Dr. Sarah�s 3610 Sketchpad Test

Follow Directions Carefully

Everything will be completed in Sketchpad.

You may use your cheat sheet and Sketchpad, but nothing else (ie you are not allowed to go to the class web pages nor search the web�)

Problem 1) In a Sketchpad document, type in

Problem 1

your name

Construct an equilateral triangle. Save your sketchpad document in the proper format and then attach it onto the bulletin board containing you and Dr. Sarah in WebCT.

Problem 2) Create a similar picture in Sketchpad as the one below and complete this picture (in Sketchpad) in order to create two triangles with the same SSA (where one side is the radius of the circle, another side is AB, and the angle is the angle marked at B) so that the triangles are not similar. Do not worry about creating the semi-circle marking the angle in your picture.

Use the measuring capabilities of Sketchpad to show that you have SSA but that the triangles are not similar. Then type in Problem 2 and your name. Save your Sketchpad document in the proper format and then attach it onto the bulletin board containing you and Dr. Sarah in WebCT.

Problem 3) From Sketchpad, open MacHD/Applications/Sketchpad/Samples/Sketches/Investigations/PoincareDisk.gsp

Create 2 sketches and the relevant angle measures in order to show that Euclid�s 5^th Postulate sometimes but not always holds in hyperbolic geometry. Be sure that Problem 3a and Problem 3b along with your name is listed. Save your Sketchpad documents in the proper format and then attach them onto the bulletin board containing you and Dr. Sarah in WebCT. Note: you cannot have two Poincare Disk model documents open at the same time unless one is saved as something else, but you can use save as to save a changed version of a document.

Problem 4) From Sketchpad, open up MacHD/Applications/Sketchpad/Samples/Sketches/Investigations/PoincareDisk.gsp

Create a hyperbolic right triangle (be sure to use a perpendicular) and perform measurements and a calculation to demonstrate that the Pythagorean Theorem doesn�t always hold in hyperbolic geometry. In the following picture, I have created a right triangle in hyperbolic geometry for which the Pythagorean Theorem seems to hold. In your sketch, explain whether this can happen in hyperbolic geometry and if not, resolve the apparent conflict (Note: This really IS a right hyperbolic triangle and these also are the correct measurements). Be sure that Problem 4 and your name are also listed. Save your Sketchpad document in the proper format and then attach it onto the bulletin board containing you and Dr. Sarah in WebCT.

Problem 5) Create a Sketch to show that the Pythagorean Theorem sometimes but not always holds in taxi-cab geometry. Be sure to show work and explain your examples in detail and be sure that Problem 5 and your name are listed. If you do not create a script to measure the taxi-cab distance, then you must explain in detail each distance calculation. You will need to use the calculate feature to compare a^2 +b^2 with c^2. Save your Sketchpad document in the proper format and then attach it onto the bulletin board containing you and Dr. Sarah in WebCT.

If you are finished early then work on your final project (references are due next Tuesday).