Your Perfect Assignment is Just a Click Away

Starting at $8.00 per Page

100% Original, Plagiarism Free, Customized to Your instructions!

glass
pen
clip
papers
heaphones

Duality in Projective Geometry and Spherical Geometry Problems

Duality in Projective Geometry and Spherical Geometry Problems

Question Description

a) Make it as easy as possible, as you will explain to a novice!

b) Add to figures when you explain the solutions.

c) Please add which theory you used to solve the questions

——

1. What is meant by ….

(a) ellipse, hyperbola and parabola;

https://1drv.ms/b/s!AgH2abs8e-hEgdxR1o9g9FaUWqspnQ

(b) spherical geometry,

https://1drv.ms/b/s!AgH2abs8e-hEgdxSiXuxBvKoXNz9rQ

(c) duality in projective geometry,

https://1drv.ms/b/s!AgH2abs8e-hEgdxTUcVPPCa7hcJ2fw

(d) hyperbolic geometry,

https://1drv.ms/b/s!AgH2abs8e-hEgdxUU5cIEkCfAWg0VA

(e) and fractals?

https://1drv.ms/b/s!AgH2abs8e-hEgdxVZTT2qvAIssucYw

—————–

2. Make below constructions with compasses and (ungraded) ruler.

(a) Show how to divide a given distance into three equal parts. Enter the theorems you use.

https://1drv.ms/b/s!AgH2abs8e-hEgdxWsuJZ4Nes2W7BKg

(b) Show how to invert a distance OA. You must therefore master a procedure such as gives a point A1 such that OA OA1 = 1. A circle with radius 1 should be used.

https://1drv.ms/b/s!AgH2abs8e-hEgdxXRWSdIYTKnPoh4w

(c) Construct √5

https://1drv.ms/b/s!AgH2abs8e-hEgdxXRWSdIYTKnPoh4w

—–

3. Some proofs:

(a) Prove Euclid’s 32nd theorem: the sum of the angles in a triangle is 180 degrees.

https://1drv.ms/b/s!AgH2abs8e-hEgdxYfoQ4KiA3xRFYqA

(b) Prove that in a circle the midpoint angle, ∠AMB, is twice the peripheral angle, ∠AP B.

https://1drv.ms/b/s!AgH2abs8e-hEgdxZ-K-ZwaORDdqnVA

(c) A circle passes through all the corners of a quadrilateral. Show that the sum of two opposite angles is always equal to 180 degrees. And vice versa: In a quadrilateral, the sum of opposite angles is 180 degrees. Show that there is a circle that goes through all the corners of the quadrilateral.

https://1drv.ms/b/s!AgH2abs8e-hEgdxakonb36BBHY4_jw

(d) Prove the chord theorem both when the point P lies inside the circle and outside and touches it. (When the point P is outside the circle, the theorem is usually called the secant theorem)

https://1drv.ms/b/s!AgH2abs8e-hEgdxbY27C4ShBTriW1g

(e) Prove that the three medians of a triangle intersect at a point.

https://1drv.ms/b/s!AgH2abs8e-hEgdxcwtnFSB_fCN4uAA

(f) Prove that a point P lies on a bisector to the angle ∠BAC ⇔ The heights from P to the angle legs AB and AC are equal in length.

https://1drv.ms/b/s!AgH2abs8e-hEgdxdRPCh17nPOGieGQ

(g) Prove that the three bisectrices of a triangle intersect at a point.

https://1drv.ms/b/s!AgH2abs8e-hEgdxcwtnFSB_fCN4uAA

(h) Prove the bisector theorem for an inner angle.

https://1drv.ms/b/s!AgH2abs8e-hEgdxdRPCh17nPOGieGQ

(i) Prove Pythagoras’ theorem. You must know two different proofs. Euclid’s proof and another that you choose yourself.

https://1drv.ms/b/s!AgH2abs8e-hEgdxfnTX_5ZcYFVPK7w

(j) Derive the expression for the area of a spherical triangle, see the course book. I have posted a Youtube clip under the course documents about this. Feel free to make your own sketch of a ball or orange.

https://www.youtube.com/watch?v=UWDI_suB-rg

course book: https://ibb.co/F3X78Vv


"Place your order now for a similar assignment and have exceptional work written by our team of experts, guaranteeing you A results."

Order Solution Now

Our Service Charter


1. Professional & Expert Writers: Eminence Papers only hires the best. Our writers are specially selected and recruited, after which they undergo further training to perfect their skills for specialization purposes. Moreover, our writers are holders of masters and Ph.D. degrees. They have impressive academic records, besides being native English speakers.

2. Top Quality Papers: Our customers are always guaranteed of papers that exceed their expectations. All our writers have +5 years of experience. This implies that all papers are written by individuals who are experts in their fields. In addition, the quality team reviews all the papers before sending them to the customers.

3. Plagiarism-Free Papers: All papers provided by Eminence Papers are written from scratch. Appropriate referencing and citation of key information are followed. Plagiarism checkers are used by the Quality assurance team and our editors just to double-check that there are no instances of plagiarism.

4. Timely Delivery: Time wasted is equivalent to a failed dedication and commitment. Eminence Papers are known for the timely delivery of any pending customer orders. Customers are well informed of the progress of their papers to ensure they keep track of what the writer is providing before the final draft is sent for grading.

5. Affordable Prices: Our prices are fairly structured to fit in all groups. Any customer willing to place their assignments with us can do so at very affordable prices. In addition, our customers enjoy regular discounts and bonuses.

6. 24/7 Customer Support: At Eminence Papers, we have put in place a team of experts who answer all customer inquiries promptly. The best part is the ever-availability of the team. Customers can make inquiries anytime.