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 |    Not for the faint of art. |
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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. ![Merit Badge in Quill Award
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| After yesterday's rant (which indeed contained an egregious error made by me; I didn't notice it until today and by my own rules it's now set in stone forevermore), how about something fun from Cracked? This could just as well have been "5 Facts About U.S. Landmarks," but that doesn't get as many challenge-accepted-clicks. What color is the White House? The Kennedy Space Center is named after which U.S. president? These are questions that you, the well-informed reader, are proud to answer with ease. They left out the old classic: Who's buried in Grant's Tomb? That's a trick question, though; U.S. Grant and Julia Grant are interred in sarcophagi therein, not buried. 5. Why Does the Pentagon Take Up So Many Acres? And why are we still using acres? For years, the Pentagon was the world’s largest office building, boasting more than six million square feet of floor space. Let's see... commercial rents in that area go for around $30/sf (okay, yes, I'm using square feet after complaining about acres). That would be $180,000,000 in rent if it were rentable. That's per month. The Pentagon is so large because it’s the headquarters of the Department of Defense, the single largest employer in the world. The DoD employs almost three million people, and 27,000 of them work in the Pentagon. The building is especially large because we built it during World War II, which was the most complicated challenge ever faced by the Department, or by anyone. Um... well... I can think of a more complicated challenge during WWII. They released a movie about it last year. None of that answers the exact question we asked. Even if the Pentagon has to contain six million square feet, why is it so spread out, across 30 acres? Because the banks of the tidal Potomac aren't known for being able to support skyscrapers? Washington, D.C. doesn’t have the skyscrapers many other cities do (no building in that town should be higher than the Washington Monument), but plenty of its buildings have 10 floors or more. (1) The Pentagon lurks in Arlington County, VA, not Washington, DC. (2) My understanding of the DC building law is that no building can be taller than the Capitol. But that's irrelevant, because (1). (3) After checking around a bit, my understanding of (2) was wrong; it's more complicated than that. But that's irrelevant, because (1). (4) Even ignoring all that, the National Cathedral in DC is built on high ground,  and its spire exceeds the elevation of the tip of the WM.Normally, a taller and narrower building would be the wiser choice. Land is scarce in most locations where a building this large is desirable. Except that building taller and narrower buildings requires better subsurface features, either bedrock (like in NYC) or massive underground structures to distribute the load. If space were truly an issue back then, there wouldn't be all surface parking around it. Plus, elevators move up and down, not side-to-side. Easy enough to fix. Wonka might have some design ideas there. But for a building to stand many floors tall, you need lots of steel, and during construction, they wanted to use as little steel as possible, to save the stuff for the war effort. Okay, there's that, too. The real question here is: why a pentagon? Even in the early 1940s, they must have expected conspiracy theories. The actual answer is more mundane: the original design was meant to be bordered by five roads. I should note that, while civil engineering technology plods along, it does eventually advance, and I'm pretty sure that right now there are no engineering barriers to building skyscrapers on the banks of the Potomac. Probably not going to happen, though, because engineers don't run governments. 4. Where Is the Center of Gravity of the Space Needle? Sure, let's hop to the entire other coast. I did that once. Took off from Washington (actually Arlington) and landed in Washington (actually Tacoma). Skipping to the spoiler: The building may look like a needle pointing from the ground to the sky, but a large bulk of the structure’s mass sits underground. The foundations run 30 feet below the surface, and these foundations weigh 5,840 tons. I told you tall buildings required big foundations. Now, I know way more about foundation requirements in Virginia than in Washington state, but I'm pretty sure the Needle was built on bedrock. Problem is, it's in an earthquake zone. Oh, and here's more fuel for the conspiracy fire: The Needle was privately financed and built by the Pentagram Corporation... 3. What Faces Did South Dakota Want to Carve into Mount Rushmore? If it were up to me, it'd be Curly, Larry, Moe, and Shemp. It started out with a more narrow focus. First of all, the idea for the monument came from South Dakota specifically, rather than from the federal government that provided funding. That's because there is literally nothing else interesting in the entirety of South Dakota. As it was conceived as a South Dakota attraction, it was originally supposed to be themed more to the region. Rather than depicting four presidents, it was supposed to depict figures from the Old West. These included Lewis and Clark and Sacagawea. Lewis and Clark were from around my hometown. We had a big statue of them, along with Sacagawea, at a prominent intersection. Remember that this is Charlottesville, and take a guess if the statue's still there. In fairness, while the statue was meant to depict the white guys staring boldly off into the distant wilderness while their Native guide did some tracking or whatever, it ended up looking like the poor girl was cowering at the heroic-looking pair's feet. I do wish they'd do something with the plinth, though. Right now, it's a big hunk of concrete. Maybe a giant inoffensive abstract hypercube. Except that abstract art also offends some people. 2. Who Was the St. Louis Arch Accused of Plagiarizing? Hint: It's not McDonald's. 1. How Long Does the Grand Canyon’s River Take to Reach the Ocean? If I'm being honest, this is the only one of these that I got right without looking at the text. The Grand Canyon's river is the Colorado, which also supplies some well-known desert reservoirs and a bunch of farms. The answer, if you just consider surface runoff and not the evaporation-clouds-rain water cycle, is infinity. Because by the time you trace the old channel of the Colorado down to the Gulf of California (an arm of the Pacific, so "ocean" isn't the trick part), all the water is gone, diverted to thirsty people or agriculture, or evaporated naturally. This is, of course, a marvel of civil engineering, and I should be quite proud of my field's accomplishments. I'm not. |
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