# 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.’’’’

Don't use plagiarized sources. Get Your Custom Essay on
Conceivable Parallel Postulate
From \$8/Page
Full satisfaction or return your money back

Our experts will write you a top-quality paper and revise it an unlimited number of times until you're 100% satisfied - or offer a refund.

Check Prices
Get the best discount and better grades here
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 that being a student these days is hard. Because of this, our prices are some of the lowest on the market.

Instead, we offer perks, discounts, and free services to enhance your experience.
Sign up, place your order, and leave the rest to our professional paper writers in less than 2 minutes.
step 1
Upload assignment instructions
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.
How to get the most out of your experience with Toptutor4me
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
Here is what our happy clients say about us.
Receiving customer feedback and reviews from legit students who have utilized our services is one of our favorite part of the job. We love seeing testimonials from happy students whom we have helped to succeed. Read through the below review page to see what our partners think.
Psychology
Thank you so much for all of your hard work, appreciate every bit of it!
Customer 452483, September 6th, 2021
Microbiology
Thank you so much for revising this paper for me. It looks great, truly appreciate it! You're awesome :)
Customer 452483, September 14th, 2021
Mathematics
Thank you so much!
Customer 452483, July 26th, 2021
Healthcare Writing & Communications
You guys are awesome! Appreciate all of your hard work! Thank you.
Customer 452483, October 15th, 2021
English 101
Perfect! Thank you so much for all of your hard work and help! Appreciate it!!
Customer 452483, August 30th, 2021
Psychology
Thank you for all of your help and hard work, truly appreciate you guys always being there with my hectic schedule. Thank you again!
Customer 452483, September 20th, 2021
Group Dynamics
Great job. I appreciate it.
Customer 452521, November 22nd, 2021
Communications
Thank you! It was great :)
Customer 452483, July 26th, 2021
Nursing
Excellent writing !! Definitely I will use your services again... Thank you.
Customer 452487, August 22nd, 2021
English 101
I would like to thank you for the writing, it was a very busy week for me and had no time this week to do a writing. I would recommend you to others and would utilize you again.
Customer 452639, October 16th, 2022
Education
Great good
Customer 452555, February 14th, 2022
Mathematics
Job WELL DONE! Thank You very much!!
Customer 452483, July 12th, 2021
11,595
Total Reviews
98%
Satsfaction rate
6 pages
Average paper length
40%
Customers referred by a friend
Enjoy the best prices and lifetime 15% discount
Use a coupon TOP15 and enjoy expert help with any task at the most affordable price.
Order Now Order in Chat