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Posts Tagged ‘corresponding’

Projections

Thursday, November 5th, 2009

Introduction to Projections

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Description

A detailed tutorial on projections. Step by step tutorial including several examples of what a projection is for reference.

Overview

A projection is another term for a transformation. But a projection is a different kind of transformation than a real transformation is. A projection is a transformation of points and lines from one plane to another plane. This is done by connecting corresponding points on the planes with parallel lines. Typically projections are used with vectors, which are entirely composed of points and lines.

Tags: corresponding, dot, infinity, lines, parallel, plane, point, product, projection, transformation, vector
Posted in Algebra | No Comments »

Intermediate Value Theorem

Thursday, September 24th, 2009

Intermediate Value Theorem Explained

Description

A detailed tutorial of the intermediate value theorem. Step by step tutorial including an explanation of the intermediate value theorem for reference. Knowledge of the intermediate value theorem is required in calculus.

Overview

The intermediate value theorem states that for each value between the upper bound and the greatest lower bound of the graph of a continuous function that there is a corresponding value in its domain. In mathematical terms, the intermediate value theorem states that if f is a continuous function on the closed interval [a, b] and M is a number between f(a) and f(b), then there exists at least one number c that f(c) = M. When writing proofs in calculus, you can say that something has been proven by the IVT if you used the intermediate value theorem to reach your conclusion.

Tags: a, b, c, Calculus, continuous, corresponding, domain, f(a), f(b), f(c), function, graph, greatest lower bound, intermediate value theorem, IVT, m, Math, upper bound, value
Posted in Calculus | No Comments »

Similar Triangles

Tuesday, September 15th, 2009

Introduction to Similar Triangles

Description

A detailed tutorial on the introduction to similar triangles. Step by step tutorial including several examples of how to solve similar triangles for reference.

Overview

Similar triangles are triangles that have the exact same angles, although the lengths of the sides may be different. This is what makes them similar, and not equal. However, the sides do correspond. Corresponding sides are sides that are opposite the same angle – meaning angles that have the same measure. Something that can help you find out the missing lengths of a similar triangle is that the ratios are always the same. As long as you have all the lengths of the sides of the other triangle, you will always be able to find the missing lengths.

Tags: angles, corresponding, corresponding sides, Geometry, lengths, Math, ratios, similar, similar triangles, triangle
Posted in Geometry | No Comments »

Angles of Parallel Lines

Tuesday, September 15th, 2009

How to Identify Angles of Parallel Lines

Description

A detailed tutorial on the identifying angles of parallel lines. Step by step tutorial including several examples of how to identify the angles of parallel lines for reference. Knowledge of angles of parallel lines is required for important tests such as the SAT.

Overview

Parallel lines are lines that go in the same direction, are perfectly straight, and are located right next to each other. In order to have an angle for these lines, another line must be drawn down the center of them, at a slant. This line is called a transverse line. There are a few different types of angles that can be found on these lines.

Alternate Interior Angles: Angles on the inside of the “shape” formed by the parallel lines, that are in alternating positions (top right and bottom left or top left and bottom right).

Alternate Exterior Angles: Angles on the outside of the “shape” formed by the parallel lines, that are in alternating positions (top right and bottom left or top left and bottom right).

Corresponding Angles: Angles that are in the same position on each of the parallel lines, for instance the the top right of both the line on the bottom and on the top.

Tags: alternate, alternate exterior, alternate interior, angles, corresponding, Geometry, lines, Math, parallel, transverse
Posted in Geometry | No Comments »