The author of Calculation of Special Velocity is Russian mathematician Jack trachtenberg (1888- 1953). It is said that during World War II, he was imprisoned in [Na? In concentration camps and prisons, he developed this mental arithmetic. This algorithm was later named Trachtenberg's fast computing system.
If you want to study systematically, you can also have a deep look at the English version of Trachtenberg Speed System of Basic Mathematics, which was edited by Ann Cutler and Rudolf paul mcshane.
Here, I'll make a basic introduction first and sort it out for you. Generally speaking, according to the following:
The traditional method is familiar to everyone. Take the title made by McKenna Grace in the movie.
If this step is disassembled in detail, it should be like this:
Obviously, as an ordinary person, if you want to do mental arithmetic in this way in your brain, the most difficult thing should be two points:
Because there are too many, it's easy to get confused. In order to solve this problem, trachtenberg came up with this set of ultra-fast calculations, which solved the problems of too much computation and alignment at one time.
He divided the intermediate calculation process into steps, and each step only did multiplication and addition of single digits, so it was easy to temporarily memorize these intermediate calculation results in his brain.
Let's take the example that the multiplier above is a two-digit number and look at its calculation steps in an ultra-fast way.
The specific operation process and memory method of the brain are shown in the following figure (everyone has his own memory method, and here is a schematic diagram for your reference):
Let's start the ultra-fast calculation from the end back, and only pay attention to the bits currently calculated.
We use solid points to represent the indicated calculation and extract the unit of the multiplication result (value: 5 in the figure below).
We use hollow points to indicate the calculation and extract the ten digits of the multiplication result. That is, the last calculated ten digits (such as the value in the above figure: 3).
Finally, add up the numbers temporarily stored in the brain and put them at the top of the final result (maybe 0? , you don't have to put it).
Then use associative memory to arrange a story for the final result:
Imagine the picture in your mind, right? .
Take the above example where the multiplier is three digits, and continue to look at its calculation steps through ultra-fast calculation.
Let's start the ultra-fast calculation from the end back, and only pay attention to the bits currently calculated.
Using the above method, the following steps 5 and 6 are analogized in turn.
Next, let's look at slightly different steps 7 and 8.
Finally, add up the numbers temporarily stored in the brain and put them at the top of the final result (maybe 0? , you don't have to put it).
Then use associative memory to arrange a more vivid story for the final result:
Of course, you can also make up a new story based on two-digit homophones (the more interesting it is, the better):
Once again, imagine the picture in your mind, right? In this way, you will remember the final result.
Through the above steps, it is much easier to look at the commonly used two-digit multiplication after mastering the ultra-fast calculation method. For example, buying pork, 23 yuan/kg, weighs about 3.8 kg. How much will it cost? Obviously, there are three quick steps:
Look, honey, it's almost 100 yuan. Buy less, I can't afford it, I can't afford it. ...
Of course, this is too simple and does not have to be calculated at a special speed. For example, if I calculate the gross weight as 4 Jin and subtract 2 Liang, it will be 23× 4-23× 0.2 = 92-4.6 = ￥ 87.4, and I can work it out soon. But if it is a 3-digit operation, this simple mental arithmetic is not suitable. Therefore, it is necessary to flexibly use various quick calculation methods according to the situation.
Well, this is the basic ultra-fast calculation method. Anyway, it takes more practice to use it skillfully. In addition, in the book "Trachtenberg Speed System of Basic Mathematics", the calculation methods of various special multipliers (such as: × 1 1, etc. ), can be further discussed. I'll give you a supplementary introduction when the back is free.