Purchase Solution

Euclid's parallel postulate, hyperbolic and spherical geometry

Not what you're looking for?

Ask Custom Question

A. Discuss differences between neutral geometry and Euclidean geometry.

B. Explain the importance of Euclid's parallel postulate and how this was important to the development of hyperbolic and spherical geometries.

Purchase this Solution

Solution Summary

The solution discusses Euclid's parallel postulate and its importance to geometry. Additionally it explains the difference between neutral geometry and Euclidean geometry.

Solution Preview

A)
Euclid had five postulates:

1) A straight line can be drawn from any point to any point.
2) A finite straight line can be extended infinitely in a straight line.
3) A circle can be drawn given any center and distance.
4) All right angles are equal to one another.
5) If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, then the two straight lines, if extended indefinitely, will meet on that side on which are the angles less than the sum of two right angles. (You may have seen equivalent statements of this postulate, such as Playfair's ...

Solution provided by:
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
Recent Feedback
  • "Excellent work. Well explained."
  • "Can you kindly take a look at 647530 and 647531. Thanks"
  • "Thank you so very much. This is very well done and presented. I certainly appreciate your hard work. I am a novice at statistics and it is nice to know there are those out there who really do understand. Thanks again for an excellent posting. SPJ"
  • "GREAT JOB!!!"
  • "Hello, thank you for your answer for my probability question. However, I think you interpreted the second and third question differently than was meant, as the assumption still stands that a person still independently ranks the n options first. The probability I am after is the probability that this independently determined ranking then is equal to one of the p fixed rankings. Similarly for the third question, where the x people choose their ranking independently, and then I want the probability that for x people this is equal to one particular ranking. I was wondering if you could help me with this. "
Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability