Math 325

Spring 04

Homework for Friday January 30

 

 

1.  Use Geometer’s Sketchpad to make a design you really like (and maybe one I can put in the display case outside our classroom).  I have a book that includes some suggestions.  You might try making a tessellation, op art, or something else.  Turn in your sketch (either on disk or a printout) and a description of how you made it.

 

2.  Find as many ways as you can to construct an equilateral triangle, using sketchpad.  For each method, explain how you know your triangle is equilateral.  Try to trace back the information that you use as far as you can (for example, suppose your method depends on knowing that the angles in a triangle sum to 180.  How do you know that they sum to 180?).  Try to keep going back until you reach an impasse.  Turn in a disk (or email to me) with your methods and a written description.

 

3.  Choose one (or more) of the following:

 

            a.  Fold an equilateral triangle from square paper.  Include a write-up that explains how to do the folding and why it works.

 

            b.  Find the largest equilateral triangle that can be inscribed in a square and prove that you’ve found the largest.  You might use sketchpad to help you.  In your write-up, be conscious of the assumptions you are making and why you feel justified in making them.

 

            c.  Prove that the quadrilateral formed by connecting the midpoints of any quadrilateral is a parallelogram.  Hint:  what can you say about the line formed by connecting the midpoints of two sides of a triangle?  In your write-up, be conscious of the assumptions you are making and why you feel justified in making them.

 

4.  Do another journal entry.  Start by responding to my comments from your last journal entry.  Include any thoughts from the article, “The Role and Function of Proofs in Sketchpad,” from looking at Euclid, and any general thoughts on using sketchpad.  Also write about what you’ve been thinking about from class or from doing this homework  just whatever stands out for you, especially focusing on things you find challenging, confusing, philosophical, etc.

 

   Copyright 2005, Debra K. Borkovitz.  You may copy or edit this material for non-profit, educational use only.

 

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