Posts Tagged ‘concave’
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 »
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 8th, 2009
Introduction to Inflection Points
Description
A detailed tutorial on inflection points. Step by step tutorial including several examples of inflection points and how to locate inflection points for reference.
Overview
An inflection point, sometimes also known as a point of inflection, is a point on the graph of a function at which the function changes sign. This means that a concave up curve will become a concave down curve, or a concave down curve will become a concave up curve. Inflection points are also points of local maxima and local minima of a function. There are two ways to categorize inflection points. There are stationary points of inflection, and non-stationary points of inflection. Stationary points are formed when the function is zero, and non-stationary points are when the function is not zero.
Tags: Calculus, concave, curve, down, function, inflection, inflexion, local, Math, maxima, minima, non-stationary, point, saddle-point, sign, stationary, up
Posted in Calculus | 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 »
