- capm`mt ݥEPw0H (^@pLC L-PL-@LCL0  56d+AWorld: Each image point in AWorld is mapped to the absolute value of its Euclidean pre-images rectangular coordinates. Thus depending on the quadrant of a pre-image (with respect to the hidden coordinate system), shapes may undergo zero, one or two reflections about (hidden) axes. P(X, Y) => P(|X|,|Y|). S1World: Each image point is horizontally sheared from its pre-image. Amount of shearing is proportional to height from a (hidden) horizontal axis. P(X, Y) => P(X+Y, Y). S2World: Images in S2World are pixellated onto the nearest gridpoints of an arbitrary square lattice. Changing the (green) unit length changes the resolution of the lattice. P(X, Y) => P([X], [Y]). S3World: Points in S3World are rotated proportionate to the magnitude of the angle they form with respect to a (hidden) polar coordinate system. Varying the (green) constant K determines the degree of rotational scaling. P(r, Theta) => P(r, k*Theta). (8TSTRS]9RSSTT]9Y ;H(^@LCL+L/@LCSCSCL+L/`L8GR5zDouble-click the Tell All button to reveal the solutions to the various mystery worlds in this archive. Dont do this til youve explored the worlds yourself, and come up with at least tentative descriptions of their behavior! For more information on Drawing Worlds, see Dynamic Drawing Worlds: Scripted Exploration Environments in The Geometers Sketchpad, N. Jackiw, in Schattschneider & Kings Dynamic Geometry volume (MAA Press, due in late 1996).teSequenceMovie Play SoundL/0L2PkLC %L1L2`LCjR (^@W;Hc5c7`W`;Hmmcc fg1+z{7Each world is stored in its own folder or directory. To explore a given world, locate its folder and: 1. Use Sketchpad v3.0 or later. 2. Open the World Starter sketch located in that folder. 3. Set the current Script Tools Folder to that folder. You can change the current Script Tools Folder in the Advanced Preferences dialog, orif using Sketchpad v3.02 or laterby using the Change Script Tool Folder item in the Script Tools menu. 4. After setting the Folder, use the Script Tools icon to access the Compass and Straightedge associated with that world. Do not use any of the regular Sketchpad tools or menu commands except for the arrow tool (to drag items in the sketch). Where applicable, dashed light-blue lines indicate the Euclidean pre-image of your straightedges segments and compasss circles; solid red lines indicate the transformed mystery image of these shapes. NOTE: Dont forget to use a given set of tools with and only with its given World Starter sketch. Most mystery worlds wont work if you dont use the right combination of sketch and tools.tools.CompassOddStraightedge cHc2c9PPc:`f1&`c9Ai0le Mm(^@Apple Video PlayerAppeCD Audio PlayerApps/Interneta UeXHThe Drawing Worlds included in this archive provide several self-guided explorations into mappings of the plane to the plane by way of some opaque, mysterious function or transformation. Each Drawing World contains a starter sketch (which contains hidden parameters that control the mystery function of that world), and two script tools that implement a compass and straightedge as transformed by that worlds function. Your job is to use the provided script tools to characterize the mystery function. You should aim first for a phenomenological description of the tools behavior, and proceed to a geometric or analytic explanation. Pay attention to your own progress in developing techniques to solve each worlds mystery. (Reading the tools scripts or showing the hidden parameters of the starter sketch is, of course, cheating.)N pNK`NHH3N`$5 (^@a;0;H   OlOqa;;Hڪ OqO a'- N. Jackiw 1995 (njackiw@keypress.com)a:;HOqa:OoOpa:;HOqa:pOp@Opa:`;HOpa:POp@%L!$(^@Op`OgHHKOMystery Drawing Worldsds>OlOgOm0 Ola>`;HOm00OlOla>@;HPc (^@ Hide Tell AllNKKBt`K@Lt`Ka`utp T(^@Tell AllNKKBt`K@Lt`Ka`utp (K4cj (^@HideINKKt`K@Lt`Ka`utp j (^@ShowINKKt`K@Lt`Ka`utp  Calcul,q? (^@Hide BNKKt`K@Lt`Ka`utp q+ (^@Show BNKKt`K@Lt`Ka`utp 3 (^@HideM 0MMM    (^@ShowH3M MKMM (K<M=7P (^@ Solutions|NKKBt`K@Lt`Ka`utp ( >Q (^@ InstructionsNKKBt`K@Lt`Ka`utp ( >Qd (^@ IntroductionNKKt`K@Lt`Ka`utp