Math eBook

a-new-coordinate-system-cover

A Three Dimensional Coordinate System for Complex Numbers

“3Di Coordinates” is a completely new concept that makes everything related to imaginary and complex numbers easier to understand. The eBook contains nearly six hundred line and surface graphs and over a hundred animations illustrating the equations so you can settle in for an enjoyable as well as informative experience. Thanks!

Note: Links to the animations have become corrupted over the years. They are currently being fixed and updated so check back to download the new version with updates, revisions and working links. If you like you can still download this old version without updates and without working links to the animations. Thanks!

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Quotes From the Book

The notion of “3Di:Third Dimension Imaginary” is probably a good example of what Victor Hugo called: “An idea whose time has come.”
Greg Ehmka,

To the degree that mathematics assists us in understanding what we perceive as we look out at life, we must acknowledge the fact that what we perceive includes both seen and imagined components. Consequently both real and imaginary values must be included in the mathematical representation of it.
Greg Ehmka,

It’s like a coffee table picture book for math people!
M. W.,

Consider an aircraft. Real slope is its climb or descent. Imaginary slope is its heading. Complex slope is the sum of the two.
Greg Ehmka,

A negative wavelength can be defined as a clockwise development of the helix rather counterclockwise which would be a positive wavelength.
Greg Ehmka,

This e-book is dedicated to all high school students, past and present, who found a spark of interest in mathematics and then decided that she or he was too math-phobic, or not smart enough, to go further. It took me nearly thirty years to write this. Don’t give up on what you love!
Greg Ehmka,

I’ve, personally found useful the realization that there are essentially only four graphed or observable dimensions - horizontal, vertical, depth and ‘animation’- And theoretically there could be many ungraphed, unobserved or embedded dimensions.
Greg Ehmka,

If it’s true that we must imagine what goes on behind the façade in the z or depth direction of perspective, then possibly imaginary numbers can be combined with the real plane to form a new three-dimensional coordinate system.
Greg Ehmka,

In section 6.0 we take Euler's Famous Formula which is stated for base e: e^iθ = cosθ + isinθ and upgrade it for all bases; positive, negative, real, imaginary and complex.
Greg Ehmka,

The exponential-natural logarithm function forms a surface on which each point on the surface has the coordinates, (x+iθ or ln(y + iz) = x +iθ
Greg Ehmka,