Mathematicians

If a planar graph G is drawn in the plane, so that no two edges cross, the plane is divided into a number of regions which may be called "faces". Euler's Theorem (for planar graphs): Let G be a connected planar graph drwawn in the plane. If there are v vertices, e edges, and f faces, then v - e + f = 2. An application of this theorem gives Euler's Theorem for polyhedra.

Euler's Theorem (for polyhedra): If a convex polyhedron has v vertices, e edges, and f faces, then v - e + f = 2 For particular polyhedra is easy to confirm the result stated in theorem. For example, a cube has 8 vertices (v = 8), 12 edges (e = 12), and 4 faces (f = 4) So, v - e + f = 8 - 12 + 4 = 2.A tetrahedrom has v = 4, e = 6, and f = 4. So, v - e + f = 4 - 6 + 4 = 2. Look at this site to understand better (you can see pictures there).

http://www.ics.uci.edu/~eppstein/junkyard/euler/ Euler formula: for any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges. Symbolically V-E+F=2 The polyhedron formula, of course, can be generalized in many important ways, some using methods described below. One important generalization is to planar graphs. To form a planar graph from a polyhedron, place a light source near one face of the polyhedron, and a plane on the other side. The shadows of the polyhedron edges form a planar graph, embedded in such a way that the edges are straight line segments. The faces of the polyhedron correspond to convex polygons that are faces of the embedding. The face nearest the light source corresponds to the outside face of the embedding, which is also convex. Conversely, any planar graph with certain connectivity properties comes from a polyhedron in this way.

You can see here that there are 8 vertices, 14 edges, and 8 faces. So,

v - e + f = 8 - 14 + 8 = 2 Look at this site also.

http://www.highpointsmath.com/SiteMap/Polyhedron.html

Polyhedron * A polyhedron is a space figure each of whose faces is a polygon. * In other words, a polyhedron is a solid shape whose faces are all polygons. * Cubes, prisms, and pyramids are polyhedra. More about Polyhedron * A regular polyhedron is a polyhedron in which all faces are regular polygons of the same shape and size. Name the polyhedron that has 4 faces, 6 edges, and 4 vertices. Choices: A. hexahedron B. cone C. tetrahedron D. octahedron Correct Answer: C Solution: Step 1:A tetrahedron or a triangular pyramid is a pyramid with a triangular base.Step 2: The net of a tetrahedron that can be folded and joined to form a tetrahedron is as shown.Step 3:The points 2, 3, and 4 forms the base, and the sides join at point 1 to form a pyramid. Step 4: There are 4 faces, 6 edges, and 4 vertices in a tetrahedron. Step 5: So, tetrahedron is a polyhedron that has 4 faces, 6 edges, and 4 vertices.

The 3 machines that Babbage designed (in order) are:

1. Difference Engine #1
2. Analytical Engine
3. Difference Engine #2

He failed to build ANY of them and Parliament cut his funding completely while he was designing the Analytical Engine because he had failed to deliver a working Difference Engine.

Two copies of Difference Engine #2 were built a few years ago, by the London Science Museum, to test if Babbage actually could have built it with early 19th century materials and machine shop practices. Both are beautiful operating Victorian era industrial automatic calculators, weighing about 4 tons. Reliability is a bit low though, mostly due to very fragile carry levers.

The Turing Machine was part of a mathematical proof in Turing's paper "On Computable Numbers". The proof showed that there are non-computable numbers, and problems that no computer (no matter how it is built or programmed) can solve. However the proof did not give an example of either (such proofs of existence usually don't produce examples).

The Turing Machine was never intended to be built, and it is a very inefficient and impractical computer.

The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus circa 150 BC, who compiled a trigonometric table using the sine for solving triangles. Ptolemy further developed trigonometric calculations circa 100 AD

Development of trigonometry is not the work of any one man or nation. It first originated in India and the basic concepts of angle and measurements was noted in Vedic texts such as Srimad Bhagavatam. However, trigonometry in its present form was established in Surya Siddhanta and later by Aryabhata [5th century CE]. It should be noted that from the time of Hipparchus until modern times there was no such thing as a trigonometric ratio. Instead, the Indian civilization and after them the Greeks and the Muslims used trigonometric lines.

Pythagoras of Samos (580? BC- 500? BC) was an Ionian Greek mathematician and also founder of the religious movement called Pythagoreanism.

Nasir al-Din al-Tusi (1135-1213) (aka Sharafeddin Tusi) widely promulgated studies in trigonometry, which was compiled by him as a new subject in its own right for the first time. He also developed the subject of spherical trigonometry.

I think you mean Inertia?

Newton's First law of motion states that:

"An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an external force."

This means that there is the natural tendency of objects to resist changes in their state of motion. This tendency to resist changes in their state of motion is described as inertia