Interesting mathematical knowledge (1) In our concept, "1" is the smallest number, the first number of an integer, and the head of a million. Yes, "1" is the head of tens of thousands, and its position is also the most special. Let's meet this magic number with me.
First, the smallest number.
The ancient and huge family of natural numbers consists of all natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The smallest one is "1", and the largest one can't be found. You can look for it if you are interested.
Second, there is no maximum natural number.
Maybe you think you can find a largest natural number (n), but you will immediately find another natural number (n+ 1) greater than n, which means that you will never find the largest natural number in the family of natural numbers.
Third, "1" is indeed the smallest in the family of natural numbers.
The natural number is infinite, and "1" is the smallest of the natural numbers. Some people disagree that "1" is the smallest natural number, saying that "0" is smaller than "1" and "0" should be the smallest natural number. This is wrong, because natural numbers refer to positive integers, and "0" is the only non-positive non-negative integer, so "0" does not belong to the family of natural numbers. "1" is indeed the smallest in the family of natural numbers.
Don't underestimate the smallest "1", which is the unit of natural numbers and the' first generation' of natural numbers. Humans first recognized "1", and only by using "1" can we get 1, 2,3,4. ...
I told you the special status of "1", which is the first in a thousand miles. Don't underestimate it.
Interesting math story (2) Speaking of the role of math, we can't finish talking for a day and a night. Without math, our life is very inconvenient. So, do you know what mathematics can do in daily life besides simple operations? Can you solve a case like a policeman? Yes, if you don't believe me, look at how Robin Hood solved the case with mathematics.
There is an ancient castle left over from the Middle Ages on the outskirts of Paris, almost as old as the famous Notre Dame de Paris, so it has become a tourist attraction and attracted tourists from all over the world. The following story comes from a tour guide.
There is a dusty bell tower on the top floor of the castle, where a strange man lives. The only access to the outside world is a creaking, steep and abnormal wooden staircase, with dozens of steps, but certainly less than 100.
One night, Alexei, Barton, Kling and Dupont, four strange strangers, visited at almost the same time. They found that the weirdo had been killed and the room looked terrible. The four people present were frightened to disgrace and rushed to escape. Running down the messy narrow stairs (only one person can pass at a time), Alexei went down two steps, Barton went down three steps, Kling went down four steps, DuPont was the most capable, and he could go down five steps.
After the accident, Arsene Robyn disguised as a decent gentleman in the upper class and volunteered to solve the case. He found the steps with four people's footprints printed at the same time, only in the highest and lowest places.
In order to trace the murderer, it is difficult to do it if the footprints are chaotic, so Arsène Lupin pays special attention to the steps with only one person's footprints. Later results fully proved that his point of view was correct, and finally the murderer was caught and brought to justice.
What I want to ask you now is, how many steps on the wooden stairs leading to the bell tower are only printed with one person's footprints (no matter who)?
Answer:
Because the multiple of 4 must be a multiple of 2, Kling's situation can be ignored, thus saving one person. The least common multiple of 2, 3, 4 and 5 is 60, and 60 is less than 100, so the wooden stairs of the bell tower have 60 steps.
Alexei's footprints fall on the 2nd, 4th, 6th, 8th, l0, 12, …, 58th and 60th steps, but the steps of 2×3 and its multiples should be excluded. Similarly, it is necessary to exclude ladders at all levels with a multiple of 4 and ladders at all levels with a multiple of 5. So there are 2 14, 22, 26, 34, 38, 46, 58 * * levels left. Its general form is 2×p (where p= 1 and prime numbers other than 2, 3 and 5).
Barton's footprints fall on the 3rd, 6th, 9th, 12, …, 60th steps, but the 6th, 12, 15, 18, … steps are mixed with others' footprints and should be excluded, leaving the 3rd, 9th and 60th steps.
I have said that Kling's situation can be ignored. Finally, let's look at DuPont's situation. Obviously, the steps that only left his footprints were level 5, 25, 35, 55 and * * * 4.
So the answer to the question is 8+8+4=20.
Introduction to Mathematicians (III) C.F. Gauss is a famous mathematician, physicist, astronomer and geodetic scientist in Germany. Known as the prince of mathematics, he is one of the greatest mathematicians in history, as well as Archimedes, Newton and Euler.
Hua (1910.1.12-1985.6.12. ), a world-famous mathematician, has studied China's analytic number theory, matrix geometry, canonical group, self-safety function theory and many other aspects. The international mathematical research achievements named after Fahrenheit include Fahrenheit theorem, Huai-Hua inequality, Fahrenheit inequality, Prawell-Gardiner theorem, Fahrenheit operator, Hua-Wang method and so on.
Chen Jingrun (1May 22, 933 ~1March 9 1996), Han nationality, was born in Fuzhou, Fujian. China famous mathematician, graduated from Xiamen University. The publication of 1966 "Representing Even Numbers as the Sum of the Products of One Prime Number and No More than Two Prime Numbers" (referred to as "1+2") became a milestone in the study of Goldbach's conjecture. And his published results are also called Chen Theorem. () This work also won him, Wang Yuan and Pan Chengdong the first prize of China Natural Science Award with 1978 * *. 1999, China issues stamps to commemorate Chen Jingrun. Purple Mountain Observatory named a planet "Chen Jingrun Star" to commemorate it. Other related film and television works are named after Chen Jingrun.
Hua (191010 12-1June 198512), Han nationality, a world-famous mathematician, China's analytic number theory, matrix geometry, etc. The international achievements in mathematical research include Fahrenheit Theorem, Huai-Hua Inequality, Fahrenheit Inequality, Pu Lawwill-Gardiner Theorem, Fahrenheit Operator, Hua-Wang Method and so on. He made outstanding contributions to the development of mathematics in China. The famous American mathematician Bateman wrote: "Hua is China's Einstein, and he is enough to be an academician of all the famous academies in the world.". It is listed as one of the 88 great mathematicians in the world in the Chicago Museum of Science and Technology.
Interior Angle of Triangle and ④ Professor Chen Shengshen, an American Chinese, is a world-famous mathematician. He was surprised by a lecture at Peking University:
"People often say that the sum of the internal angles of a triangle is equal to 180 degrees. However, this is wrong! "
Everyone was shocked. What's going on here? The sum of the internal angles of a triangle is 180 degrees. Isn't this common sense in mathematics?
Then, the old professor gave an incisive answer to everyone's question: "It is wrong to say that the sum of the internal angles of a triangle is 180 degrees, not that this fact is wrong, but that this way of looking at the problem is wrong. It should be said that the sum of the outer angles of the triangle is 360 degrees. "
"Look at the inside corner, we can only see:
The sum of the internal angles of the triangle is 180 degrees;
The sum of the internal angles of the quadrilateral is 360 degrees;
The sum of the internal angles of the Pentagon is 540 degrees;