Ref: /abs/1910.06709 : A Simple Proof of the Quadratic FormulaĬorrection: We amended a sentence to say that the method has never been widely shared before and included a quote from Loh. Either way, Babylonian tax calculators would surely have been impressed. To speed adoption, Loh has produced a video about the method. The question now is how widely it will spread and how quickly. The derivation emerged from this process. Loh, who is a mathematics educator and popularizer of some note, discovered his approach while analyzing mathematics curricula for schoolchildren, with the goal of developing new explanations. “Perhaps the reason is because it is actually mathematically nontrivial to make the reverse implication: that always has two roots, and that those roots have sum −B and product C,” he says. So why now? Loh thinks it is related to the way the conventional approach proves that quadratic equations have two roots. None of them appear to have made this step, even though the algebra is simple and has been known for centuries. He has looked at methods developed by the ancient Babylonians, Chinese, Greeks, Indians, and Arabs as well as modern mathematicians from the Renaissance until today. Loh has searched the history of mathematics for an approach that resembles his, without success. Learn how to use the Quadratic Formula, the discriminant and other methods to find the solutions, and see examples and graphs. Yet this technique is certainly not widely taught or known." Enter the values of a, b and c to solve a quadratic equation of the form ax2 + bx + c 0. This "size" concept is called "the modulus" of a complex-valued point.Loh says he "would actually be very surprised if this approach has entirely eluded human discovery until the present day, given the 4,000 years of history on this topic, and the billions of people who have encountered the formula and its proof. Complexes that are closer to the origin will have smaller sizes complexes further away will have larger values. To find a point's size, you use the Distance Formula. Pretty much all you can do is compare the "sizes" of the different points, and, for complex numbers as for regular x, y-points, "size" means "how far from the origin". You can't say that one point "comes after" another point in the same way that you can say that one number comes after another number you can't say that (4, 5) "comes after" (4, 3) in the way that you can say that 5 comes after 3. But x, y-points don't come in any particular order. When you learned about regular (that is, about "real") numbers, you also learned about their order on the number line. This graphability of complex numbers leads somewhere interesting.
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