SCHOPENHAUER'S 38 STRATAGEMS, OR 38 WAYS TO WIN AN ARGUMENT. Arthur Schopenhauer (1788-1860), was a brilliant German philosopher.
These 38 Stratagems are excerpts from "The Art of Controversy", first translated into English and published in 1896. Carry your opponent's proposition beyond its natural limits; exaggerate it. The more general your opponent's statement becomes, the more objections you can find against it. The more restricted and narrow his or her propositions remain, the easier they are to defend by him or her. Use different meanings of your opponent's words to refute his or her argument. (abstracted from the book:Numerical Lists You Never Knew or Once Knew and Probably Forget, by: John Boswell and Dan Starer)
This list will hopefully improve your general knowledge of mathematical tricks and your speed when you need to do math in your head. 1. Multiplying by 9, or 99, or 999 Multiplying by 9 is really multiplying by 10-1. So, 9×9 is just 9x(10-1) which is 9×10-9 which is 90-9 or 81. Let’s try a harder example: 46×9 = 46×10-46 = 460-46 = 414. One more example: 68×9 = 680-68 = 612. To multiply by 99, you multiply by 100-1. So, 46×99 = 46x(100-1) = 4600-46 = 4554. Multiplying by 999 is similar to multiplying by 9 and by 99. 38×999 = 38x(1000-1) = 38000-38 = 37962. 2. To multiply a number by 11 you add pairs of numbers next to each other, except for the numbers on the edges. Let me illustrate: To multiply 436 by 11 go from right to left. First write down the 6 then add 6 to its neighbor on the left, 3, to get 9. Write down 9 to the left of 6. Then add 4 to 3 to get 7. Then, write down the leftmost digit, 4. Impress your friends with mental Math tricks » Fun Math Blog.
See Math tricks on video at the Wild About Math!
Mathcasts page. Being able to perform arithmetic quickly and mentally can greatly boost your self-esteem, especially if you don't consider yourself to be very good at Math. And, getting comfortable with arithmetic might just motivate you to dive deeper into other things mathematical. This article presents nine ideas that will hopefully get you to look at arithmetic as a game, one in which you can see patterns among numbers and pick then apply the right trick to quickly doing the calculation. The tricks in this article all involve multiplication. Don't be discouraged if the tricks seem difficult at first.
As you learn and practice the tricks make sure you check your results by doing multiplication the way you're used to, until the tricks start to become second nature. 1. Multiplying by 9 is really multiplying by 10-1.So, 9x9 is just 9x(10-1) which is 9x10-9 which is 90-9 or 81. Octave. GNU Octave is a high-level interpreted language, primarily intended for numerical computations.
It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments. It also provides extensive graphics capabilities for data visualization and manipulation. Octave is normally used through its interactive command line interface, but it can also be used to write non-interactive programs. The Octave language is quite similar to Matlab so that most programs are easily portable. Octave is distributed under the terms of the GNU General Public License. Version 4.0.0 has been released and is now available for download. An official Windows binary installer is also available from A list of important user-visible changes is availble at by selecting the Release Notes item in the News menu of the GUI, or by typing news at the Octave command prompt. Thanks to the many people who contributed to this release!