Posts Tagged ‘box’
Friday, December 18th, 2009
Explanation of the Pigeon-Hole Principle
Description
A detailed tutorial on the pigeon-hole principle. Step by step tutorial including several examples of the pigeon-hole principle for reference.
Overview
The pigeon-hole principle is an important principle in math that states that if n items are to be put into m pigeon-holes, and n > m, then at least one pigeon-hole must contain more than one item. It is thought of as an extension of the counting principle. The pigeon-hole principle was first referred to as the drawer principle, or the shelf principle. Because of this, it is commonly called Dirichlet’s box principle or Dirichlet’s drawer principle. It is most commonly used with finite sets of elements; however, this principle can also be used with infinite sets.
Tags: algebra, box, counting, Dirichlet, drawer, elements, extension, finite, infinite, leftover, more, pigeon-hole, principle, remainder, sets, shelf, theory
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Friday, December 18th, 2009
Your Guide to Lattice Multiplication
Description
A detailed tutorial on lattice multiplication. Step by step tutorial including several examples of lattice multiplication for reference.
Overview
Lattice multiplication is a method that is used to multiply large numbers. It uses the multiplication of smaller numbers to figure out the product of two larger numbers. Because of this, basic knowledge of times tables is required. Lattice multiplication is compromised of boxes with diagonal lines through them. Draw the diagonal line in each box from the top right corner to the bottom left corner. The top left is for your tens place (the first digit in a two digit number) and the bottom right is for your ones place (the second digit in a two digit number). The number of boxes you have depends on the number you are multiplying – for example, if you are multiplying two one-digit numbers, there is one box. If you are multiplying two 2-digit numbers, there are four boxes. The first number is across the top, and the second down the side. Where each single digit number instersects, multiply them together using the box technique. Then, using the same pattern you drew the diagonals with, mutliply the diagonals. If you have two 2-digit numbers, there will be four diagonals. Multiply together the diagonals to come up with four numbers, and the pattern you use to put them together is going from the top down and then to the right.
Tags: algebra, box, combine, diagonal, digit, double, larger, lattice, multiplication, multiply, single, small, tables, times
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Tuesday, November 10th, 2009
How to Make a Box-and-Whisker Plot
Description
A detailed tutorial on how to make a box-and-whisker plot. Step by step tutorial including several examples of how to make a box-and-whisker plot for reference.
Overview
A box-and-whisker plot is named for it’s resemblance to a cat’s face – the box is the face of the cat, and the lines extending out from either side are known as whiskers. Sometimes box-and-whisker plots are simply called box plots. They are used to graph sets of numbers according to five values: the highest value, known as the maximum, the second highest value, known as the upper quartile, the median, or the middle, the second lowest value, known as the lower quartile, and the lowest value, known as the minimum. The box centers around the median and the whiskers extend out to the other numbers.
Tags: algebra, box, box-and-whisker, boxplot, diagram, graph, highest, line, lower, lowest, maximum, median, middle, minimum, plot, quartile, upper, value, whisker
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Tuesday, October 27th, 2009
Definition of a Scalar Triple Product
Description
A detailed tutorial on scalar triple products. Step by step tutorial including several examples of scalar triple products for reference.
Overview
A scalar triple product is a way of applying other multiplication operators to three vectors. Quite often, the scalar triple product is denoted as (a, b, c). It can also be defined as (a b c) = a(b x c). The scalar triple product has three main properties. The first one is that the absolute value of the scalar triple product is the volume of the three dimensional figure that is formed by the three vectors. The second one is the scalar triple product is only zero if the three vectors are linearly independent. The three vectors must lie in the same plane for this to be true. The third one is that the scalar triple product is only positive if all three of the vectors are considered right-handed.
A simple way to write the scalar triple product is to line up the coordinates of the vectors in this form: 
This is the same as saying 
Tags: absolute, algebra, box, coordinates, figure, independent, linear, mixed, multiplication, operator, parallelpiped, positive, product, properties, right-handed, scalar, three-dimensional, triple, value, zero
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