Euclidean Geometry ?

Question

·Explain how the rules of Logic are used within a deductive system.

• Explain “Deductive Reasoning” vs. “Inductive Reasoning” and explain why Euclidean geometry is a deductive system.

• What are the official tools of construction? What tool is specifically excluded?

·What were Euclid’s main contributions to the field of Geometry?

• Explain the value of and necessity for formal proof in a Euclidean geometry course.

• Explain why Euclid’s “Parallel Postulate” was the most controversial and how this postulate is used to differentiate Euclidean vs. Non-Euclidean geometries.

• Explain the value of construction in learning geometry.

Answer 1

- Logic is used to deduce an answer. By knowing the rules and the cuase and effect of things, we can use logic to explain something.

- Deductive reasoning is using a set of rules and reasonal thinking to conclude something. While Inductive thinking is answering the question using things from the 5 senses to patterns presented by the question.

- If its related to geometry and not architecture, research about Euclid's book, The Elements

- He set the rules of the deductive system by writing The Elements. It is the 5 elements that make up the basic structures in geometry.

- The best advice I can give is to look at the figure in all possible ways, becuase some figures are a combination of multiple figures by overlapping them.

- "If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles."

If you notice, this postulate is VERY long compared to the other 4. Parallel Postulate is contraversial becuase the postulate is very long. A postulate is a discription of the structure in a short manner. Another reason why its contraversial is becuase it's hard to imagine infinite lines that never meet.

- Don't understand the question...

I know I did your homework, but it was fun. :D

Answer 2

You've asked way too many questions here. To answer them would take a book, which no answerer should have to write.

Separate your one question above into multiple ones and ask each of the multiple questions with a single question.