Constructible Numbers Presentation

In summary, the conversation is about a student who is working on a presentation for their Intro Analysis class on the topic of Constructible Numbers. The professor suggested using examples with a straight edge and ruler or filming it for the presentation. The student is seeking ideas to make the presentation more entertaining for their classmates, including examples of non-constructible numbers. They mention that their textbook, Gallian's Contemporary Abstract Algebra, has interesting anecdotes that could be helpful.
  • #1
mitymouse55
1
0
Hey all,
I am currently in an Intro Analysis class. As our final project, the professor asked a few of us to do a presentation on special topic that we haven't covered. He gave me Constructible Numbers. He said that it would be a fun project for me. He said I could do a bunch of example with a straight edge and ruler or film it and put it in with the rest of the power point presentation.
Anyways, I was trying to think of ways to make it as entertaining as possible for the rest of the class, maybe a few examples of non-constructible numbers? I guess its nice that no one in my class knows what constructible numbers are, but it still has to have some solid proof and definition behind it for my Prof. If you guys have any ideas, I would really appreciate it.

Thanks
 
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  • #2
Gallian, Contemporary Abstract Algebra, 391-4 has interesting anecdotes.
 

1. What are constructible numbers?

Constructible numbers are real numbers that can be constructed using only a compass and straightedge, starting with the number 1 and using basic geometric operations such as addition, subtraction, multiplication, division, and square root extraction.

2. How are constructible numbers different from other numbers?

Constructible numbers are different from other numbers because they can be constructed geometrically, while other numbers, such as irrational numbers, cannot be constructed using basic geometric operations.

3. Who first discovered constructible numbers?

The ancient Greek mathematicians, specifically Euclid and Pythagoras, were the first to explore constructible numbers and their properties. However, the concept was formalized by French mathematician Pierre Wantzel in the 19th century.

4. What are some examples of constructible numbers?

Examples of constructible numbers include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0.5, 0.25, 0.125, and any rational number that can be expressed through the basic geometric operations mentioned above.

5. What is the significance of constructible numbers in mathematics?

Constructible numbers have played a significant role in the development of geometry and algebra, and have been used to prove important theorems, such as the impossibility of trisecting an angle with a compass and straightedge. They also provide insight into the nature of numbers and their relationship to geometry.

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