Sheet A (Mathematics 244-Geometric Structures)

Prepared by:

Joseph Malkevitch

Department of Mathematics and Computing

York College (CUNY)

Jamaica, New York 11451

email: jmalkevitch@york.cuny.edu

1. What is the name of the object shown:

(Note: What is shown is a representation on a flat piece of paper of an object that exists in 3-dimensional space.)

2. Are there other objects which are “different” from the one above but

for which you would use the same name?

3. Write down a list of as many properties (facts about) the object in

Question 1 as you can.

(Unless your list contains at least 25 items you have not looked at the

object as carefully as you might. However, it takes practice to “look”

at a geometric object as carefully as we are aiming for.)

4. How would you describe the object in Question 1 over the phone to a

friend? (or to an intelligent alien!)

5. Why do mathematicians care about giving “precise” definitions of the

technical terms used in mathematics?

6. Think about how you would define the terms you use to describe the

properties of the object in Question 1.

7. Can you give examples of words whose technical meaning in mathematics

is not the same as the meaning these words have in everyday use?

8. What are the pros and cons of requiring great precision in

“defining” words?