Projective geometry problems

Projective Geometry Problem 1 i. Prove that a set of four points in a projective plane P (i.e. dim P = 2) form a projective frame if and only if no three of the points are collinear, i.e. no three lie on the same projective line. ii. Find a necessary and sufficient condition for five points to form a projective frame in a t ...continues

Projective geometry; linear maps

Let F be an affine map. Prove that the corresponding linear map is unique. See attached file for full problem description.

Projective geom, hyperplane, complex affine plane, proj closure

Projective Geometry Problem 4 Let C be the curve in a complex affine plane E. Find the infinite points of C, i.e. the points of the projective closure of that lie on the hyperplane at infinity. See attached file for full problem description.

You are part of a panel of parents, teachers, and administrators working to revise the geometry curriculum for the local high school. On tonight's agenda, you will be brainstorming creative ways to teach surface area and volume. The teachers are especially interested in methods which will help the students connect geometry to life in the "real world" because student motivation has sometimes been lacking in this course. What suggestions do you make to the panel during your discussion? Why do you think students would benefit from this idea being used in the classroom? .

You are part of a panel of parents, teachers, and administrators working to revise the geometry curriculum for the local high school. On tonight's agenda, you will be brainstorming creative ways to teach surface area and volume. The teachers are especially interested in methods which will help the students connect geometry to li ...continues

Let K be the Euclidean circle with equation

Let K be the Euclidean circle with equation...See attached file for full problem description.

In this question ABCD is a trapezium in which AC is parallel to BD and AC is 4/5 times

In this question ABCD is a trapezium in which AC is parallel to BD and AC is 4/5 times the length of BD....See attached file for full problem description.

Adjacency matrix, order, valency

Let A be the adjacency matrix of a regular graph of order v and valency k. Let J be the all-ones matrix of the same order. Show that A*J = J*A = K*J "Definition 2.1 A graph r with adjacency matrix A = A(r) is called regular if there exists a natural number k such that AJ = JA = kJ. The number k is called valency of r."

Solve the following five geometry problems

The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, as shown in the diagram attached. See attached file for full problem description. Solve the following problems in a Word document. 1. A Little League team is building a backstop f ...continues

How to cut the rug into two pieces.

If there is a rectangular rug with a hole in the middle, how do you cut the rug into two pieces, so that when you put the pieces back together, you have a square rug with no hole? See attached file for full problem description (including diagram).

How many different parallelograms can be identified?

How many different parallelograms can be identified in the picture? See attached file for full problem description.