Sketchpad is based largely on a Euclidean view of geometry. (Constructions like this can be made with the author's 3D Invisibility Toolkit.)ģD ToolkitsCheck out the custom toolkits for developing 3D sketches available in the Toolkits section as well: 3D Plotting Toolkit 3D Invisibility Toolkit. The shape can be spun, lit from different angles, and viewed from any reference point. Nick Jackiw, Kate Mackrell, Paul Kunkel, Yao Liu.Ī remarkable model of a regular icosahedron, with an exercise page describing a construction of this Platonic solid. Conic ConnectionsĪn extensive exploration of commonly studied properties of conic sections, including foci, directrices, eccentricities and discriminants, especially in the context of how these properties relate to the definition of conics as the intersection of a plane with a double-napped cone.Ī collection of constructions in three dimensions, including curves, surfaces, and various solids. This sketch provides a set of Boolean operators, comparison tools, and Boolean functions, as well as detailed explanations of how these tools were created and how you can make them for yourself.Īlthough Sketchpad's native domain is the geometry of the plane rather than the geometry of space, many sketches construct the projection of higher-dimensional mathematical models onto the two dimensions of the computer screen. This set of advanced analytic tools from Sketchpad's Samples collection includes calculations for tangents and function sectors, definitions of piecewise functions, and more. (Tools like these were used to construct the author's Icosahedron.) The tools in this kit are designed for drawing dynamic models of convex polyhedra whose faces, edges, and vertices correctly change their appearance depending on their visibility: edges become dashed and faces and vertices vanish when they appear on the back side of the solid as its shape is changed by dragging vertices or by spinning the entire image. This toolkit contains a template 3D coordinate system you can reuse in other sketches, and tools and instructions for plotting points (given 3D coordinates), segments, and curves. The tools can also be extended to graph functions with restricted domains. This sketch contains tools and instructions for defining and graphing piecewise functions in Sketchpad. This set of tools and accompanying Instructional Manual (16 page PDF file) add many capabilities of advanced graphing calculators to Sketchpad, including finding roots, plotting tangents, and calculating integrals. This toolkit showcases several example knots, provides some exercises for the reader, and supplies both a knot grid and the tools for constructing your own knots. Toolkit documents contain collections of related custom tools you may find useful in your own explorations.
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