Posts Tagged ‘area’
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
Overview of Half-Circles
Description
A detailed tutorial on equations of a half-circle. Step by step tutorial including several examples and an explanation of half-circles for reference.
Overview
A half-circle is truely half of a circle. If you take a circle and cut it in half, you will get a half circle. Because of this, the equations of the half-circle are very similar to the equations of a full circle – simply divide the equation by two. The only ones that you cannot find that way are the radius, diameter, and circumference. The radius and diameter do not change on a half-circle. There is no circumference on the half-circle, but if you need the circumference for another formula you can use the circumference of the whole circle of that half-circle.
Tags: area, basic, circle, circumference, coordinates, cut, diameter, divide, equation, Geometry, half, half-circle, pi, radius, shape, split, two, whole
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
An Overview of Area Models
Description
A detailed tutorial on how to use area models. Step by step tutorial including several examples of how to use area models for reference.
Overview
An area model is used to help mutliply and divide integers. It is called an area model because of the way it is set up – it looks like you are solving for area when the model is used correctly. These models are typically composed of many small one by one squares, although different sizes can be used in order to make mulitplication and division earlier. Area models are used to provide a visual representation of the multiplication and division algorithms.
Tags: algorithms, area, arithmetic, division, integers, manipulatives, model, multiplication, rectangle, representation, square, visual
Posted in Arithmetic | No Comments »
Tuesday, September 29th, 2009
Introduction to Magnitude
Description
A detailed tutorial of how to solve for magnitude. Step by step tutorial including several examples of how to solve for magnitude for reference.
Overview
The magnitude refers to size – in mathematical concepts, what is larger? What has a greater value or quantity? This is what you look for when arranging things in order of magnitude. Several different measurements are considered to be types of magnitude – examples are volume, area, and length. Things that can be ordered by magnitude are fractions, line segments, planes, solids, and angles. Magnitude is considered to be measured only in positive, not in negative – not to say that the absolute value is taken, just that negative numbers are not included.
Tags: angles, area, arithmetic, fractions, greater, length, line segments, magnitude, Math, measurement, planes, positive, solids, value, volume
Posted in Arithmetic | No Comments »
Friday, September 25th, 2009
Using Simpson’s Rule to Solve Error Bounds
Description
A detailed tutorial on using Simpson’s rule and solving error bounds. Step by step tutorial including examples of solving error bounds using Simpson’s rule for reference.
Overview
Simpson’s rule is a rule in calculus that is used to solve error bounds. It is the more complicated form of both the trapezoidal rule and the midpoint rule, both of which are also used to calculate error bounds. Although this rule is harder to use than either one of those, it is more accurate. The Simpson’s rule does not use anything except for numbers to calculate the space under a graph, and is expressed by this formula:
![\int_{a}^{b} f(x) \, dx \approx \frac{b-a}{6}\left[f(a) + 4f\left(\frac{a+b}{2}\right)+f(b)\right]](http://s.wordpress.com/latex.php?latex=%20%5Cint_%7Ba%7D%5E%7Bb%7D%20f%28x%29%20%5C%2C%20dx%20%5Capprox%20%5Cfrac%7Bb-a%7D%7B6%7D%5Cleft%5Bf%28a%29%20%2B%204f%5Cleft%28%5Cfrac%7Ba%2Bb%7D%7B2%7D%5Cright%29%2Bf%28b%29%5Cright%5D&bg=ffffff&fg=000000&s=0 "\int_{a}^{b} f(x) \, dx \approx \frac{b-a}{6}\left[f(a) + 4f\left(\frac{a+b}{2}\right)+f(b)\right]")
Tags: accurate, area, calculate, Calculus, error bounds, formula, function, graph, Math, midpoint, Simpson's rule, trapezoidal
Posted in Calculus | No Comments »
Friday, September 25th, 2009
Using the Midpoint Rule to Solve Error Bounds
Description
A detailed tutorial on using the midpoint rule and solving error bounds. Step by step tutorial including examples of solving error bounds using the midpoint rule for reference.
Overview
The midpoint rule, also known as the rectangle method, is the easiest way of solving error bounds. The region under the graph of a function is sectioned off into rectangles of equal width. You then must find the areas of these rectangles. Then all the areas are added together to find the approximation of the integral. The formula for this is:
The least complicated form of the midpoint rule is expressed as:
Tags: addition, approximation, area, Calculus, definite integral, error bounds, formula, function, graph, Math, mid-ordinate rule, midpoint rule, rectangle, rectangle method, sum, width
Posted in Calculus | No Comments »
Tuesday, September 15th, 2009
How to Use Heron’s Formula
Description
A detailed tutorial on the solving of the area of a triangle using Heron’s Formula. Step by step tutorial including several examples of how to solve for the area of a triangle using Heron’s Formula for reference.
Overview
Heron’s formula is kind of like the Pythagorean theorem for triangles that are not right triangles – although it could also be used with right triangles. However, Heron’s Formula helps you solve for the area, and something called a “semi-perimeter.” Heron’s formula states that:
s = (a + b + c) / 2
Where a, b, and c represent the sides of the triangle and s stands for the semi-perimeter. Once you have the semi-perimeter, you can solve for area using this formula:
A = sqrt[s * (s - a) * (s - b) * (s - c)]
Tags: area, Heron's Formula, Math, precalculus, semi-perimeter, sides, triangle, trigonometry
Posted in Trigonometry | No Comments »
Tuesday, September 8th, 2009
How to Find the Surface Area of a Cone
Description
This video gives a clear example on how to solve for the surface area of a cone. The formula is explained and a sample problem is solved in the video.
Overview
The surface area is the area of each side, or face, of the shape added together. Cones are a very tricky shape to calculate the surface area of, because there is something called a “slant height” that needs to be used. The formula for the surface area of a cone is:
SA = B + pi * r * l
B is the area of a base. The base of a cone is always a circle. r is the radius of the circle – the base. l is the slant height. Sometimes you are given the slant height, but not always. If the slant height is not given to you then you can use this formula to find it:
l = sqrt(r^2 + h^2)
h represents the regular height of the cone, as opposed to the slant height. This is actually the pythagorean theorem – you can form a right triangle with it if you draw a picture.
Tags: area, circle, cone, formula, Geometry, Math, surface, surface area
Posted in Geometry | No Comments »
