Posts Tagged ‘figure’
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
How to Find Slant Height
Description
A detailed tutorial on how to find the slant height. Step by step tutorial including several examples of how to find the slant height for reference.
Overview
The slant height is an additional measure of height that is used for the different types of triangular prisms. The common traingular prisms are your typical pyramid, and cones. On a pyramid, the slant height is the height of one of the triangular faces. On a cone, the slant height is to be found using a formula that is only for the cone. It is the square root of the radius squared added to the real height squared.
Tags: 3D, base, cone, face, figure, geometrical, Geometry, height, polyhedron, prism, pyramid, shape, side, slant, triangle, triangular
Posted in Geometry | No Comments »
Tuesday, November 17th, 2009
Overview of Sides and Bases of Polyhedrons
Description
A detailed tutorial on sides and bases of polyhedrons. Step by step tutorial including several examples of sides and bases of polyhedrons for reference.
Overview
Sides and bases of polyhedrons are more commonly known as faces of 3D geometrical shapes. Typically on a polyhedron you will have 2 bases and several sides, although there are exceptions to that rule. The cylinder only has one side, and the triangular prism, or pyramid, only has one base. You can identify the base because it is a unique shape on the polyhedron. Everything else is a side. This only applied to your normal polyhedron shapes such as prisms.
Tags: 3D, bases, cylinder, faces, figure, geometrical, Geometry, polyhedron, prism, rectangular, regular, shape, sides, triangular, unique
Posted in Geometry | No Comments »
Friday, November 13th, 2009
An Overview of Composite Solids
Description
A detailed tutorial on what a composite solid is. Step by step tutorial including several examples of composite solids for reference.
Overview
A composite solid is exactly the same as a composite figure, only it is in 3D instead of in 2D. It is any kind of polyhedron (like a prism or a pyramid) that can be split into two or more of the basic types of polyhedrons in order to solve for the volume of the figure. Composite solids are very rare, and there are no regular types of solids that would be considered a composite solid.
Tags: 2D, 3D, area, basic, composite, difference, dimension, figure, Geometry, polyhedron, prism, pyramid, rare, solid, split, types, volume
Posted in Geometry | No Comments »
Friday, November 13th, 2009
An Overview of Composite Figures
Description
A detailed tutorial on what composite figures are. Step by step tutorial including several examples of how to identify composite figures for reference.
Overview
A composite figure is any figure that can be split into more than one shape. Hardly any regular shapes are considered to be composite shapes. The only one is a regular trapezoid – it can be split into three shapes, two triangles and a rectangle. You could technically consider a rectangle to be a composite figure – you can split it into squares or smaller rectangles – but since it doesn’t need to be split into different shapes to solve for area, then it is not considered a composite figure.
Tags: 2D, area, composite, different, figure, flat, geometrical, Geometry, rectangle, regular, shape, smaller, split, square, trapezoid, triangle, volume
Posted in Geometry | No Comments »
Friday, November 13th, 2009
Overview of Polyhedrons
Description
A detailed tutorial on polyhedrons. Step by step tutorial including several examples and a visual example of polyhedrons for reference.
Overview
Mathematicians have not yet decided what truely makes something a polyhedron, but in general they are accepted to be some 3D geometrical figure that has sides or faces, and usually at least one base. There are regular polyhedrons, which have all the same polygon making up their faces, and irregular polyhedrons – which are actually more common – where there are 2 or more shapes in them.
Tags: base, common, decagon, face, figure, geometrical, Geometry, hexagon, irregular, pentagon, polygon, polyhedron, regular, shape, side, square, triangle
Posted in Geometry | No Comments »
Thursday, October 29th, 2009
Definition of a Terminal Point
Description
A detailed tutorial on the definition of a terminal point. Step by step tutorial including several examples of terminal points for reference.
Overview
A terminal point is just a way of saying the ending point. The terminal point of a line or a figure is the point where it ends. The term terminal point is used often when talking about vectors – they end at the terminal point. The terminal point is referred as the head of the vector.
Tags: arithmetic, arrow, direct, ending, figure, head, initial, line, point, ray, segment, starting, tail, terminal, vector
Posted in Arithmetic | No Comments »
Thursday, October 29th, 2009
Definition of an Initial Point
Description
A detailed tutorial on the definition of an initial point. Step by step tutorial including several examples of initial points for reference.
Overview
An initial point is just a way of saying the starting point. The initial point of a line or a figure is the point where it begin. The term initial point is used often when talking about vectors – they start at the initial point. The initial point is referred as the tail of the vector.
Tags: arithmetic, arrow, direct, ending, figure, head, initial, line, point, ray, segment, starting, tail, terminal, vector
Posted in Arithmetic | No Comments »
Tuesday, October 27th, 2009
Definition of a Scalar Triple Product
Description
A detailed tutorial on scalar triple products. Step by step tutorial including several examples of scalar triple products for reference.
Overview
A scalar triple product is a way of applying other multiplication operators to three vectors. Quite often, the scalar triple product is denoted as (a, b, c). It can also be defined as (a b c) = a(b x c). The scalar triple product has three main properties. The first one is that the absolute value of the scalar triple product is the volume of the three dimensional figure that is formed by the three vectors. The second one is the scalar triple product is only zero if the three vectors are linearly independent. The three vectors must lie in the same plane for this to be true. The third one is that the scalar triple product is only positive if all three of the vectors are considered right-handed.
A simple way to write the scalar triple product is to line up the coordinates of the vectors in this form: 
This is the same as saying 
Tags: absolute, algebra, box, coordinates, figure, independent, linear, mixed, multiplication, operator, parallelpiped, positive, product, properties, right-handed, scalar, three-dimensional, triple, value, zero
Posted in Algebra | No Comments »
Friday, October 9th, 2009
Lissajous Curve Explained
Description
A detailed tutorial of a lissajous curve. Step by step tutorial including several visual examples of lissajous curves for reference.
Overview
A Lissajous curve represents the graph of a system of parametric equations, which can be mathematically expressed as 
. This also decribes complex harmonic motion. The way that the figure appears is very sensitive to the ratio a / b, so the figure can appear in many different forms.
Tags: Bowditch, Calculus, complex, curve, equation, figure, form, graph, harmonic, Lissajous, Math, motion, paramentric, ratio, system
Posted in Calculus | No Comments »
