Visual Problem Solving Paul Eakin and Carl Eberhart, University of Kentucky Summer 1998  

Introduction  A Lament  Part of the problem and a remedy  Levels of problem solving.  Use of the Maple language and worksheets.  Chapter 1 First steps -- Drawing boxes  What is visual Problem solving?  Mathematical Boxes  Introductory Exercises: Drawing in the Plane  More Introductory Exercises and Drawing in Space  Translating Geometric Objects  Duplicating and moving cubes  The steps in building a cube  Building a TEE  Exercises: More Pictures in the Plane  Exercises: Making 3d Alphabet Blocks  Building a Block Factory: Creating a Maple Procedure  Start with a single cube.  Another Example of how to 'procedurize' a sequence of commands  EXERCISES  Laying Bricks:Getting the Computer to do Repetitive Tasks  Working with expression sequences and lists  How to Build a list by hand  Automatically Generating Sequences and Lists  Boring List of Numbers from 672345 To 677345  Exercises: Sequences and Lists  Laying bricks. Applications of sequences and lists  EXERCISES: Making Brick Patterns With seq  Stacking Colored Bricks:  A Chromatic Brick Placer  Exercises: DO .. OD  Conditional statements  Exercises: If .. elif .. fi; and if .. else.. fi  A vertical chromatic brick placer  Exercises: Colored Brick Stacking  Making it Move - an Introduction to Animations  Exercises on Movie Making  New Problems from Old-A Case Study  The lawn mowing problem  Visual problems arising from the lawn mowing problem.  A specific problem.  A lawn mowing word  Two Mowers mowing side by side.  Exercises  Mowing Yards (part 2)  Starting at Different Corners: Going in Different Directions  Sam and Bill Mowing the Same Lawn  EXERCISES  Shadows: Problems from Nature  Problems:  Moving shadows  More Exercises  DIAGRAM CODE  GROUND PLACEMENT  Wall Placement  PARTIAL STICKPERSON  Pyramids and Prisms  Exercise.  More drawing exercises on pyramids.  Exercises  A solution  Cross Sections of pyramids and prisms  Cross Sections of triangular prisms  The Theorem and its proof.  A prism with an equilateral base and a 3-4-5 right cross-section  EXERCISES  Exploring Desargues Theorem.  Points and Lines at Infinity  Exercises On Points and Lines at Infinity  Desargues's Theroem  Proof of Desargue's Theorems  Remarks on Using Desargues Theorem To Represent one Object as a Shadow of Another  The Harmonic rays theorem.  A diagram  PROOF  EXERCISES  Cross sections of quadrilateral pryamids  Exercises  Solution.  Mirrors: More Problems from Nature  Discussion.  Diagram "light1"  Questions:  Some solutions  geombouncer instructions  Solution  Closed reflective paths in a polygon.  Closed reflective paths in a triangle.  Problems  Hints on a solution  Hints on a solution.  Reflective paths in an ellipse  Preliminary discussion: More on reflecting from lines and planes and the analytic expression of the principle of reflection.  An eliptical reflector  index.mws An index of bookmarks