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A Visual, Intuitive Guide to Imaginary Numbers

A Visual, Intuitive Guide to Imaginary Numbers
Imaginary numbers always confused me. Like understanding e, most explanations fell into one of two categories: It’s a mathematical abstraction, and the equations work out. Deal with it.It’s used in advanced physics, trust us. Just wait until college. Gee, what a great way to encourage math in kids! Focusing on relationships, not mechanical formulas.Seeing complex numbers as an upgrade to our number system, just like zero, decimals and negatives were.Using visual diagrams, not just text, to understand the idea. And our secret weapon: learning by analogy. It doesn’t make sense yet, but hang in there. Video Walkthrough: Really Understanding Negative Numbers Negative numbers aren’t easy. But what about 3-4? Negatives were considered absurd, something that “darkened the very whole doctrines of the equations” (Francis Maseres, 1759). What happened? Rather than saying “I owe you 30” and reading words to see if I’m up or down, I can write “-30” and know it means I’m in the hole. Uh oh. Wrong. or

Conceptual Taxi System Puts Civility Back in Urban Transport When summoning a taxi in a busy urban center, waiting for a driver who is available, paying attention and willing to pick you up can get frustrating…not to mention the annoying “upstreamers” just waiting to snag that ride before you. This curbside taxi communication system was created by a group of design students at the Xi’an University of Design and Technology and recently won the Red Dot Award for a public space concept. It uses a system of lights, tactile curbside buttons and driver interaction to make hailing a taxi quick and easy. When a customer needs a cab, they just step onto the pressure-sensitive plate on the curb. Game Theory 101: Game Theory Made Easy MIT's free online classes can carry credit The Massachusetts Institute of Technology has offered free online courses for the last four years with one major downside: They didn't count toward a degree. That's about to change. In a pilot project announced Wednesday, students will be able to take a semester of free online courses in one of MIT's graduate programs and then, if they pay a "modest fee," earn a "MicroMaster's" degree, the school said. The new degree represents half of the university's one-year master's degree program in supply chain management. The fee for the MicroMaster's degree amounts to what it now costs to receive a "verified certificate" for finishing online classes, the university said. "The rising cost of education, combined with the transformative potential of online teaching and learning technologies, presents a long-term challenge that no university can afford to ignore," MIT President L. MIT didn't immediately say when the new pilot project would launch.

Personal and Historical Perspectives of Hans Bethe Quirky Mouse Design Requires You Take Play Breaks at Work If there’s one thing just about every office could use, it’s more fun, right? Sitting in front of a computer for eight (or ten, or twelve…) hours a day just isn’t natural. For optimum mental and physical health it’s important to take frequent breaks. This mouse concept from Shih-Chan Chiu forces you to stop working once in a while and act like a kid. The Yo-Yo Mouse is just what it says: a wireless mouse that’s also a yo-yo. The fun part of this design (other than the fact that it’s a toy) is that it is actually charged by the yo-yo action.

How Mathematics Can Make Smart People Dumb - Ben O'Neill Mathematics can sometimes make smart people dumb. Let me explain what I mean by this. I don't mean that it is dumb not to be good at mathematics. After all, mathematics is a highly abstract and challenging discipline requiring many years (decades even) of study, and there are plenty of very smart people who have little understanding of it, and little ability to use it. What I mean is that mathematics quite often bamboozles people into accepting very silly arguments — arguments that are so silly that if you stated them without draping them in mathematical negligee, you would instantly become an object of ridicule to all those people who flunked out at basic algebra back in high school. The danger of mathematical arguments is that a person can sometimes follow an absurd path of reasoning without being alerted to its absurdity, due to the fact that their mind is so lost in the verbiage of mathematical equations that their common sense fails to penetrate it. But wait a minute. Notes

Hillary Clinton to unveil $350-billion plan to make college more affordable Hillary Rodham Clinton outlined a plan Monday to slash student loan interest rates while aiming to guarantee students could attend college without needing to take out loans in the first place, tapping into an issue that has risen in prominence among Democrats. Under Clinton’s plan, state governments, higher education institutions and students would play roles alongside the federal government in addressing the affordability of higher education and the debt that can come from it. “We need to make a quality education affordable and available to everyone willing to work for it without saddling them with decades of debt,” she said. The $350-billion plan Clinton outlined at a New Hampshire town hall meeting was the most expensive and expansive policy proposal of her campaign thus far. States that agree to increase spending on higher education would be eligible for federal grants to help reduce the gap between what families can afford to pay and full tuition. Sen. Former Maryland Gov.

11 cheap gifts guaranteed to impress science geeks Science comes up with a lot of awesome stuff, and you don't need a Ph.D, a secret lab, or government funding to get your hands on some of the coolest discoveries. We've got a list of 11 mostly affordable gifts that are guaranteed to blow your mind, whether or not you're a science geek. Click on any image to see it enlarged. 1. Aerogel Also known as frozen smoke, Aerogel is the world's lowest density solid, clocking in at 96% air. Aerogel isn't just neat, it's useful. Price: $35 2. Inside these sealed glass balls live shrimp, algae, and bacteria, all swimming around in filtered seawater. EcoSpheres came out of research looking at ways to develop self-contained ecosystems for long duration space travel. Price: $80 3. NASA has been trying to figure out how to get a sample of rock back from Mars for a while now. Every once in a while, a meteorite smashes into Mars hard enough to eject some rocks out into orbit around the sun. Price: $70+ 4. Price: $150 5. Price: $110 6. Price: $80 7. Price: $15 8.

Pointer in Disguise: Weird Mouse Looks Like a Plastic Battery Although we’ve seen plenty of wacky mouse designs and concepts, this one deviates so much from the familiar form factor that it would be easy to miss the fact that it’s a mouse at all. It looks more like a battery with buttons – but it could in fact be the future of input devices. The wireless MENDO Kandenshi Mouse is a small cylinder that you grasp with your thumb on top and index and middle fingers wrapped around the side. The left and right buttons occupy one side of the cylinder while the top houses a hidden USB plug, which is presumably the dongle that pairs the mouse with the computer. The Kandenshi Mouse really does look just like a large battery, complete with the little nubbin on top. It looks like some design student’s thesis project (and probably was at some point) but this unusual mouse is actually set to go on sale in Japan very soon.

Math doesn't suck, you do. Every time I hear someone say "I suck at math," I immediately think he or she is a moron. If you suck at math, what you really suck at is following instructions. This shirt is birth control. Sucking at math is like sucking at cooking. I'm tired of eating shitty food because you're too much of a dipshit to follow a recipe. Also, I'm tired of hearing people brag about how they can't cook like it's some kind of badge of honor. Math is exactly like cooking: just follow the recipe. Math isn't some voodoo that only smart people understand. Theoretical math is cool as shit. Ever heard of Pascal's triangle? No, because you're too busy saying the same tired excuse every other dickhead spews out about math: "when will I ever use this in life?" First of all, if you're leading your life in such a way that you never have to do math, congratulations, you are a donkey. Why is math the only discipline that has to put up with this bullshit? People didn't invent this stuff because they were bored.

Privately educated graduates 'earn more' than state school colleagues - BBC News Privately educated UK graduates in high status jobs earn more than their state school counterparts, says a study. The report, by the Sutton Trust and UpReach, examined those in careers such as law and financial services. It found that, on average, three years after graduation, those who attended fee-paying schools earned £4,500 more. The government said it was "determined... to ensure every child, regardless of background, reaches their potential" through its policies. The report put the earnings gap down to factors such as the university attended, but also suggested non-academic factors, such as assertiveness, were at play. The research also found salaries of the privately-educated increased more quickly, growing by £3,000 more over the same three-and-a-half year period. Average salaries, six months after graduation, were more generous for those who had attended independent schools - £24,066 compared to £22,735, a difference of £1,331.

Watch Your Mouth: Toothbrush Keeps an Eye on Cavities We all know how important brushing is for healthy teeth, but it’s not easy to know if you’re brushing as well as you should. The Tooth Guardian concept integrates a tiny camera into a toothbrush to let you see exactly what’s going on with your pearly whites. Designed by Yu-Hsin Lin, Chu-Che Chang and Shang-Hsuan Lu, the Tooth Guardian is a conceptual design that would help cut down on dentist visits by giving you a good look at potential problem areas. You can see where plaque is starting to build up and even catch cavities when they’re still small. There’s a small LED on the head of the toothbrush to illuminate your mouth, and the tiny closed-circuit camera projects images from your pie hole right onto your bathroom mirror.

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