16May 2017 by Vincent Summers No Comments

Simple Algebra II Graph Symmetries Discussion and Examples

Education, Mathematics
[caption id="attachment_17854" align="alignright" width="480"] Typical functions in two variables.[/caption] College preparatory classes in high school often include Algebra and Algebra II. Perhaps the most memorable aspect of Algebra II is the two-dimensional (2D) graphing of mathematical functions in two variables. This is typically introduced beginning with the Cartesian coordinate system. The generic function is written y = f (x). This reads y equals a function of x. See the illustration for some examples of functions. Cartesian Coordinate System In the Cartesian system, two variables, often x and y, are assigned their own line, one horizontal (x), one vertical (y). The intersection between the two axes is called the origin, and is assigned the value (0, 0). The value of x is the value written on the left in the brackets;…
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14Nov 2014 by Vincent Summers No Comments

Introduction to Cylindrical Coordinates

Mathematics
What are cylindrical coordinates? A coordinate system is a system that provides a way to describe points and other features of geometric figures in Euclidean space. Generally the best coordinate system is that system which adequately does the job in simplest fashion. In this article, we will use (r, Φ, z) for our new coordinate system. Many use this, but others use a different assortment of letters, unfortunately. Forewarned is forearmed. Cylindrical Coordinates - Introspection When we're working in two dimension, we are able to draw our coordinate axes using the sheet of the paper, representing a plane. Two orthogonal axes are drawn, one horizontal the other vertical. When using r and Φ the way we view the axes is really different from how we view them when they represent x…
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21Feb 2014 by Vincent Summers 1 Comment

Determining the Equation for a Line from Two Points

Mathematics
Lines can be drawn in three dimensions, but most analytical geometry courses stick to lines in two dimensions, generally using the Cartesian or XY coordinate system. The generic equation for a line may follow the form: y = mx + b where m is the slope (measure of tilt or steep-ness) of the line, while b is its intercept or intersection with the y-axis. Equation for a Line from Two Points A line can be determined and an equation derived from two points. In the Cartesian system, for instance, take two points, (2 , 3) and (– 1 , 5). The first number in each pair represents the x-value of a point and the second number in each pair represents the y-value. Writing these points into the general equation y…
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