Euclidean circle

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.

Graphs : Adjacency Matrix, Order and 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.

Construction Proofs : Pentagon Proportionality and Hexagons

Please see the attached file for the fully formatted problems.

Duality of Pappus' Theorem

State the dual of Pappus' Theorem. Give an illustration.

This problem is relevant to Geometry, in which we have asked to find the Maximum area that a goat can graze outside a rectangular barn, when it is tied with a lead to the barn and outside of it.

If a goat is tied on a 50 foot lead to a corner on the outside of a rectangular barn and the barn is 20 feet by 20 feet and the goat can not get into the barn nor is the barn a grazing area, what is the maximum grazing area and show how the maximum grazing area was determined. A man has a barn that is 20 feet by 10 feet, he t ...continues

Geometry : Finding the Side of a Hexagon; Finding the Surface Area and Volume of a Football

1. Show the necessary steps for finding the length of each side of a regular hexagon if opposite sides from midpoint to midpoint are 18 inches apart. 2. Without cutting or destroying a football, how would you find the area and volume of a football. Include any necessary formulas and measurements to implement your idea.