About the author of this book, arthur benjamin, Baidu and "12 magic math class" have not introduced it. I will only share with you the information I have learned. arthur benjamin is a TED speaker, a math magician and the author of many popular math books. The picture below shows arthur benjamin's speech at a TED. His super-fast speech speed, quick thinking and quick calculation ability surprised the audience.
Two. Content introduction
Chapter 1 2 of the book *** 12 introduces the dance of numbers, magic algebra, magic number "9", delicious and fun permutation and combination, cool Fibonacci sequence, eternal mathematical theorem, geometry with wide brain opening, endless π, multi-purpose trigonometry, I and E outside the box, calculus with fast thinking and slow thinking. In the preface, the author makes some reading rules, such as skipping unread content, skimming chapters and paragraphs, and reading necessary chapters. Show the magic of numbers themselves and explore the mystery behind magical phenomena. The equation of God mentions: 0, 1 arithmetic. Basically, the important number of π geometry, e is the most important number in calculus, and I is the square root of-1. I hope all people who like mathematics and have a phobia about mathematics are crazy about mathematics.
Three. Wonderful sharing
In the dance of numbers in chapter 1, the author mentioned Gaussian summation: find the sum of all numbers from 1 to 100. Gauss divides all numbers between 1 and 100 into two lines, the first line is 1 to 50, and the next line is 5 1 to 100. Gauss found that the sum of two numbers in each column is equal to 10 1, so the sum of all numbers is 50× 10 1, which is equal to 5050. This process is represented by a chart. It can be represented by small circles, and these small circles can be arranged in triangles, so we call these numbers "triangular numbers". If two triangles are arranged side by side to form a rectangle, then the number of small circles contained in each triangle should be rectangular 1/2.
In the second chapter "Magic Algebra", the author mentioned how to quickly calculate the product of two numbers slightly less than 100 and the algebraic identity behind it. For example: 96× 97 = (100–4) (100–3) = (100× 93)+(–4 )× (–3) = 9 300+12 =
In practical application, I only look at the last digit of two numbers, which is 6+7 in this example, which means that the last digit of this number multiplied by 100 is 3, so I know this number must be 93. And after mastering this method skillfully, we don't need to calculate the product of two negative numbers, but directly take their positive values and then find their products. In practice, we can use this method to complete the multiplication of any two similar numbers.
In the magic number "9" in the third chapter, the author mentioned the nine-discard method and the operations of addition, subtraction, multiplication and division. () Throw out nine: Add the numbers of a number and repeat this step until you get a number root. The method of discarding nine has an interesting application, which can be used to check whether the number of addition, subtraction, multiplication and division operations is correct. Let's take multiplication as an example: the multiplied two numbers can be written as 9x+5 and 9y +6, where x is an integer. (9x+5) (9y+6) = 81xy+54x+45y+30 = 9 (9xy+6x+5y)+30 = multiples of 9+(27+3) = multiples of 9+3.
The fourth chapter introduces factorial in delicious and interesting permutation and combination. The author thinks that n! The symbol ""means factorial is very suitable, because factorial grows very fast and has many exciting or surprising applications. As follows:
000! = 1
00 1! = 1
002! = 2
003! = 6
004! = 24
005! = 120
006! = 720
007! = 5 040
008! = 40 320
020XX！ = 362 880
0 10! = 3 628 800
0 1 1! = 39 9 16 800
0 12! = 479 00 1 600
0 13! = 6 227 020 800
How big are these figures? It is estimated that there are about 10 22-power gravel in the world, and there are about 10 80-power atoms in the whole universe. There are 52 cards in a deck of playing cards (excluding kings and kings), so there are 52 cards! This arrangement, so the arrangement you see may be unprecedented. Assuming that everyone on the earth washes their cards every minute, they may never see the previous arrangement again in the next 6,543,800 years.
Four. reaction to a book or an article
1, the more you learn, the less you learn. As the ancients said, learning is more and more harmful. Sometimes learning mathematics is for Tao. take for example
Modular operation: any positive integer m, if the difference between a and b is an integer multiple of m, then we say that if a and b are all equal to the modular m, it is recorded as a ≡ b (mod m). Using modular operation, we can solve the characteristics of divisible numbers of some special numbers and greatly save the working memory of the brain.
2. Mental arithmetic should be worth popularizing. In fact, many students with poor academic level in mathematics study hard, not only solving problems, but also calculating! Calculate!
3. Teaching should let children see the value of learning mathematics. The real use value, not the preaching of learning significance: examination! Go to school!