Posts Tagged ‘measure’
Friday, December 18th, 2009
How to Define Cardinal Numbers
Description
A detailed tutorial on the definition of cardinal numbers. Step by step tutorial including several examples of how to define cardinal numbers for reference.
Overview
Cardinal numbers are natural numbers that are used to measure cardinality of sets. Cardinality is a fancy way of saying the size of a set. This means the cardinality is the number of elements in a set, provided that the set is finite. If the set is infinite, something called a transfinite cardinal number is used to describe the cardinality of the set. Cardinal numbers are a very important part of set theory, even though they are not studied often or used constantly.
Tags: abstract, algebra, analysis, cardinal, cardinality, combinatorics, elements, finite, infinite, mathematical, measure, natural, number, set, set theory, size, transfinite
Posted in Algebra | No Comments »
Friday, November 20th, 2009
Interior Angles of Polygons
Description
A detailed tutorial on interior angles of polygons. Step by step tutorial including several examples of interior angles of polygons for reference.
Overview
There are two types of angles on a polygon: interior and exterior angles. In this tutorial, we will focus on interior angles. Interior angles are the angles that are found along the inside of the polygon. Interior angles may seem more difficult to find than exterior angles, because they don’t always add up to the same measurement of degrees. However, there is a formula that can be used to find the total measure of the interior angles. This formula is (n – 2) * 180 = D, where n is the number of sides on the polygon, and D is the total measure of the degrees.
Tags: 180, angle, concave, convex, degrees, formula, Geometry, Inside, interior, irregular, measure, negative, polygon, positive, regular
Posted in Geometry | No Comments »
Friday, November 20th, 2009
Exterior Angles of Polygons
Description
A detailed tutorial on exterior angles of polygons. Step by step tutorial including several examples of exterior angles of polygons for reference.
Overview
There are two types of angles on a polygon: interior and exterior angles. In this tutorial, we will focus on exterior angles. Exterior angles are the angles that are found when you draw a line of an angle on the outside of the polygon to form another angle. On a regular polygon, all the exterior angles should have the same measure. No matter what kind of polygon you have, the exterior angles will always add up to 360 degrees. Concave polygons are harder to find the measure of, because the exterior angles are negative, but they should still add up to 360 degrees. In order to find the measure of each individual exterior angle, simply use the formula 360 / n = D, where n is the number of sides, and D is the degree of each of the angles seperately. However, this formula only works for regular polygons, not irregular polygons.
Tags: 360, angle, concave, convex, degrees, exterior, formula, Geometry, irregular, measure, negative, Outside, polygon, positive, regular
Posted in Geometry | No Comments »
Friday, November 13th, 2009
Introduction to Aspect Ratio
Description
A detailed tutorial on what aspect ratio is. Step by step tutorial including several examples of how to find the aspect ratio for reference.
Overview
The aspect ratio can only be used when referring to a shape, typically a square type of shape, such as a square, rhombus, rectangle, or parallelogram. The aspect ratio is used very often for describing measurements. It is the ratio of the longer dimension to the shorter dimension – that is, the length to the width. In a 3D shape, the depth – which is the second measurement of width – is added to the end of this measurement.
Tags: 2D, 3D, aspect, depth, Geometry, length, measure, measurement, parallelogram, ratio, rectangle, rhombus, shape, square, width
Posted in Geometry | No Comments »
Thursday, November 12th, 2009
How to Identify Pythagorean Triples
Description
A detailed tutorial on Pythagorean triples. Step by step tutorial including several examples of Pythagorean triples for reference.
Overview
A Pythagorean triple is a set of three numbers that make up a right triangle. They are the measure of the sides, not the measure of the angles. This you should know by looking at the name. The Pythagorean theorem deals with only the sides of the right triangle, so Pythagorean triples should also only deal with the sides of a right triangle. All the numbers must be integers, and they must be positive. They are written rather like coordinates are, in a (a, b, c) pattern. A common example is is (3, 4, 5). From any triple, any other triple can be found. If (a, b, c) is a triple, then (ka, kb, kc) also must be a triple, according to the rule of similar triangles.
Tags: angles, Geometry, integer, measure, multiple, number, positive, pythagorean, right, sides, similar, theorem, three, triangle, triples
Posted in Geometry | No Comments »
Thursday, November 12th, 2009
How to Find an Angle Bisector
Description
A detailed tutorial on how to find an angle bisector. Step by step tutorial including several examples on how to find angle bisectors for reference.
Overview
The bisector of an angle is the straight line or line segment that runs right down the center of the angle, splitting in into two rays and creating two angles, that are each half of the measure of the original angle. The bisector is always on the interior of an angle, and because of this it is sometimes called the internal angle bisector. Bisectors can be used with many things, but it is most common to find them used with angles, which is why other bisectors are simply called bisectors, while these are given the name of angle bisectors.
Tags: angle, bisector, center, Geometry, half, interior, internal, line, measure, original, ray, segment
Posted in Geometry | No Comments »
Thursday, November 5th, 2009
Overview of Mass-Energy Equivalence
Description
A detailed tutorial on mass-energy equivalence. Step by step tutorial including several examples of mass-energy equivalence for reference.
Overview
Mass-energy equivalence is the concept that the mass of a body is the measure of its energy content. This is often expressed by a formula written by Einstein, who is also the one that proposed the idea of mass-energy equivalence. This formula is 
, where E is energy, m is the mass, and c is the speed of light in a vacuum.
Tags: Albert, body, c, content, differential equations, E, Einstein, energy, equivalence, equivalent, formula, idea, light, m, mass, measure, speed, vacuum
Posted in Differential Equations | No Comments »
Tuesday, September 29th, 2009
An Overview of Eccentricity
Description
A detailed tutorial on eccentricity. Step by step tutorial including sample problems and a visual representation of eccentricity for reference.
Overview
Eccentricity is a parameter associated with every conic section. Another way to think of it is as a measure of how much the conic section deviates from being circular. Each shape has a different eccentricity. The eccentricity of a circle is zero – because it does not deviate at all from being circular. The eccentricity of an ellipse that is not a circle is less than one but greater than zero, because it is almost a circle. The eccentricity of a parabola is one, and the eccentricity of a hyperbola is greater than one. Eccentricity plays an important part in calculations because two conic sections are only similar if they have the same eccentricity.
Tags: algebra, circle, circular, cones, conic section, eccentricity, ellipse, hyperbola, Math, measure, parabola, similar
Posted in Geometry | No Comments »
Tuesday, September 15th, 2009
An Overview of the Different Types of Triangles
Description
A detailed tutorial on the different types of triangles. Step by step tutorial including several examples of the different types of triangles for reference. Knowledge of the different types of triangles is required for all geometry classes.
Overview
Everyone knows what a triangle is, but a triangle is more than just “a triangle” – it could be one of several different types of triangles. Different types of triangles are identified by the different traits of their sides and their angles. The types are as follows:
Scalene Triangles: All sides and all angles are of different measures and lengths.
Right Triangles: One angle of the triangle is 90 degrees.
Isosceles Triangles: 2 sides and 2 angles have the same measures and lengths.
Equilateral Triangles: All side lengths are the same and all angles are 60 degrees.
Equiangular Triangles: All angles measure 60 degrees but all sides could have different lengths.
Tags: 60, 90, angle, degrees, equal, equiangular, equilateral, Geometry, isosceles, length, Math, measure, right, scalene, side, triangle
Posted in Geometry | No Comments »
