Posts Tagged ‘ratio’
Thursday, November 19th, 2009
How to Find the Common Ratio of a Geometric Series
Description
A detailed tutorial on how to find the common ratio of a geometric series. Step by step tutorial including several examples of the common ratio for reference.
Overview
The common ratio is part of a geometric series, used commonly in calculus. The common ratio is the ratio of each term to the next – in other words, the common ratio is the pattern that the series or sequence follows. This is possible because in a geometric series, terms are only being multiplied by one number to get the next number, and it is always the same number. If a series is not geometric, it will not have a common ratio.
Tags: Calculus, common, geometric, multiplication, multiply, number, pattern, ratio, sequence, series, term
Posted in Calculus | No Comments »
Friday, November 13th, 2009
Introduction to Aspect Ratio
Description
A detailed tutorial on what aspect ratio is. Step by step tutorial including several examples of how to find the aspect ratio for reference.
Overview
The aspect ratio can only be used when referring to a shape, typically a square type of shape, such as a square, rhombus, rectangle, or parallelogram. The aspect ratio is used very often for describing measurements. It is the ratio of the longer dimension to the shorter dimension – that is, the length to the width. In a 3D shape, the depth – which is the second measurement of width – is added to the end of this measurement.
Tags: 2D, 3D, aspect, depth, Geometry, length, measure, measurement, parallelogram, ratio, rectangle, rhombus, shape, square, width
Posted in Geometry | 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 »
Tuesday, October 6th, 2009
How to Test for Convergence Using the Geometric Series Test
Description
A detailed tutorial on how to test for convergence using the geometric series test. Step by step tutorial including several examples of testing for convergence using the geometric series test for reference.
Overview
A geometric series is a series that maintains a constant ratio between a set of terms. This series is an addition series, and would be expressed as 1/a + 1/2a + 1/4a, extending as far as you wish in either direction. If a series does not have that constant ratio, then it is not a geometric series. The series should converge at one, because as all the numbers are added they get closer and closer to one. The first term of a geometric series is given by a, and the ratio of a geometric series is given by r. If the ratio is less than one, then the geometric series converges to a / (1 – r). If the ratio is greater than or equal to one, then the series diverges. Usually the series will converge, which is why this is considered a test for convergence and not for divergence.
Tags: a, addition, Calculus, converge, convergence, diverge, divergence, equal to, first term, geometric, greater than, less than, Math, notation, r, ratio, series, summation, test
Posted in Calculus | No Comments »
Thursday, October 1st, 2009
Identifying the Radicand
Description
A detailed tutorial on identifying the radicand. Step by step tutorial including several examples of how to identify the radicand for reference.
Overview
The radicand is associated with what we know as a square root. However, there is a common misconception that a radicand and a square root are the same thing, and they are not. A square root is the entire number – the square root symbol, the number inside, and whatever number it equals. A radicand is simply the number that is inside the square root symbol. For example, take the expression ![\scriptstyle \sqrt[n]{ab+2}](http://s.wordpress.com/latex.php?latex=%5Cscriptstyle%20%5Csqrt%5Bn%5D%7Bab%2B2%7D&bg=ffffff&fg=000000&s=0 "\scriptstyle \sqrt[n]{ab+2}")
. In this expression, the radicand is ab + 2, because that is what we are taking the square root of.
Tags: algebra, exponent, integer, Math, number, perfect square, radicand, ratio, real number, square, square root, symbol
Posted in Algebra | No Comments »
Friday, September 25th, 2009
An Introduction to the Golden Ratio
Description
A detailed tutorial on the golden ratio. Step by step tutorial including several examples of the golden ratio for reference.
Overview
The golden ratio is a ratio in mathematics and the arts that is closely related to the Fibonacci numbers. It is said that two quantities are in the g0lden ratio if the ratio of the sum of the quantities to the larger number equals the ratio of the larger number to the smaller number. The algebraic expression of this is:
This equation has a unique solution, which is:
Tags: algebra, divine proportion, divine section, extreme and mean ratio, golden, golden cut, golden mean, golden number, golden proportion, golden ratio, golden section, Math, mean of Phidias, medial section, proportion, ratio
Posted in Algebra | No Comments »
Friday, September 18th, 2009
Introduction to Irrational Numbers
Description
A detailed tutorial on the definition of an irrational number. Step by step tutorial including several examples of irrational numbers for reference.
Overview
An irrational number is a number that cannot be written as the ratio of 2 integers. However, this does not mean they have no place on a number line. One of the most famous irrational numbers is pi, which is approximately equal to 3.14 – however, this is just a simplified version of the actual number. Another famous irrational number is the square root of 2. This is equal to around 1.41. Both irrational numbers and rational numbers are real numbers, which include all integers.
Tags: arithmetic, imaginary, integers, irrational, Math, natural, number, numbers, pi, ratio, rational, real, sqrt(2), square root
Posted in Arithmetic | No Comments »
