Loading...

Messages

Proposals

Stuck in your homework and missing deadline? Get urgent help in $10/Page with 24 hours deadline

Get Urgent Writing Help In Your Essays, Assignments, Homeworks, Dissertation, Thesis Or Coursework & Achieve A+ Grades.

Privacy Guaranteed - 100% Plagiarism Free Writing - Free Turnitin Report - Professional And Experienced Writers - 24/7 Online Support

Curvature of Space-Time Tutorial

22/09/2020 Client: carolinb Deadline: 10 Days

Material Required: 



  • Paper

  • String

  • Clear tape

  • Thumbtacks

  • Round object (ball or globe)

  • Computer and internet access

  • Protractor (if you don't have one on hand you can get one here.

  • Digital camera and/or scanner

  • Java


**Java: for any Java issues see the alternative procedure at the end of Exercise 3.


Time Required: approximately 2-3 hours


Pre-exploration Study and Information


I. Introduction


Tutorial


Did you know that there is more than one possible geometry, or shape, of  the Universe?  Possible geometries include, 1) Euclidean (or flat space) or, 2)  Non-Euclidean (or curved space.) Your text explains both of these types of geometry to you but in this lesson you will investigate each. Remember this theorem (called the Triangle Sum Theorem).  In this theorem the sum of the angles of a triangle is equal to 180 degrees.


The three possible geometries of space are shown, positive, negative and flat curvature.


 Activity


Exercise 1: Test the Theorem.


Test out this theorem by using a piece of string to form the perimeter of a triangle on a sheet of paper. Because we are using a flat sheet of paper, this investigation is a test of Euclidean Geometry. (Include at least three images of the following triangles you have created in your table.)



  1. Stretch the string tightly and tape down the corners with clear tape or use thumbtacks in each corner.

  2. Measure the angles of the triangle and record them on the following table.

  3. Measure the perimeter of this triangle and record it. (Perimeter = a + b + c) Take a photo of at least three.

  4. Calculate the sum of the angles of this triangle and record that also.Triangle with sides labeled a, b, & c.

  5. Repeat this process at least 5 times for 5 different triangles.


Euclidean Geometry


Angle 1

Angle 2

Angle 3

Sum of Angles

Perimeter

QUESTIONS:

1A.  Describe your data on the sum of the angles on a flat sheet of paper for 5 different triangles. . 


2A.  Does this agree with the Triangle Sum Theorem?  Why or why not?


Exercise 2: Investigate Elliptic Geometry


Let's try this investigation in Elliptic Geometry. Specifically, you will measure the angles in a triangle formed on the surface of a sphere, rather than a flat piece of paper. In your table, include at least three images of the triangles you create.



  1. Use the surface of any spherical object – a tennis ball, globe, etc.  

  2. You may be able to use tacks to hold the string in a triangular shape, so you can measure the angles. Take photos.

  3. Make sure you record at least 5 sets of measurements.


Elliptic Geometry


Angle 1


Angle 2


Angle 3


Sum of Angles


Perimeter


QUESTIONS:

2A.  Describe your data on the sum of the angles on a sphere for 5 different triangles.


2B.  Does this agree with the Triangle Sum Theorem?  Why or why not?


Exercise 3: Investigating Hyperbolic Geometry


There aren’t too many readily available objects that have hyperbolic geometry, so instead we’ll use a computer model.  



  1. Go to Triangles, Angles, and AreaNOTE: If the applet does not work for you perform your measurements on the triangles located at the end of this instruction document. Otherwise, an alternate site you can use is http://www.cs.unm.edu/~Joel/NonEuclid/NonEuclid.html

  2. Read through the information on the site and then at the bottom of the page Click to launch the applet.

  3. Look at the image there. This is a hyperbolic surface.  

  4. You can make your angle measurements on the triangle shown (remember that your lines are special arcs in Hyperbolic Geometry).

  5. To measure the angle formed by two lines, measure the angle formed by the tangents to the arcs at the intersection points (the bow of each line). It might be tough to do this on the computer, but try your best.

  6. In the applet, create one more triangle, again measure the angles.


Hyperbolic Geometry


Angle 1


Angle 2


Angle 3


Sum of Angles


Perimeter


QUESTIONS:

3A.  Describe your data on the sum of the angles on a hyperbolic surface for 2 different triangles.


3B.  Does this agree with the Triangle Sum Theorem? Why or why not?


Exercise 4: What is the Relationship?


When all of the data have been recorded, look to see if you can find a relationship between the value of the perimeter of the triangle and the sum of the angles in flat, elliptic, and “saddle-shaped” (hyperbolic) geometries.


QUESTIONS:

4A.  Describe your data on the sum of the angles on a flat sheet of paper and their perimeters in Euclidean geometry? Is there a relationship between the perimeters and the angles?


4B.  Describe your data on the sum of the angles on a sphere and their perimeters in elliptic geometry? Is there a relationship between the perimeters and the angles? 


4C.  Describe your data on the sum of the angles on a hyperbolic surface and their perimeters in hyperbolic geometry? Is there a relationship between the perimeters and the angles?


Exercise 5: Apply to the Universe


You will need outside sources  to answer these questions including the video viewed earlier, the textbook, and/or other website resources.


QUESTIONS

5A. The large-scale structure of the universe is said to be overall homogenous in nature. Describe what astronomers mean by this.


5B. The large-scale structure of the universe is said to be overall isotropic in nature. Describe what astronomers mean by this.


5C. Describe any real life situation where there exists a homogenous state but one that is not isotropic. 


5D.Describe any real life situation where there exists an isotropic state but one that is not homogenous.


5E. According to the latest research (in the last two or so years), which geometry is the universe believed to be flat, spherical or saddle-shaped? What evidence is given for this? 


5F. Explain how the universe may be geometrically spherical in shape but appear to be flat.


5G. Research and write a short essay of 2-3 paragraphs (minimum of 150 words) on what each of these three geometries means to our view of the universe. (flat geometry, spherical geometry, and “saddle-shaped” geometry).


NOTE: You must provide a reference list showing the source(s) that you used, including our own textbook, in proper APA citation format.



Homework is Completed By:

Writer Writer Name Amount Client Comments & Rating
Instant Homework Helper

ONLINE

Instant Homework Helper

$36

She helped me in last minute in a very reasonable price. She is a lifesaver, I got A+ grade in my homework, I will surely hire her again for my next assignments, Thumbs Up!

Order & Get This Solution Within 3 Hours in $25/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 3 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

Order & Get This Solution Within 6 Hours in $20/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 6 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

Order & Get This Solution Within 12 Hours in $15/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 12 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

6 writers have sent their proposals to do this homework:

Peter O.
Top Academic Guru
Ideas & Innovations
Academic Master
Writing Factory
University Coursework Help
Writer Writer Name Offer Chat
Peter O.

ONLINE

Peter O.

Hi, I am an MS Research Scholar, and after carefully reading the description of the project I can confidently say that I am a suitable candidate, equipped with right skills, to complete this valuable task of yours. I assure you timely completion, originality and grammatically correct content, according to your needs. Please feel free to contact me for completion of this task. Thank you very much.

$75 Chat With Writer
Top Academic Guru

ONLINE

Top Academic Guru

This project is my strength and I can fulfill your requirements properly within your given deadline. I always give plagiarism-free work to my clients at very competitive prices.

$50 Chat With Writer
Ideas & Innovations

ONLINE

Ideas & Innovations

Hi, Hope you are doing well. I can do this easily because I have several experiences to write articles on different web sites, creative content for several blogs & also SEO writing. Even I have written many kindle ebooks, Being a creative writer, I think I am the most eligible person for your Ghostwriting project. So lets make no longer delay & start chatting immediately.

$75 Chat With Writer
Academic Master

ONLINE

Academic Master

I have super grip on essays, case studies, reports and discussion posts. I am working on this forum from last 6 years with full amount of satisfaction of my clients.

$55 Chat With Writer
Writing Factory

ONLINE

Writing Factory

I can help you with creating a presentation of one slide for The Word of William Hunter. I will be happy to offer you 100% original work with high-quality standard, professional research and writing services of various complexities.

$40 Chat With Writer
University Coursework Help

ONLINE

University Coursework Help

Greetings! I’m very much interested to write for attendance systems. I am a Professional Writer with over 5 years of experience, therefore, I can easily do this job. I will also provide you with TURNITIN PLAGIARISM REPORT. You can message me to discuss the details.

$55 Chat With Writer

Let our expert academic writers to help you in achieving a+ grades in your homework, assignment, quiz or exam.

Similar Homework Questions

Fish cheeks questions and answers - Wrap it up case study solution - Red cross financial statements 2015 - Kelana jaya golf club - Identifying motherboard components worksheet - Coordinate battleship online game - Business management 3 4 - Sec 450 week 1 ilab - Mymatj - Advice to youth mark twain worksheet - Cultural influences on training and development - Gapu monuk saltwater - English 102 - Culminating Argument - Ben wade hand of god - Microstrip line width calculator - Bromination of acetone rate law - Data for hermann corporation are shown below - 6 3 skills practice similar triangles answers - Meaning of exceptionality in special education - Persuasive speech on sleep - What are the capacity implications of the marketing campaign - Hary96 - Roye kennel uses tenant days as its measure of activity - List two explicit premises that you find the most compelling in “give thanks to meat.” - Product management plan template - Brands that are promoted through comparative advertising are most likely to be - Family life merit badge workbook - History essay - Pastor encuentra dinero en su cartera para pagar las medicinas de su esposa. - An economy is experiencing a recessionary gap the government can - Choose a specific regulatory behavior - Gre pipe jointing methods - Week 11 assignment NS - Glass container in lab - WK4 Assignment-Quantitative Research Critique - Advantages of a multicultural society and labor force - Unit 2 Law discussion - Dr muhammad virk auburn - Rob dobs menu bloomington il - Dr susan sinclair dermatologist mona vale - Socially conscience organization - Economics - If the activity level increases 10 total variable costs will - Calculate the missing amounts in the following table - GLOBAL HEALTH- RESEARCH PAPER - 6 basic principles of government - Discussion question, 350 words and 2 references. - The dark side of interpersonal communication pdf - Informatics in healthcare - Effective approaches in leadership and management in nursing - Opal rt real time simulator - Manufacturing process planning ppt - Herbert gans functions of poverty - Should students be allowed to have phones in class - Pgem t vector sequence - Stats modeling the world answer key chapter 6 - Study of human movement - Why is lopeswrite a valuable tool for students - Are car headlights in series or parallel - Business Intelligence (Disc) - 128 64 32 16 - What is bavarian sausage inc s operating cash flow - Encounter by jane yolen - Week 7 - The lincoln electric company case study solution - Cardboard chairs with dimensions - Pros and cons of code of ethics in journalism - What is symbolism in literature - West coast vets hokitika - Act 4 scene 3 - Where do you enter cheat codes for bloody roads california - Discussion - Plight of the little emperors summary - Love vashikaran specialist In mAhARAshtRA +[91%%9928097710] Top And Best Tantrik Aghori Baba - Example of a dietary analysis - Conceptual Relationships and Assumptions - Las islas galápagos están cerca de la costa - Renunciation of probate victoria - Sequence diagram for registration of student - The lakota way chapters - Four process strategies - Common places mythologies of everyday life in russia - 3 methyl 2 butanone msds - Human resources due in 16 hours - Urgent 2 - Country Presentation to the Board of Directors - How to find markdown percent - CASE STUDY - REGRESSION MODEL - Resolving ethical business challenges case study solution - Arndale mental health resource centre - Conchita keena in mexico 2002 - Week 3 assignment - Food a fact of life explore food - Factor v leiden and flying - World civilizations the global experience fifth edition notes - Ig lintels load tables - EDUC-6263 - Sign language courses serc - Conduit spacers for duct bank