Photo by Annie Spratt on Unsplash, this article is from WeChat public account: Almost Human (ID: almosthuman2014) , author: Lize Nan, formerly titled “Chinese professor found quadratic equation” minimalist “solution: lose formula , Global textbooks may have to be changed “
Whether you have a cold in mathematics or not, people in high schools all over the world will face the challenge of solving quadratic equations. Formula and then learn how to use it. But recently, researchers from Carnegie Mellon University’s (CMU) have found a super simple method of derivation. For the first time in 4000 years, the method of solving the equation has changed.
Recently, a study called “A Simple Proof of the Quadratic Formula” appeared on arXiv, a pre-print publication platform, and attracted people’s attention.
This article proposes a “minimalist” derivation of quadratic equations. This method is computationally lightweight. The concept is also natural, and it is likely to make junior high schools around the world. The process of solving the generated quadratic equation has never been more difficult.
This simple method was discovered by Robson, a Chinese-American mathematician and head coach of the Orsay national team.
The quadratic equation is one of the important achievements of the ancients in mathematical exploration. Its history can be traced back to the Babylonian period from 2000 to 1600 BC. In more than 4,000 years of history, many famous mathematicians have “rediscovered” their solution methods.
Of course for most people, quadratic equations are a standard part of today’s first-stage course in algebra.
Unfortunately, for billions of people worldwide, the quadratic formula is the first complex formula that must be written down. (There is Probably the only one) , this is the Weida theorem we all have to learn:
Let a quadratic equation ax ^ 2 + bx + c = 0 (abc is a real number, a ≠ 0) The two x_1, x_2 have the following relationship,
From the root formula of the quadratic equation of one element
Compared with many mathematical formulas we will learn during high school and college, although this method is relatively simple, it relies on another basic mathematical technique “matching method”, which is far from intuitive.
So it took centuries for mathematicians to stumble upon this proof after the Babylonians first proposed it. Before and after, many other derivation formulas appeared, but all the ways seemed complicated and “anti-human”.
Luo Boshen found a surprising way to derive quadratic equations, which also resulted in an efficient, natural and easy to remember algorithm for solving general quadratic equations.
Considering that this subject has been in existence for more than 4,000 years and has been contacted by billions of people, it is really surprising that it was not discovered until today.
Robsen’s method does not rely on recipes or any other relatively difficult mathematical skills. It’s very simple and can be used as a general method to get students to abandon current formulas. The derivation of this method is like this:
Assuming that the quadratic equation has two roots R and S, like the classic method above, we can write it,
When x = R or x = S, the right side is equal to zero. Take apart the right side,
So -B = R + S and C = RS, the equation holds,
Now that it’s interesting, Luo Boshen pointed out that the sum of R and S at this time is -B, so the average of the two roots of the quadratic equation is -B / 2. “So we ask for the root, which is to find -B / 2 ± z, where z is a single unknown.” (Of course if z is zero, then R = S = -B / 2) . Because C = RS,
After finishing,
So the solution to the quadratic equation is,
It doesn’t look easy? However, this new method has some important improvements compared to the previous method. Robo gave an example to explain.
Solve this equation, x ^ 2-2x + 4 = 0:
The traditional method is to take the values of a, b, and c in the equation and bring them into the classic formula and then solve. In the new method, first, the two roots of the equation are equal to -B / 2 ± z, which is 1 ± z;
The product of the two roots is C = 4, so:
So the root of the equation is 1 ± i√3
Irrational and imaginary numbers are stress-free. You can try to solve this equation with traditional methods, it will definitely be much more difficult.
Link to the paper: https://arxiv.org/abs/1910.06709
I found a new and better solution to a “simple” problem. Is this really the first discovery by humans? Not long ago, Tao Zhexuan et al.’S research on eigenvalue vectors, “Eigenvectors from Eigenvalues”, was also regarded as “repeating the wheel” after the exciting publication. In this regard, Robb deeply discussed the originality of his proposed method.
In short, he studied the vast literature on the history of mathematics, including the methods of the Babylonians, Chinese, Greeks, Indians, and Arabs, and modern mathematicians from the Renaissance to today. Look for possibilities that have been discovered before, but have not been successful.
It looks like we have a new method for solving quadratic equations.
Chinese scholar Luo Boshen who found this method (Po-Shen Loh) is not only a mathematics professor at CMU but also Social activist dedicated to the study of global mathematics education. The scholar is currently the head coach of the US International Mathematical Olympiad.
Robosin graduated from California Institute of Technology in 2004 with a master’s degree in mathematics from Cambridge University in 2005. In terms of academics and competitions, Robson has also won many honors, including the Silver Medal of the International Mathematical Olympiad, and the Early Career Award of Presidential Scientist and Engineer. (PECASE) . His research interests include areas such as discrete systems, probability theory, and the intersection of computer science.
This article is from the WeChat public account: Heart of the Machine (ID: almosthuman2014) , of: Li Zenan