# Conceivable Parallel Postulate

Problem 10.1 Parallel Transport on the PlaneShow that if l and h are lines on the plane such that they are parallel transports along a transversal l, then they are parallel transports along any transversal. Prove this using any assumptions you find necessary. Make as few assumptions as you can, and make them as simple as possible. Be sure to state your assumptions clearly.a. What part of your proof does not work on a sphere or on a hyperbolic plane?SuggestionsThis problem is by no means as trivial as it at first may appear. In order to prove this theorem, you will have to assume something  there are many possible assumptions* so use your imagination. But at the same time, try not to assume any more than is necessary. If you are having trouble deciding what to assume, try to solve the problem in a way that seems natural to you and then see what develops while making explicit any assumptions you are using.On spheres and hyperbolic planes, try the same construction and proof you used for the plane. What happens? You should find that your proof does not work on these surfaces. So what is it about your proof (on a sphere and hyperbolic plane) that creates difficulties?Problem 10.1 emphasizes the differences between parallelism on the plane and parallelism on spheres and hyperbolic planes. On the plane, non-intersecting lines exist, and one can parallel transport everywhere. Yet, as was seen in Problems 8.2 and 8.3, on spheres and hyperbolic planes two lines are cut at congruent angles if and only if the transversal line goes through the center of symmetry formed by the two lines. That is, on spheres and hyperbolic planes two lines are parallel transports only when they can be parallel transported through the center of symmetry formed by them. Be sure to draw a picture locating the center of symmetry and the transversal. On spheres and hyperbolic planes it is impossible to slide the transversal along two parallel transported lines while keeping both angles constant (something you can do on the plane). In Figures 10.1, the line r’ is a parallel transport of line r along line /, but it is not a parallel transport of r along /’.We will now divide parallel postulates into three groups: those involving mostly parallel transport, those involving mostly equidistance, and those involving mostly intersecting or non-intersecting lines. This division is useful even though it is rough and unlikely to fit every conceivable parallel postulate.b. Which of these three groups is the most appropriate for your assumption from Problem 10.1? We will call the assumption you made in Problem 10.1 your parallel postulate.

Struggling to find relevant content? Order a custom essay on
Conceivable Parallel Postulate
Let our experts save you the hassle
Calculate the price
Pages (550 words)
\$0.00
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
Sign up, place your order, and leave the rest to our professional paper writers in less than 2 minutes.
step 1
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
s
Get personalized services with GPA Fix
One writer for all your papers
You can select one writer for all your papers. This option enhances the consistency in the quality of your assignments. Select your preferred writer from the list of writers who have handledf your previous assignments
Same paper from different writers
Are you ordering the same assignment for a friend? You can get the same paper from different writers. The goal is to produce 100% unique and original papers
Copy of sources used
Our homework writers will provide you with copies of sources used on your request. Just add the option when plaing your order
What our partners say about us
We appreciate every review and are always looking for ways to grow. See what other students think about our do my paper service.
Social Work and Human Services
Great Job!
Customer 452587, October 27th, 2021
ENVIRONMENT SCIENCE
great
Customer 452813, June 26th, 2022
Other
I requested two pages and only have one page and the second pages is references.
Customer 452475, August 22nd, 2022
Exploring Gender in Science, Technology, and Mathematics
Very good work
Customer 452769, July 2nd, 2022
Human Resources Management (HRM)
Thanks for the paper. Hopefully this one will receive higher than a C and has followed all guidelines.
Customer 452701, November 16th, 2022
Criminal Justice
Thank you for the great paper. I like how the writer structured it.
Customer 452627, October 2nd, 2021
Other
AWESOME
Customer 452813, June 20th, 2022
Social Work and Human Services
Awesome Work!
Customer 452587, October 20th, 2021
Other
GREAT
Customer 452813, June 25th, 2022
IT, Web
Excellent job on the paper.
Customer 452885, January 25th, 2023
Nursing
Excellent work! Thank you again!
Customer 452707, December 20th, 2022
Social Work and Human Services
Great Work!
Customer 452587, August 31st, 2021