I need more than 90% on this project.. Please understand the project before bidding: Euclidean and Non-Euclidean Geometries

I need a experienced tutor, with geometry.. Euclidean and Non-Euclidean Geometries..

Late projects will not be accepted.

Project Rules. This project is to be a collaborative e↵ort between three or four people. You may select your collaborators (they do not have to be from your table.)

Share the work equally. There is to be one write-up per group.

The projects pose questions for you to investigate. There is no unique answer–

just do you own thinking. You are not allowed to consult texts, other people, or the internet. You can talk to the instructor, but nobody else outside of your group. If you consult outside sources you will receive a score of zero on the project.

There are a number of possible projects and di↵erent groups will receive di↵er-

ent problems. If you have seen this project before, request another project.

Your Question. In class we introduced the study of arrangements of lines. We didn’t prove many details, but we did look at the diagrams in the Grunbaum article

where he displays the di↵erent possible of arrangements of small numbers of lines.

In this project you are asked to work out some details and then generalize the

problem to that of arrangements of lines and conics.

Your first problem is to work out the details that show Gunbaum’s figures give

all possible arrangements of three, four or five lines. Provide careful proofs. This

is a good warm up for the next problem which is a more open-ended investigation.

Your second problem is to consider the question of arrangements of lines and

conics. What are the possible ways to arrange one line and one conic, up to projec-

tive equivalence. What about two lines and one conic, or one line and two conics?

What about two lines and two conics, and so forth. If this question is a bit vague,

it is supposed to be–you need to define the parameters. You will note that if the

horizon line does not intersect any of the conics, then they all will appear as el-

lipses. Can you always simplify to this case using projective changes of the plane?

A second issue is what we might mean by cell structure, because now some edges

will be lines and others may be conics.

There are many issues that will come up. Some have multiple resolutions

depending upon how you devise the definitions. Get started and see how far you

can go. Ask your own questions—you are free to take this anywhere that makes

sense. Talk to Prof. Jacob if you need more direction.

Project Write-up. Your project write up should have three parts.

The first section should discuss your process. Include discussion of your con-

jectures and whether they ended up being true or false. Don’t be shy to share

ideas that ended up wrong. This is part of mathematical learning. Also include

where you got stuck and how you overcame being stuck. The writing here should

be informal (but clear) and your ideas can be described intuitively. You might pay

attention to how the precision of your thinking increased with time.

The second part should contain your results. This should consist of carefully

formulated definitions and proofs based upon those definitions. If you cannot prove

a result, but instead give a “plausibility argument”, that is fine, but be sure to

indicate that this is what you are doing. In some projects, you may not have the

tools to prove every result you need. Discuss this issue with the instructor if you

need to. In some projects you may give several di↵erent definitions of a term, and

then be exploring how the results di↵er depending upon the definition. If you are

doing this, be sure to label the dependency of results upon definitions clearly.

The third section is your Appendix. It includes samples of your scratch work,

diagrams, models, etc. All you need to do is organize it. Your writing in part 1

(part 2 possibly as well) should contain references to this Appendix.

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
$26
The price is based on these factors:
Academic level
Number of pages
Urgency
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more
error: Content is protected !!