REVIEW: "The magic of numbers"

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44

Do you think math is boring, useless, and incapable of generating interest? You may be right. However, will you remain unconvinced after reading The Magic of Numbers? This book will turn mathematics into real magic and allow you to do the most difficult calculations in your head.

The Magic of Numbers - the book that turns mathematics into magic

I really love books with a bunch of useful and accessible information. They do not need to look for the author's necessary thought between the lines, guess what he wanted to say, and try to find wisdom where it may not be. Such books are good because sometimes you just want to get as much useful information as possible and go further. After all, we are far from always interested in the author's reasoning and thoughts.

With this review, I decided to do the same as Arthur Benjamin and Michael Shermer did with their book. A maximum of useful information and a minimum of distant thoughts and reasoning. Actually, there is nothing to talk about.

Michael Shermer Editor and Columnist of Scientific American, Publisher of Skeptic Magazine (www.skeptic.com), Executive Director of the Skeptic Society and Chair of Caltech's Public Science Lecture Course. He is the author of numerous scientific books, including Why People Believe Weird Things, How We Believe, The Science of Good and Evil, The Borderlands of Science and Science Friction.

What awaits you

The authors of the book will teach you how to raise to a power, divide, multiply and perform other operations with large numbers in your mind. I’ve made sure myself that you don’t need to be a genius or have an incredible memory for numbers. It is enough just to remember the templates given by the authors and spend a little time.

Each chapter introduces new ways of calculating:

Simple mental calculations.
Oral addition and subtraction of large numbers.
The art of approximate estimation.
Memorable numbers.

How to instantly multiply any number by 11

One of the easiest tricks. In order to multiply any two-digit number by 11, it is enough to add the two extreme numbers and put their sum between them.

Example: 45 × 11.

4 + 5 = 9, put 9 between 4 and 5 and get the answer 495.

Three-digit numbers are only a little more complicated.

Example: 416 × 11.

The extreme numbers will remain in their places, that is, the answer will be 4 ∗∗ 6. In order to find the two missing digits, you need to add the first digit with the second and the second with the third. 4 + 1 = 5; 1 + 6 = 7. Answer: 4,576.

Squaring 3-digit numbers

This is a fairly complex problem that can be easily solved using a simple template.

To square a three-digit number, you need to round it up or down to get a multiple of 100.

That is, to find 193 ^ 2, you need to divide it by two numbers. Imagine one number is at the top and the other is at the bottom. The upper one needs to be rounded up to 200, adding 7, from the lower number you need to subtract the same figure that we added to the upper one, and get 186. Now you need to multiply 2 by 186 and add two zeros, and then add the square of that number to the resulting number, which we subtracted and added, that is, 7 ^ 2 = 49.

Example:193^2.

We round to a multiple of 100 and subtract the same number (7), getting two numbers - 200 and 186.
Multiply them to get 37,200 (2 × 186 = 372 and add two zeros).
Add the square of the number from the first step (7 ^ 2 = 49) and get 37,249.

It looks a little confusing, but the authors managed to convey the idea much easier, and after several solved examples, these actions are already done automatically.

The rule of thumb

To memorize numbers from 0 to 5, it is enough to bend the required number of fingers on the hand. Here's what to do if you need to memorize more numbers:

6 - place your thumb on top of your little finger;
7 - on top of the nameless;
8 - top of the middle;
9 - on top of the index.

Accordingly, using two hands, you can memorize twice as many numbers, or use one hand to memorize hundreds, and the other to memorize tens.

Some interesting calculations

Rule 70:to find the number of years it takes to double your money, divide 70 by the annual interest rate. For example, if the annual interest rate is 5%, then 70: 5 = 14 - it will take 14 years to double the amount.

Rule 110:to find the number of years it takes to triple money, divide 110 by the annual interest rate.

Output

The Magic of Numbers is an incredibly useful book for those who deal with a lot of calculations, or for those who want to impress their friends with instant calculations with three-, four- and five-digit numbers. The book contains a huge number of practical problems, and at the end of each chapter there are examples for solving. The correct answers can be found at the end of the book.

The book left a very good impression. This is one of those books in which there is so much useful information that you simply do not have time to assimilate it. Such a book should always be at hand to refresh your memory or strain your brain by solving complex problems in your mind.