Posts Tagged ‘algorithm’
Friday, October 30th, 2009
Introduction to the Euclidean Algorithm
Description
A detailed tutorial on the Euclidean algorithm. Step by step tutorial including several examples of the Euclidean algorithm for reference.
Overview
The Euclidean algorithm, sometimes referred to as Euclid’s algorithm, is the most efficient way of determining the greatest common factor of two numbers. The greatest common factor of two numbers is the largest number that divides them both evenly. The Euclidean algorithm is used in a series of steps – it follows a pattern that helps to find numbers and their factors with accuracy.
Tags: algebra, algorithm, common, divides, divisor, Euclid, Euclidean, evenly, factor, greatest, highest, negative, pattern, positive, remainder, steps
Posted in Algebra | No Comments »
Friday, October 2nd, 2009
Overview of Polynomial Long Division
Description
A detailed tutorial on polynomial long division. Step by step tutorial including several examples of polynomial long division for reference.
Overview
Polynomial long division is a mix of regular long division and rules of polynomials – it looks confusing at first, but isn’t too difficult to follow. Polynomial long division is actually a type of algorithm. It is only used when dividing a polynomial by another polynomial of either the same or a lower degree. The “degree” of a polynomial is the highest power in the polynomial, and the terms in the polynomial should be ordered from highest degree to lowest degree. When using polynomial long division, you must write out all coefficients and terms, even “invisible” ones – ones that have a coefficient of zero and so are typically not written in the polynomial. Polynomial long division is solved the same way as regular long division
Tags: algebra, algorithm, coefficient, degree, division, long division, Math, polynomial, polynomial long division, synthetic division, term, value, zero
Posted in Algebra | No Comments »
Thursday, October 1st, 2009
An Overview of Bézier Curves
Description
A detailed tutorial on Bézier curves. Step by step tutorial including several examples of when and how to use Bézier curves for reference.
Overview
A Bézier curve is any parametric curve. They are extremely important in animation and computer graphic. Bézier curves can be linear, quadratic, and cubic. When Bézier curves are linear, they are expressed by the equation ![\mathbf{B}(t)=\mathbf{P}_0 + t(\mathbf{P}_1-\mathbf{P}_0)=(1-t)\mathbf{P}_0 + t\mathbf{P}_1 \mbox{ , } t \in [0,1]](http://s.wordpress.com/latex.php?latex=%5Cmathbf%7BB%7D%28t%29%3D%5Cmathbf%7BP%7D_0%20%2B%20t%28%5Cmathbf%7BP%7D_1-%5Cmathbf%7BP%7D_0%29%3D%281-t%29%5Cmathbf%7BP%7D_0%20%2B%20t%5Cmathbf%7BP%7D_1%20%5Cmbox%7B%20%2C%20%7D%20t%20%5Cin%20%5B0%2C1%5D&bg=ffffff&fg=000000&s=0 "\mathbf{B}(t)=\mathbf{P}_0 + t(\mathbf{P}_1-\mathbf{P}_0)=(1-t)\mathbf{P}_0 + t\mathbf{P}_1 \mbox{ , } t \in [0,1]")
. This is equivalent to linear interpolation.When Bézier curves are quadratic, they are expressed by the equation ![\mathbf{B}(t) = (1 - t)^{2}\mathbf{P}_0 + 2(1 - t)t\mathbf{P}_1 + t^{2}\mathbf{P}_2 \mbox{ , } t \in [0,1].](http://s.wordpress.com/latex.php?latex=%5Cmathbf%7BB%7D%28t%29%20%3D%20%281%20-%20t%29%5E%7B2%7D%5Cmathbf%7BP%7D_0%20%2B%202%281%20-%20t%29t%5Cmathbf%7BP%7D_1%20%2B%20t%5E%7B2%7D%5Cmathbf%7BP%7D_2%20%5Cmbox%7B%20%2C%20%7D%20t%20%5Cin%20%5B0%2C1%5D.&bg=ffffff&fg=000000&s=0 "\mathbf{B}(t) = (1 - t)^{2}\mathbf{P}_0 + 2(1 - t)t\mathbf{P}_1 + t^{2}\mathbf{P}_2 \mbox{ , } t \in [0,1].")
. They are also known as parabolic segments. When Bézier curves are cubic, they are expressed by the equation ![\mathbf{B}(t)=(1-t)^3\mathbf{P}_0+3(1-t)^2t\mathbf{P}_1+3(1-t)t^2\mathbf{P}_2+t^3\mathbf{P}_3 \mbox{ , } t \in [0,1].](http://s.wordpress.com/latex.php?latex=%5Cmathbf%7BB%7D%28t%29%3D%281-t%29%5E3%5Cmathbf%7BP%7D_0%2B3%281-t%29%5E2t%5Cmathbf%7BP%7D_1%2B3%281-t%29t%5E2%5Cmathbf%7BP%7D_2%2Bt%5E3%5Cmathbf%7BP%7D_3%20%5Cmbox%7B%20%2C%20%7D%20t%20%5Cin%20%5B0%2C1%5D.&bg=ffffff&fg=000000&s=0 "\mathbf{B}(t)=(1-t)^3\mathbf{P}_0+3(1-t)^2t\mathbf{P}_1+3(1-t)t^2\mathbf{P}_2+t^3\mathbf{P}_3 \mbox{ , } t \in [0,1].")
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Tags: algebra, algorithm, Bézier, curve, curves, Math, paths, Pierre Bézier
Posted in Algebra | No Comments »
Thursday, September 24th, 2009
Algorithms Explained
Description
A detailed tutorial on the solving of algorithms. Step by step tutorial including several example problems of how to solve algorithms for reference.
Overview
An algorithm is something that you will find at almost any level of math – the more advanced the level of math, the more advanced the algorithm will be. When you use an algorithm, what you are doing is solving a problem by using a finite sequence of instructions. The visual representation of an algorithm is a flow chart…every time you use a flow chart or sequence to solve a problem, even one that isn’t mathematical, you are using an algorithm.
Tags: algorithm, algorithms, calculation, Calculus, data processing, finite, flow charts, instructions, Math, representation, sequence, visual
Posted in Calculus | No Comments »
