Differentiable geometry (tangent bundle, orientations)

Prove that the tangent bundle TM of a differentiable manifold M is (always) orientable (even though M may not be)

Differential Geometry (projective space, orientations)

Prove that the real projective space P^n(R) is orientable if and only if n is odd. Please if you are not sure about your proof, don't sign out my problem.

Geometry/construction

Construct triangle ABC given just 3 points ,namely S= its circumcenter, H = its orthocenter and F = the foot of one of its alititudes.

Geometry

How many distinct points does the 9-point circle have when the triangle is - isosceles - equlateral - right-angled isosceles.

Geometry Applications

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. 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 below. The problems in this Unit will give you an opportunity to practice these applications. Solve the following problems and submit them in a Word document. 1. A Little League team is building a backstop for its practice field. It is made up ... click for more