can use Sketchpad to construct and transform geometric shapes and functions-from linear to trigonometric-promoting deep understanding. Middle school students can build their readiness for algebra by exploring ratio and proportion, rate of change, and functional relationships through numeric, tabular, and graphical representations. Make math more meaningful and memorable using Sketchpad.Elementary students can manipulate dynamic models of fractions, number lines, and geometric patterns. Sketchpad gives students at all levels-from third grade through college-a tangible, visual way to learn mathematics that increases their engagement, understanding, and achievement.

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The Geometer's Sketchpad is the world's leading software for teaching mathematics.

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If you have the money, it can be an incredibly valuable study aid though.Įditors' note: This is a review of the trial version of The Geometer's Sketchpad 5.05.

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Students who want a similar experience have to pony up cash or try to make the program's limited free features work. However, by making the price a little restrictive for anyone but educators, The Geometer's Sketchpad makes it so the program only works in a classroom. There are hundreds of different applications for the program. There is a freehand tool, but drawing shapes is as simple as clicking where the points and midsections of the shape should be. There are dozens of different graph types supported by the program, complete with customizable coordinates and axes. Then, you can measure the angles and midpoints of the shapes to solve or create equations. The Geometer's Sketchpad offers five different tools to create geometric shapes to help you visualize math problems. You can only access the drawing features of the program and not the measurement features if you don't pay, as well. This price supports up to four computers. The program costs $69.95 to unlock anything more than a 20-minute session that won't save or print your work. The price is probably too restrictive for home use, but could make it a great tool for classroom use. The Geometer's Sketchpad looks to give you a platform to create mathematical shapes and figures, but you'll have to pay up to use it. A digital chalkboard would be an awesome tool for any math classroom.