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Complex Numbers
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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July 5, 2024 at 8:05am
July 5, 2024 at 8:05am
#1073565
It should be well-known by now that one shouldn't get one's facts from comedy sites like Cracked. Especially when that source tells us we shouldn't be getting our facts from movies, either.



If you see something in enough movies, you assume it’s true. If every movie has bears growling or frogs ribbiting or vampires hating lemons, we assume that’s how the real world works, because movies are the only form of education we have.

For instance, thanks to movies, I know that cars inevitably explode when run off cliffs.

Sometimes, however, no trend is necessary. All it takes is one influential movie...

Kind of like how the documentary Willy Wonka and the Chocolate Factory taught me how candy gets made.

5 Presidents Are Supposed to Wear Flag Pins

A few years ago, a friend of mine got married. The bride asked me to be her Dude of Honor, so I had to buy a suit. The suit came with a flag lapel pin.

I didn't wear the pin to the wedding. Too political.

You might even say a president wearing a flag pin is redundant, since he’s already the president and his nationality isn’t in question.

Oh, how quickly we forget.

The first president to wear the pin was Richard Nixon, and his staff convinced him to adopt it after watching a 1972 Robert Redford movie called The Candidate.

So, to be clear, the clowns we have in office these days all emulate a disgraced former president, who in turn got the idea from typical Hollywood bullshit.

This explains a lot.

As for Redford, a few years after The Candidate, he starred in All the President's Men, a movie we trust Nixon enjoyed just as much.

Ooooooh, sick burn.

One final amusing note: in the alternate universe of The Watchmen (the original graphic novel, published in the late 80s), the President was Robert Redford. Imagine that, an actor as President.

4 Pirates Used the Pirate Accent

We have this concept of “pirate speak,” of a single accent that pirates use. The more pirate-y the pirate, the closer they’ll adhere to this accent... Our idea of the pirate accent comes entirely from one actor, Robert Newton, and his performance in 1950’s Treasure Island.


Eh, doesn't matter. It's iconic at this point. Arrr. Shiver me timbers.

3 Rabbits Like Carrots

We all associate rabbits with carrots, but the two don’t go together naturally at all. The carrots we eat don’t exist in nature at all, as they’re the result of a whole lot of selective breeding.


Otherwise known as genetic modification.

Rabbit like greens, and they can eat the leafy top of a carrot, but if a rabbit gorges itself on carrots, that’d be like you trying to live on cotton candy.

Or on rabbit meat, for that matter.

Of course, Bugs Bunny wasn't a movie star at the time, but as the article notes, he was emulating Clark Gable.

2 Mohawks Wear Mohawks

The mohawk is a hairstyle. It’s also a name for an indigenous people from the eastern United States, so you probably think that hairstyle is named after the people.


Gosh... Hollywood getting Native American culture wrong. Who could have expected that?

1 Rockets Should Count Down to Takeoff

Except that there's sound reasons for a lot of the countdown. Rockets are somewhat intricate and complicated machines (hence the equating of "rocket scientist" with "genius,") and their launch preparations require a checklist of things to be done in a precise order at precise times. Not that I know anything about it, though; I'm not exactly a rocket surgeon.

NASA got the idea of counting down to launches from a German film called Woman in the Moon. This Fritz Lang silent picture was the first ever big-screen depiction of rocket travel — Georges Méliès’ earlier A Trip to the Moon was a far less serious look at lunar travel.

The MĂŠliès film (itself a Verne adaptation) is the one with the absolutely iconic image of a space capsule getting in the eye  Open in new Window. of the Man in the Moon.

Anyway, it's no surprise that NASA got its idea from German cinema instead of French, considering the history of NASA.

Countdowns really are thrilling. Just look at this very article. It could have counted up from one to five, and newcomers to this site may be baffled at why it doesn’t. “Is this a ranking from five to one?” they might ask. It’s not.

Anyone here not expect the self-referential humor? I certainly did.


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