Posts Tagged ‘curve’
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 »
Thursday, November 12th, 2009
How to Draw Best-Fitting Lines
Description
A detailed tutorial on how to draw best-fitting lines. Step by step tutorial including several examples on how to draw best-fitting lines for reference.
Overview
Best-fitting lines are lines that are drawn on a graph or on scatter plots. However, a best-fitting line is different than a normal line found on a graph. A normal graph simply requires you to connect the dots. A best fitting line focuses not on what dots to connect, but how to connect them. The line will curve or go in different directions, not just straight to the other line, depending on the relationship of the two dots to each other. Best-fitting lines typically require more information than simply the graph, you must explore the equation and each point to find the true relationships, and from that you can find the best-fitting line.
Tags: algebra, best, best-fitting, connect, coordinate, curve, direction, dots, equation, fitting, graph, line, plot, points, relationship, scatter, straight
Posted in Algebra | No Comments »
Tuesday, November 10th, 2009
Identifying Convex Polygons
Description
A detailed tutorial on identifying convex polygons. Step by step tutorial including several examples of how to identify convex polygons for reference.
Overview
Convex polygons are polygons that seem to curve inwards. They may appear rather big compared to concave polygons. The best way to identify a convex polygon is to check for a reflex angle. A reflex angle looks like an obtuse angle, or an arrow cutting into the figure. Concave polygons have reflex angles, convex polygons don’t. All regular polygons are considered convex polygons.
Tags: angle, big, convex, curve, Geometry, obtuse, out, polygon, reflex, regular
Posted in Geometry | No Comments »
Tuesday, November 10th, 2009
Identifying Concave Polygons
Description
A detailed tutorial on identifying concave polygons. Step by step tutorial including several examples of how to identify concave polygons for reference.
Overview
Concave polygons are polygons that seem to curve inwards. They may appear rather small compared to convex polygons. The best way to identify a concave polygon is to check for a reflex angle. A reflex angle looks like an obtuse angle, or an arrow cutting into the figure. Concave polygons have reflex angles, convex polygons don’t.
Tags: angle, arrow, concave, curve, Geometry, in, obtuse, polygon, reflex, small
Posted in Geometry | No Comments »
Thursday, October 22nd, 2009
How to Identify a Concave Function
Description
A detailed tutorial on concave functions. Step by step tutorial including several examples of concave functions and concave down curves for reference.
Overview
When a function forms the graph of a curve, there are two types of functions it could be: a convex function, or a concave function. In this tutorial, we will discuss concave functions. A concave function is one with the endpoints facing down, forming the shape of an upside down bowl. When looking at the graph of a concave function, we say that it is concave down. Concavity can be found by the second derivative test in calculus.
Tags: Calculus, concave, concavity, convex, curve, derivative, down, endpoint, equation, function, graph, interval, second, test, up
Posted in Calculus | No Comments »
Thursday, October 22nd, 2009
How to Identify a Convex Function
Description
A detailed tutorial on convex functions. Step by step tutorial including several examples of convex functions and concave up curves for reference.
Overview
When a function forms the graph of a curve, there are two types of functions it could be: a convex function, or a concave function. In this tutorial, we will discuss convex functions. A convex function is one with the endpoints facing up, forming the shape of a bowl. When looking at the graph of a convex function, we say that it is concave up. Concavity can be found by the second derivative test in calculus.
Tags: Calculus, concave, concavity, convex, curve, derivative, down, endpoint, equation, function, graph, interval, second, test, up
Posted in Calculus | No Comments »
Thursday, October 22nd, 2009
How to Find Nonlinear Asymptotes
Description
A detailed tutorial on finding nonlinear asymptotes. Step by step tutorial including several examples of how to find nonlinear asymptotes for reference.
Overview
An asymptote is used to describe the behavior of a curve as it heads away from the origin and towards infinity. Typically it is meant to describe two curves that are doing this, and these curves are said to be asymptotic. In most cases, the asymptote is linear – which means the curves have the same behavior. Whenever someone is talking about an asymptote, they are talking about a linear asymptote unless they specify a different type of asymptote. In rare cases, asymptotes are nonlinear. Both curves are still heading towards infinity, but they do not have the same behavior. This can be determined by the limit of either the subtraction or the division of these curves.
Tags: algebra, asymptote, asymptotic, behavior, curve, division, function, horizontal, infinity, limit, linear, nonlinear, oblique, origin, subtraction, vertical
Posted in Algebra | No Comments »
Thursday, October 15th, 2009
How to Find the Directrix of a Parabola
Description
A detailed tutorial on how to find the directrix of a parabola. Step by step tutorial including several examples of how to find the directrix of a parabola for reference.
Overview
A parabola is a curved shape that is formed by the graph of the function x squared. A parabola is technically known as the locus of points where the distance to the focus equals the distance to the directrix. The directrix is a given line on a parabola that does not go through the focus.
Tags: algebra, curve, directrix, focus, function, graph, line, locus, Math, parabola, points, squared, x
Posted in Algebra | 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 »
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 »
