Department of Mathematics, University of Kentucky, 2009. — 161 pages.Contents
Introduction
A Lament
Part of the problem and a remedy
Levels of problem solving
Use of the Maple language and worksheets
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 Exercises: Making 3d Alphabet Blocks
Building a Block Factory: Creating a Maple Procedure
Start with a single cube
Another Example of how to ’procedurize’ ’procedurize’ a sequence of commands
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
Shadows: Problems from Nature
Problems
Moving shadows
More Exercises
DIAGRAM CODE
GROUND PLACEMENT
Wall Placement
PARTIAL STICKPERSON
Pyramids and Prisms
Drawing exercises on pyramids
Exercises on prisms
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
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
Mirrors: More Problems from Nature
Discussion
Diagram light1
Questions:
Some solutions
geombouncer instructions
Solution
Index
