Mnemonics and mental systems
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- QUICK CALCULATIONS: MENTAL ARITHMETIC
- Extraction of Square Roots
- Extraction of Cube Roots
Calling the Objects Back
When you have "accepted" the thirty objects, hand the sheet to someone who acts as "Scorer". He is to tick off every time you are right. The audience are now invited to call out ANY number from one to thirty. You immedi- ately call back the name of the object given for whatever number they say. It is very easy. As soon as you hear the number—think of your "Key" and the very moment you remember your key—you will find you also remember their object! When you do this for the first time—you will be amazed that it really works. That is all there is to it—and a very good effect can thus be performed. To conclude the performance, you may if you wish run through the complete list of objects backwards, starting from thirty. You may also have an object called here and there—and you give the correct number. One aspect of presentation that improves the effect is to enlarge in detail on one or two objects as they are given. For example, suppose at Number 8 we were asked to accept " C A T " as the object. We could say. "Any particular type of cat?" And even though you are told it is a Cheshire Cat wearing a yellow spotted cravat and dancing the Hornpipe"—you will still get it! Moreover, it adds comedy to the presentation. Such is the Amazing Memory. QUICK CALCULATIONS: MENTAL ARITHMETIC There are several methods whereby the Mentalist can render an impressive demonstration of his ability by a show of rapid calculations. The business of mentally squaring or cubing a number, or extracting the square or cube root can cause quite a stir amidst intelligent people. (1) Squaring Since it is very easy to square small numbers in the head we shall not bother to deal with anything under twenty-five. Most people, having to square say 15—could do so with little trouble. However, dealing with num- bers from twenty-five and up to a hundred (which is more than enough):— 63 For numbers from 25 to 50. First take the difference between the number and 25 for the hundreds and square the difference between the number and 50 for the tens and units. As for example, to square 39:— The difference between 25 and 39 is 14. The number 14 gives the first two numbers of the answer. The difference between 50 and 39 is 11. Which when squared gives 121:— To 121, we add fourteen hundred from the first step, and the answer 1521 equals 39 squared. For numbers from 50 to 100. First take twice the difference between the number given and fifty for the hundreds and then square the difference between the given number and 100 for the tens and units. (2) Extraction of Square Roots The performer must first memorise the following table which shows the square of the digits one to nine:— Digit 1 2 3 4 5 6 7 8 9 Square 1 4 9 16 25 36 49 64 81 Suppose we are asked to extract the square root of the number 3136. First we consider only the two starting figures; the number nearest to 31 in the above table is 25—it must be more than 25 but not greater than 36. The table shows that 25 is represented by 5. Hence 5 will be the first figure of the square root of 3136. The last digit of this number is 6. There are two squares terminating with 6 in the above table and the number opposite them is one that will end the answer. However, we must be able to tell which of the sixes to use since one represents six and the other four. Take the answer to the first step—which was 5, multiply this by itself giving 25, deduct this from the first two figures in the original number (31) and six remains. This figure six is larger than the one we have multiplied (5) so select from the above table the larger of the two numbers terminating with six. The figure opposite then gives the second number in the root; the root of 3136 is 56. (3) Cubing To find the cube of any two figure number, you must first know or work out the cube of the units one to nine. It will pay you to learn these because they can be used for other calculating effects shown later:— Digit 1 2 3 4 5 6 7 8 9 Cube 1 8 27 64 125 216 343 512 729 Suppose now you are requested to find the cube of the number 62. Cube the first figure—6 and put it down in thousands, to the left of the cube of two. That is of six, 216, and of two, 8, which equals 216,008. To this add the product of:— 62 x 6 x 2 x 3. i.e. 62 x 36. equals 2232. Place this under the first number, moving the units figure one step to the left and add the two lines together. 62. 216008 2232 (62 x 6 x 2 x 3 equals 2232) 238,328 equals 62 CUBED. 64 (4) Extraction of Cube Roots Of the various calculating systems given so far, this is probably the most effective and oddly enough, the easiest. The table shown for Cubing Numbers is used and it can be made to reveal the cube root of any number from one to a hundred. For higher numbers, the extraction of cube roots of numbers resulting in more than a hundred, it is only necessary to add noughts to the cubes accordingly. Ask a member of your audience to work out the cube of any number (say "Two figure number") under one hundred. Suppose their answer came to 804,357. To find the number cubed is very simple:— Refer to the table for Cubing. The first three figures are 804—greater than 729, the highest possible number. 729 represents the unit 9, so this will be the first figure in the answer. Next take the last number in the total given by the audience—7. Find the cube which ends with seven in the table, it is 27—represented by three—so 3 will be the last figure of the answer. Therefore the cube root of 804,357 is 93. Download 368.41 Kb. Do'stlaringiz bilan baham: |
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