Posts Tagged ‘line’
Tuesday, January 5th, 2010
How to Determine Dedekind Cuts
Description
A detailed tutorial on how to determine Dedekind cuts. Step by step tutorial including several examples of Dedekind cuts for reference.
Overview
A Dedekind cut is a partition of rational numbers into two non-empty sets A and B, such that all elements of A are less than elements of B, and A has no greatest element. The cut itself is a gap that is located between A and B, which is normally found by creating a new, irrational number, and setting it in the gap. What irrational number you use depends on what numbers you have partitioned into the two sets. It is like the number line of advanced algebra, that has both rational and irrational numbers on it instead of just integers. The Dedekind cut was named after Richard Dedekind.
Tags: algebra, between, cut, Dedekind, elements, empty, gap, greater, integer, irrational, less, line, non, non-empty, numbers, partition, rational, Richard, sets, than
Posted in Algebra | No Comments »
Thursday, December 31st, 2009
How to Write Step Functions
Description
A detailed tutorial on how to write step functions. Step by step tutorial including several examples of how to write step functions for reference.
Overview
A step function, also called a staircase function, is a finite linear combination composed of several different intervals. They are considered to be a piecewise constant function. The graph of a step function is often expressed as steps, or a staircase, which is how it got its name. It simply looks like several disconnected lines, with alternate open and closed ends so that it easily passes the vertical line test for functions.
Tags: closed, combination, constant, diconnected, discrete math, ends, finite, function, graph, intervals, line, linear, lines, open, piecewise, staircase, step, test, vertical
Posted in Discrete Math | No Comments »
Tuesday, November 24th, 2009
How to Calculate the Angle of Depression
Description
A detailed tutorial on calculating the angle of depression. Step by step tutorial including several examples of the angle of depression for reference.
Overview
The angle of depression is the angle at which a person must be looking in order to see an object that is lower than the observer. Typically, the angle of elevation is a term used in trigonometry, when calculating angles of a right triangle. In a right triangle, the angle of elevation is the angle between the hypotenuse and the base, when the base of the triangle is actually located at the top of the figure. It can be calculated by using SOHCAHTOA and solving for the sine, cosine, or tangent.
Tags: angle, calculate, cosine, depression, horizontal, line, lower, object, point, right, sine, SOHCAHTOA, tangent, triangle, trig, trigonometry
Posted in Trigonometry | No Comments »
Tuesday, November 24th, 2009
How to Calculate the Angle of Elevation
Description
A detailed tutorial on how to calculate the angle of elevation. Step by step tutorial including several examples of the angle of elevation for reference.
Overview
The angle of elevation is the angle at which a person must be looking in order to see an object that is higer than the observer. Typically, the angle of elevation is a term used in trigonometry, when calculating angles of a right triangle. In a right triangle, the angle of elevation is the angle between the hypotenuse and the base. It can be calculated by using SOHCAHTOA and solving for the sine, cosine, or tangent.
Tags: angle, calculate, cosine, elevation, higher, horizontal, line, object, point, right, sine, SOHCAHTOA, tangent, triangle, trig, trigonometry
Posted in Trigonometry | No Comments »
Friday, November 20th, 2009
Overview of the Vertices of a Graph
Description
A detailed tutorial on the vertices of a grpah. Step by step tutorial including several examples of the vertices of a graph for reference.
Overview
The vertices of a graph are the number of lines extending from points on the graph. This is not the total number of edges – it is the number of edges extending from each point all added together. Each point has at least one vertex. Not every single point can have an odd number of vertices, and all the vertices cannot add up to an odd number, or it is not considered to be the graph of a function.
Tags: add, discrete math, edges, even, extending, function, graph, line, odd, point, vertex, vertices
Posted in Discrete Math | No Comments »
Thursday, November 19th, 2009
Finding the Altitude of a Triangle
Description
A detailed tutorial on how to find the altitude of a triangle. Step by step tutorial including several examples of how to find the altitude of a triangle for reference.
Overview
The altitude is just a way of saying the height of something. Typically, the term altitude is only used to refer to triangles. In triangles, the altitude is a little different from the height. Unlike the height, the altitude can be taken from three points of the triangle – it can be taken through the center of any of the three vertexes of the triangle. The altitude goes from the vertex to the line across from it, forming a right angle with that line. All three altitudes should intersect at a common point in the center of the triangle, known as the orthocenter.
Tags: altitude, angle, center, edge, Geometry, height, intersect, line, orthocenter, perpendicular, point, triangle, vertex
Posted in Geometry | No Comments »
Thursday, November 19th, 2009
Overview of Negative Square Roots
Description
A detailed tutorial on negative square roots. Step by step tutorial including several examples of negative square roots for reference.
Overview
Negative square roots are just like negative numbers. Just like positive and negative numbers have the same true value, only on opposite sides of the number line, negative square roots and positive square roots also have that same property. However, they should not be confused with the square root of a negative number. The square root of a negative number is known as an imaginary number, and is not used in basic algebra. The negative square root is expressed by the square root of a number, with a negative sign in front of the square root symbol, and the square root of a negative number is expressed as a negative number with a square root symbol placed over it.
Tags: absolute, algebra, arithmetic, imaginary, line, negative, number, positive, root, square, squareroot, symbol, true, value
Posted in Arithmetic | No Comments »
Tuesday, November 17th, 2009
Definition of a Bisector
Description
A detailed tutorial on the definition of a bisector. Step by step tutorial including several examples of bisectors for reference.
Overview
A bisector is any line that evenly divides a symmetrical shape or object. The only difference between the bisector and the test for symmetry is that when testing for symmetry, the line is not really there. A bisector is really there. The most common kind of bisector is an angle bisector. In order to remember bisectors, think of them as perpendicular lines that cross right in the middle.
Tags: angle, bisector, cross, divides, evenly, Geometry, line, middle, object, perpendicular, shape, symmetrical, symmetry, test
Posted in Geometry | No Comments »
Tuesday, November 17th, 2009
How to Draw a Boundary Line
Description
A detailed tutorial on how to draw a boundary line. Step by step tutorial including several examples on how to draw a boundary line for reference.
Overview
A boundary line is used when graphing inequalities on a number line or a regular Cartesian graphing system. What the boundary line does is connect the two points in the inequality – in other words, it sets a boundary of what an unknown variable would be on that inequality. The boundary line can either be solid or dashed. The boundary line is only dashed when it is drawn on a regular graph, to express that the line was somewhere else at one point and was then moved. In all other cases, the boundary line is solid.
Tags: algebra, boundary, closed, coordinates, dashed, equal, graph, greater, inequality, interval, less, line, number, open, points, solid, then, to
Posted in Algebra | No Comments »
Thursday, November 12th, 2009
How to Draw Best-Fitting Lines
Description
A detailed tutorial on how to draw best-fitting lines. Step by step tutorial including several examples on how to draw best-fitting lines for reference.
Overview
Best-fitting lines are lines that are drawn on a graph or on scatter plots. However, a best-fitting line is different than a normal line found on a graph. A normal graph simply requires you to connect the dots. A best fitting line focuses not on what dots to connect, but how to connect them. The line will curve or go in different directions, not just straight to the other line, depending on the relationship of the two dots to each other. Best-fitting lines typically require more information than simply the graph, you must explore the equation and each point to find the true relationships, and from that you can find the best-fitting line.
Tags: algebra, best, best-fitting, connect, coordinate, curve, direction, dots, equation, fitting, graph, line, plot, points, relationship, scatter, straight
Posted in Algebra | No Comments »
