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Rated: 18+ · Book · Personal · #1196512
Not for the faint of art.
Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.




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March 14, 2019 at 12:01am
March 14, 2019 at 12:01am
#954305
As the literal interpretation of the name of this blog refers to math, and as today (3/14) is Pi Day, I thought I'd say something about pi.

Pi is cool.

That is all.

...

Okay, that's not all.

I had an engineering professor who told some version of the following joke (it helps to imagine it being told in a rural Virginia accent, but most of you probably haven't been exposed to this particular linguistic jewel collection, so just imagine a standard Southern accent):

Jim-Bob was the first in his family to go to college. He comes back for Thanksgiving dinner and they're sitting around the table.

"So," says Grandpa, "what did you learn in that there fancy school of yours?"

"Well... we learned πr2."

"Pi r square? What the hell are they teaching you younguns these days, anyway? Everybody knows pie are round. Cornbread are square!"

I didn't say it was a good joke.
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