02Aug 2016 by Vincent Summers 2 Comments

XY-Coordinate System Symmetry with Examples

Logic, Mathematics
[caption id="attachment_28582" align="alignright" width="480"] Image Department of Energy[/caption]In high school mathematics, the topic of symmetry is bound to arise. Especially is this so in analytic geometry. For curve C, what is its XY coordinate system symmetry? How is it symmetric about the y-axis? The x-axis? The origin? The line y = x? The line y = -x? Symmetric about some point other than the origin? Symmetry About the Y-Axis Symmetry about the y-axis means that if there is a curve that lies to the right of the y-axis, there is an identical copy of it to the left of the y-axis. That is, it is symmetrical if each x value can be replaced with –x. Thus, the parabola y = 1/2x2 is symmetric with regard to the y-axis. For every…
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14Dec 2013 by Vincent Summers 2 Comments

Imaginary Space, Imaginary Time?

Physics
[caption id="attachment_5427" align="alignright" width="480"] Square Root of -1[/caption] What do you think? Could there be imaginary space? imaginary time? In the real world, there are many and varied ideas we can comprehend, or at least find conceivable. However, there are concepts beyond our comprehension. This does not automatically make them unreal. One such concept is the imaginary number. Physically, the imaginary number is real. To date, however, no one has satisfactorily explained the phenomenon. Simplest Case The simplest imaginary number is the square root of –1. Does that sound like it should be no problem? Well, the square root of 1 has two values: –1 and 1. That can be proven. 1 x 1 = 1, right? And –1 x –1 = 1, right? Well, what number n is there,…
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