Posts Tagged ‘plane’
Friday, November 20th, 2009
Overview of Isoperimetric Inequalities
Description
A detailed tutorial on isoperimetric inequalities. Step by step tutorial including several examples of isoperimetric inequalities for reference.
Overview
An isoperimetric inequality is actually a geometric inquality. It deals with the square of a circumference of a closed curve in a plane and the area of the region it encloses. Isoperimetric means to have the same perimeter. The isoperimetric problem is used in conjunction the isoperimetric inequality to determine the measure of the plane figure.
Tags: area, circumeference, closed, curve, differential equations, figure, geometric, inequalities, inequality, isoperimetric, meausre, perimeter, plane, problem, region, square
Posted in Differential Equations | No Comments »
Tuesday, November 17th, 2009
Introduction to Half-Planes
Description
A detailed tutorial on half-planes. Step by step tutorial including several examples of half-planes for reference.
Overview
A half-plane is simply half a plane, that includes all the lines on half of the plane and sometimes the points. If the plane includes the points, it is a closed half-plane. If it doesn’t, then it is an open half-plane. The most common half planes are upper, lower, right, and left planes, where that side of the plane is all that is included. However, there are many other kinds of half planes that are all a variety of diagonal half-planes.
Tags: bottom, closed, Geometry, half, half-plane, left, lines, lower, open, plane, points, region, right, top, upper
Posted in Geometry | No Comments »
Thursday, November 12th, 2009
Definition of Skew Lines
Description
A detailed tutorial on skew lines. Step by step tutorial including several examples and a visual example of skew lines and what they are for reference.
Overview
Skew lines are two lines that do not intersect and are not parallel. In general, these lines have nothing in common. Think of dropping two sticks on the ground from high up. Provided they do not intersect each other (cross or touch each other in any way), those sticks are now a perfect example of skew lines. Typically, these lines are also not found in the same plane. Skew lines can only exist in three or more dimensions.
Tags: arithmetic, common, cross, different, dimension, Geometry, intersect, line, lines, nothing, parallel, plane, skew, three, touch
Posted in Arithmetic | No Comments »
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 »
Friday, October 23rd, 2009
Introduction to Vector Space
Description
A detailed tutorial on vector space. Step by step tutorial including several examples of vector space and how to solve for vector space for reference.
Overview
Vector space is simply a structure in mathematics that is formed by a collection of vectors. Vector space can be calculated using vector addition and scalar multiplication. Vector space is very dependent on the definition of a vector. Some vectors are simply arrows on a fixed plane. But in general, the term vector just means there is an object for which two operations can be performed. The definition of vector space is defined in algebraic terms, as opposed to the geometric terms that can sometimes be applied.
Tags: addition, algebra, arrow, collection, definition, Geometry, multiplication, object, operation, plane, scalar, space, vector
Posted in Algebra | No Comments »
Tuesday, September 29th, 2009
Definition of a Hyperbola
Description
A detailed tutorial of the definition of a hyperbola. Step by steo tutorial including several examples of the definition of a hyperbola for reference.
Overview
A hyperbola is similar to a parabola, but there is one difference – the hyperbola has two branches. You can think of it in the 2D form as a concave up parabola on top of a concave down parabola. Many people refer to the hyperbola as the “bow” because that is what it resembles. Like the parabola, a hyperbola is caused by the intersection of a conical surface and a plane.
Tags: concave, conic, conical surface, curve, focus, Geometry, graph, hyperbola, intersect, Math, parabola, plane
Posted in Geometry | No Comments »
Tuesday, September 29th, 2009
Definition of a Parabola
Description
A detailed tutorial of the definition of a parabola. Step by step tutorial including a visual example of the definition of a parabola for reference.
Overview
A parabola is an elongated curve that is used often in graphing. A parabola is formed by the graph of y = x^2, and its traditional form is concave up. Technically, the parabola is actually a conic section, which is the intersection of a conical surface and a plane parallel to the generated straight line of that surface.
Tags: concave, conic, conical surface, curve, focus, Geometry, graph, intersect, Math, parabola, plane, y=x^2
Posted in Geometry | No Comments »
Thursday, September 17th, 2009
An Introduction to Points, Lines, and Planes
Description
A detailed tutorial on identifying points, lines, and planes. Step by step tutorial including several examples of how to indentify different types of points, lines, and planes for reference.
Overview
Points, lines and planes might not seem very similar, but they are all connected. Points can be found in or on a line or plane, and lines form the planes. Points are simply locations, and are represented by small dots. There are a few different kinds of points. Collinear points are points that lie on the same line, while noncollinear points are points that don’t lie on the same line. Coplaner points lie in the same plane, while noncoplaner points do not. Lines have no thickness to them and extend infinitely in both directions. There are several different types of lines. There are skew lines, which run next to each other (although not parallel) but never touch each other. There are parallel lines and perpendicular lines, and there are intersecting lines. Planes have no thickness and are perfectly flat figures represented by a rectangle shape. Lines and planes can run in many different directions with each other, but have no special names.
Tags: collinear, coplaner, Geometry, intersecting, line, Math, noncollinear, noncoplaner, parallel, perpendicular, plane, point, skew
Posted in Geometry | No Comments »
Thursday, September 3rd, 2009
A Basic Look at Graphing on the Coordinate Plane
Description
This video outlines the different parts of the graphs and illustrates how to properly label all parts of the coordinate plane. Real world examples are given of graphs and graphing systems. Examples of how to plot points are provided in the video.
Overview
The coordinate plane, or the cartesian plane, is commonly known by math students as a blank graph. Graphs consist of two lines that are perpendicular to each other – the horizontal x axis and the vertical y axis. Each axis has a set of numbers, where the top and right of the lines are positive and the bottom and left of the lines are negative. The very center of the graph is known as the origin. The origin is the point (0, 0). Because of the two lines, the graph is split up into 4 sections, called quadrants. The quadrants are labelled at I, II, III, and IV (roman numerals for 1, 2, 3, and 4). They start at the top right corner and continue counter-clockwise around the graph. Quadrant I is a positive quadrant, Quadrant III is a negative quadrant, and Quadrants II and IV have both positive and negative numbers. Points on the graph are found in these four quadrants. The points are written as (x, y) and can be found by tracing up and down along the number values on the graphs until the two lines meet. The place where the lines meet is your point.
Tags: algebra, arithmetic, axis, cartesian, coordinate, graphing, graphs, Math, origin, plane, quadrants, x-axis, y-axis
Posted in Arithmetic | No Comments »
