Triangluar Array

The positive integers are written in a triangular array as shown. in what row is the number 1000? 1 23 456 78910 11...

Geometry has many practical applications in everyday life

See attached file for full problem description. Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations ...continues

Cylindrical can holding tennis ball

A cylindrical can is just big enough to hold three tennis balls. The radius of a tennis ball is 5 cm. What is the volume of air that surrounds the tennis balls?

A Little League team is building a backstop for its practice field

A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high. All sides of the backstop including base and the center pole are to be made of aluminum tubing. How many feet of ...continues

An Indian sand painter begins his picture

An Indian sand painter begins his picture with a circle of dark sand. He then inscribes a square with a side length of 1 foot inside the circle. What is the area of the circle? See picture in attached file.

Strongly Regular Graph

Let n >= 2 be a number. Define the graph L2(n) as follows: Vertices are ordered pairs from the set {1, ..., n}. Two vertices are adjacent if they have the same first coordinate, or the same second coordinate (but not both). Show that this is a strongly regular graph, and find its parameters.

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 geometry hyperplane

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.

Geometry

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