Khanacademy. Oughtred Society Slide Rule Home Page. Per Square Mile. Correlated - Discover surprising correlations. MAKE. The Museum of Mathematics. MAKE. History of elementary algebra. As a branch of mathematics, algebra emerged at the end of 16th century, with the work of François Viète. Algebra can essentially be considered as doing computations similar to that of arithmetic with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra.
This article describes the history of the theory of equations, called here "algebra", from the origins to the emergence of algebra as a separate area of mathematics. Etymology[edit] Stages of algebra[edit] Algebraic expression[edit] Algebra did not always make use of the symbolism that is now ubiquitous in mathematics, rather, it went through three distinct stages. Rhetorical algebra, where equations are written in full sentences. Where p and q are positive. . , with p and q positive, have no positive roots.[2] Conceptual stages[edit] Trachtenberg system. The Trachtenberg system is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly.
It was developed by the Russian Jewish engineer Jakow Trachtenberg in order to keep his mind occupied while being held in a Nazi concentration camp. The rest of this article presents some methods devised by Trachtenberg. The most important algorithms are the ones for general multiplication, division and addition[citation needed]. Also, the Trachtenberg system includes some specialized methods for multiplying small numbers between 5 and 13. The chapter on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.
General multiplication[edit] The method for general multiplication is a method to achieve multiplications with low space complexity, i.e. as few temporary results as possible to be kept in memory. Times the next-to-last digit of . Example: Web. This is the story of the late Jakow Trachtenberg, and how to scam people using your mathematical tricks. The Jedi Mind-Trick It's time for another little diversion.
Let's look at an easy way to subtract nine. Most people work out that you first subtract 10, then add one. But my brain sometimes gets a bit lost, forgetting to add the right way – not being sure of the answer, needing to re-work the logic. It's all a mind-trick. Here is the same information, but presented with a different slant. To subtract nine, just read out the number, digit by digit, but when you get the the second-last one, take one away, and add it to the one on the right. For some reason, this is much easier, even though we are doing exactly the same thing as taking 10 away and adding 1 to compensate for taking 10 away.
There is a tiny complication when you get a 0 in an awkward spot: But you can read the original as “three seven six seven tenty three” and say “three seven six seven ninety four” and get the answer right. It's handy to be able to subtract 9. Read this number, then turn away and recite it: How far did you get?