Posts Tagged ‘cartesian’
Thursday, November 19th, 2009
The X and Y Axis on a Cartesian Graph
Description
A detailed tutorial of the x axis and the y axis. Step by step tutorial including several examples of the x axis and the y axis for reference.
Overview
The the Cartesian coordinate system, there is an x axis and a y axis. The x axis runs horizontally across the system and all first terms in ordered pairs are x coordinates, from the x axis. The y axis runs vertically across the system and all second terms in ordered pairs are y coordinates, from the y axis. The x and y axis work together to use a pattern of right angles and perpendicular lines in order to find ordered pairs and coordinates of x and y on the graph.
Tags: algebra, angle, axis, basic, cartesian, coordinate, graphing, graphs, horizontal, lines, ordered, pairs, perpendicular, right, system, vertical, x, y
Posted in Algebra | No Comments »
Tuesday, October 27th, 2009
The Range of Relations
Description
A detailed tutorial on the range of relations. Step by step tutorial including several examples of the range of relations for reference.
Overview
The range of a relation is denoted as Rng(R) and looks like a normal set. For each ordered pair in a relation, there are two endpoints, x and y. The range is the set of all the y endpoints – that is to say, all the endpoints that come second in the ordered pair. If you are taking the range of the inverse of a relation, then that would be all the x endpoints. When writing the range, the notation used is just the normal notation, not the ordered pair notation.
Tags: cartesian, coordinates, discrete math, element, endpoint, ordered pair, range, relations, second, set, subset
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
The Domain of Relations
Description
A detailed tutorial on the domain of relations. Step by step tutorial including several examples of the domain of relations for reference.
Overview
The domain of a relation is denoted as Dom(R) and looks like a normal set. For each ordered pair in a relation, there are two endpoints, x and y. The domain is the set of all x endpoints – that is to say, all the endpoints that come first in the ordered pair. If you are taking the domain of the inverse of a relation, then that would be all the y endpoints. When writing the domain, the notation used is just the normal notation, not the ordered pair notation.
Tags: cartesian, coordinates, discrete math, domain, element, endpoint, First, ordered pair, relations, set, subset
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
The Inverse of Relations
Description
A detailed tutorial on the inverse of relations. Step by step tutorial including several examples of the inverse of relations for reference.
Overview
Inverse is a term you should be familiar with. An inverse operation is one that undoes the original operation. But what is an inverse relation? When you take the inverse of a relation, you are switching the endpoints in every ordered pair in the original relation. For each ordered pair in the relation, instead of being written as (x, y) it will now be written as (y, x).
Tags: cartesian, coordinates, discrete math, endpoint, inverse, operation, ordered pair, relations, x, y
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
An Introduction to Relations
Description
A detailed tutorial on the introduction to relations. Step by step tutorial including several examples of the introduction to relations for reference.
Overview
A relation is defined as an ordered pair. However, that is not entirely accurate. A relation could either be an ordered pair or a set of ordered pairs. A relation can be used with either one or more normal sets, or one Cartesian product set. When used with a normal set, it is a set of ordered pairs. When used with a Cartesian product, it is the power set of that set.
Tags: cartesian, coordinates, discrete math, element, ordered pair, power, product, relation, set, subset, theory
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
Cartesian Products in Set Theory
Description
A detailed tutorial of Cartesian products in set theory. Step by step tutorial including several examples of Cartesian products in set theory for reference.
Overview
A Cartesian product is an operation that can be performed in set theory. It is named not for the multiplication that occurs, but for the way the resulting set is written: it is written in ordered pairs, just like Cartesian coordinates. Two sets are said to be multiplied, such as A and B. Whichever set is written first in the operation has its first coordinate written with the second coordinate of the second set. This continues until all coordinates have been used at least once.
Tags: cartesian, coordinates, discrete math, element, multiplication, operation, ordered pair, product, set, subset, theory
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
How to Find the Component of a Vector
Description
A detailed tutorial on finding the component of a vector. Step by step tutorial including several examples of how to find the component of a vector for reference.
Overview
There are three different kinds of components that can be found in vectors: axial components, radial components, and tangential components. Just like the vectors themselves, different types of components are found in different coordinate systems. Axial components are found in the Cartesian coordinate system, while radial and tangential components are found in the polar coordinate system. A component is exactly the same as it’s dictionary definition: it is just a small part that makes up a whole, so in this case they are small parts of a vector. The vector itself is also a component.
Tags: algebra, axial, cartesian, component, coordinate, polar, radial, system, tangential, vector
Posted in Algebra | No Comments »
Tuesday, October 27th, 2009
Overview of Euclidean Vectors
Description
A detailed tutorial on Euclidean vectors. Step by step tutorial including several examples and visual examples of Euclidean vectors for reference.
Overview
A vector is a geometric object that has both a magnitude (also known as the length) and a direction. They are usually drawn as arrows that have a similar starting point and connect two points together. The difference between different kinds of vectors is what coordinate system is used to describe them. Euclidean vectors are vectors that are described by the Cartesian coordinate system.
Tags: algebra, arrow, cartesian, coordinate, direction, Euclidean, geometric, graph, initial, length, magnitude, point, system, terminal, vector
Posted in Algebra | No Comments »
Tuesday, October 13th, 2009
How to Locate the Origin of a Graph
Description
A detailed tutorial on locating the origin of a graph. Step by step tutorial including several examples of how to locate the origin for reference.
Overview
The origin in mathematical terms means the center. Typically, the term origin is used with a graph in the Cartesian coordinate system. When on a graph, the origin is found at the point (0, 0), where the x-axis and y-axis intersect. Other common things to hear an origin being attributed to are geometrical shapes, most often a circle.
Tags: arithmetic, axis, cartesian, center, circle, coordinate, geometrical, graph, intersect, Math, middle, origin, shape, x, y
Posted in Arithmetic | No Comments »
Friday, October 9th, 2009
Witch of Agnesi Explained
Description
A detailed tutorial of the Witch of Agnesi. Step by step tutorial including a visual example of the Witch of Agnesi for reference.
Overview
The Witch of Agnesi is actually a curve. This curve can be a circle, or it can be a regular curve. The movement of the curve flows up and down, and the curve itself changes as it moves. This curve is defined by the Cartesian equation 
.
It is called the Witch of Agnesi by a simple mistranslation into English. This curve was named in Italian – la versiera di Agnesi, which means the Curve of Agnesi. When translating the name, “la versiera” was accidentally read as “l’awersiera”, which means a woman who is contrary to God, or a demon or witch. Hence it was called the Witch of Agnesi.
Tags: Calculus, cartesian, circle, curve, equation, l'awersiera di Agnesi, la versiera di Agnesi, Maria Agnesi, Math, Witch of Agnesi, Witch of Maria Agnesi
Posted in Calculus | No Comments »
