In life, we often use the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Do you know who invented these numbers?
These digital symbols were first invented by ancient Indians and later spread to Arabia and Europe. Europeans mistakenly thought it was invented by Arabs, so they called it "Arabic numerals". Because they have been circulating for many years, people still call them Arabic numerals, so people still get them wrong.
Now, Arabic numerals have become the universal numeric characters all over the world.
multiplication table
Jiujiuge is the multiplication formula we use now.
As early as the Spring and Autumn Period and the Warring States Period BC, Jiujiu songs have been widely used by people. In many works at that time, there were records about Jiujiu songs. The original 99 songs started from "99.8 1" to "22.24", with 36 sentences. Because it started with "998 1", it was named 99 Song. The expansion of Jiujiu Song to "One for One" was between the 5th century and10th century. It was in the 13 and 14 centuries that the order of Jiujiu songs became the same as it is now, from "one for one" to "9981".
At present, there are two kinds of multiplication formulas used in China. One is a 45-sentence formula, usually called "Xiao Jiujiu"; There is also a sentence 8 1, which is usually called "Big Uncle Nine".
The origin of mathematical symbols
Besides counting, mathematics needs a set of mathematical symbols to express the relationship between number and number, number and shape. The invention and use of mathematical symbols are later than numbers, but they are much more numerous. Now there are more than 200 kinds in common use, and there are more than 20 kinds in junior high school math books. They all had an interesting experience.
For example, there used to be several kinds of plus signs, but now the "+"sign is widely used.
+comes from the Latin "et" (meaning "and"). /kloc-in the 6th century, the Italian scientist Nicolo Tartaglia used the initial letter of "più" (meaning "add") to indicate adding, and the grass was "μ" and finally became "+".
The number "-"evolved from the Latin word "minus" (meaning "minus"), abbreviated as m, and then omitted the letter, it became "-".
/kloc-In the 5th century, German mathematician Wei Demei officially determined that "+"was used as a plus sign and "-"was used as a minus sign.
Multipliers have been used for more than a dozen times, and now they are commonly used in two ways. One is "x", which was first proposed by British mathematician orcutt on 163 1; One is "",which was first created by British mathematician heriott. Leibniz, a German mathematician, thinks that "×" is like the Latin letter "X", so he opposes it and agrees to use "×". He himself proposed to use "п" to represent multiplication. But this symbol is now applied to set theory.
/kloc-In the 8th century, American mathematician Audley decided to use "×" as the multiplication symbol. He thinks "×" is an oblique writing of "+",which is another symbol of increase.
""was originally used as a minus sign and has been popular in continental Europe for a long time. Until 163 1 year, the British mathematician Orkut used ":"to represent division or ratio, while others used "-"(except lines) to represent division. Later, in his book Algebra, the Swiss mathematician Laha officially used "∫" as a division symbol according to the creation of the masses.
/kloc-in the 6th century, the French mathematician Viette used "=" to indicate the difference between two quantities. However, Calder, a professor of mathematics and rhetoric at Oxford University in the United Kingdom, thinks that it is most appropriate to use two parallel and equal straight lines to indicate that two numbers are equal, so the symbol "=" has been used since 1540.
159 1 year, the French mathematician Veda used this symbol extensively in Spirit, and it was gradually accepted by people. /kloc-In the 7th century, Leibniz in Germany widely used the symbol "=", and he also used "∽" to indicate similarity and ""to indicate congruence in geometry.
Greater than sign ">" and less than sign "
Wonderful circle
The circle is a seemingly simple, but actually wonderful circle.
The ancients first got the concept of circle from the sun and the moon on the fifteenth day of the lunar calendar. /kloc-Neanderthals 0/8000 years ago used to drill holes in animal teeth, gravel and beads, some of which were round.
Later, in the pottery age, many pottery were round. Round pottery is made by putting clay on a turntable.
When people start spinning, they make round stones or ceramic cocoons.
The ancients also found that rolling logs was more economical. Later, when they were carrying heavy objects, they put some logs under big trees and stones and rolled them around, which was of course much more labor-saving than carrying them.
About 6000 years ago, Mesopotamia made the world's first wheel-a round board. About 4000 years ago, people fixed round boards under wooden frames, which was the original car.
You can make a circle, but you don't necessarily know its nature. The ancient Egyptians believed that the circle was a sacred figure given by God. It was not until more than 2,000 years ago that China's Mozi (about 468- 376 BC) defined the circle: "One China has the same length". It means that a circle has a center and the length from the center to the circumference is equal. This definition is 100 years earlier than that of the Greek mathematician Euclid (about 330 BC-275 BC).
Pi, the ratio of circumference to diameter, is a very strange number.
The Book of Weekly Calculations says that "the diameter is three times a week", and pi is considered to be 3, which is only an approximate value. When the Mesopotamians made the first wheel, they only knew that pi was 3.
In 263 AD, Liu Hui of Wei and Jin Dynasties annotated Nine Chapters of Arithmetic. He found that "the diameter is three times that of a week" is just the ratio of the circumference to the diameter of a regular hexagon inscribed in a circle. He founded secant technology, and thought that when the number of inscribed sides of a circle increased infinitely, the circumference was closer to the circumference of a circle. He calculated the pi of a regular 3072 polygon inscribed in a circle = 3927/1250. Liu Hui applied the concept of limit to solving practical mathematical problems, which is also a great achievement in the history of mathematics in the world.
Zu Chongzhi (AD 429-500) continued to calculate on the basis of predecessors' calculations, and found that pi was between 3. 14 15926 and 3. 14 15927, which was the earliest numerical value accurate to seven decimal places in the world. He also used two decimal values to express pi: 22/7 is called about.
In Europe, it was not until 1000 years later16th century that the Germans Otto (A.D. 1573) and Antoine Z got this value.
Now that there is an electronic computer, pi has been calculated to more than 10 million after the decimal point.
From one to one hundred
At the age of seven, Goss entered St. Catherine's Primary School. About ten years old, the teacher had a difficult problem in the arithmetic class: "Write down the integers from 1 to 100, and then add them up!" Whenever there is an exam, they have this habit: the first person who finishes it puts the slate face down on the teacher's desk, and the second person puts the slate on the first slate, thus falling one by one. Of course, this question is not difficult for people who have studied arithmetic progression, but these children are just beginning to learn arithmetic! The teacher thinks he can have a rest. But he was wrong, because in less than a few seconds, Gauss had put the slate on the lecture table and said, "Here's the answer! Other students added up the numbers one by one, sweating on their foreheads, but Gauss sat quietly, ignoring the contemptuous and suspicious eyes cast by the teacher. After the exam, the teacher checked the slate one by one. Most of them were wrong, so the students were whipped. Finally, Gauss's slate was turned over and there was only one number on it: 5050 (needless to say, this is the correct answer. The teacher was taken aback, and Gauss explained how he found the answer:1+100 =1,2+99 =10/,3+98 =/kloc-. A * * * has 50 pairs, and the sum is 10 1, so the answer is 50 × 10 1 = 5050. It can be seen that Gauss found the symmetry of arithmetic progression, and then put the numbers together in pairs, just like the general arithmetic progression summation process.
pythagorean theorem
Pythagorean Theorem: In any right triangle, the sum of the squares of two right-angled sides must be equal to the square of the hypotenuse.
This theorem is also called "quotient height theorem" at home and "Pythagoras theorem" abroad. Why does a theorem have so many names? Shang Gao was a native of China in 1 1 century BC. At that time, China's dynasty was the Western Zhou Dynasty, which was a slave society. In ancient China, a dialogue between Shang Yang and Duke Zhou was recorded in Zhou Pian Shu Jing, a mathematical work of the Western Han Dynasty during the Warring States Period. Shang Gao said, "... so the moment is folded, the stock is repaired four times, and the angle is five times." What is "hook, stock"? In ancient China, people called the upper part of an arm bent at right angles "hook" and the lower part "thigh". Quotient height means that when two right-angled sides of a right-angled triangle are 3 (short side) and 4 (long side) respectively, the radius angle (chord) is 5. In the future, people will simply refer to this fact as "hooking three strands, four strings and five". Because the content of Pythagorean theorem was first seen in the text of quotient height, people call this theorem "quotient height theorem". Pythagoras was an ancient Greek mathematician. He was born in the 5th century BC, more than 500 years later than Shang Gao. Another mathematician in Greece, Euclid (who lived around 300 BC), thought that this theorem was first discovered by Pythagoras when compiling the Elements of Geometry, so he called this theorem "Pythagoras Theorem" and spread it from now on.
Regarding the discovery of Pythagorean theorem, Zhou said: "So, Yu ruled the world because of the birth of this number." "This number" refers to "hooking three strands, four chords and five", which means that Dayu discovered the relationship between hooking three strands, four chords and five when he was controlling water.
Pythagorean theorem is widely used. Another ancient book in the Warring States period in China, Twelve Notes on the Postscript of the History of the Road, recorded this: "Yu ruled the flood and decided to flow in the rivers, watching the shape of mountains and rivers, and decided to compete. In addition to catastrophic disasters, the East China Sea is flooded and there is no danger of drowning. " In order to control the flood, Dayu decided the direction of the water flow according to the height of the terrain, guided the situation to make the flood flow into the sea, so that there would be no more flood disaster. This is the result of applying Pythagorean theorem.
Silence is better than sound.
There is no lack of artistic conception in mathematics that silence is better than sound. 1903, at a mathematics report meeting in new york, mathematician Le Ke stepped onto the platform. He didn't say a word, but wrote down the calculation results of two numbers on the blackboard with chalk. One is the 67th power of 2- 1, and the other is19370721× 7665438+. Why is this?
Because Lecco has solved the problem that has been unclear for 200 years, that is, 2 is the power of 67-is1a prime number? Since it is equal to the product of two numbers, it can be decomposed into two factors, thus proving that 2 is the power of 67-1is not a prime number, but a composite number.
Cole only gave a short silent report, but it took him three years to reach a conclusion on all Sundays. The courage, perseverance and hard work contained in this simple formula are more attractive than the voluminous report.
Why are the units of time and angle in hexadecimal? The unit of time is hours, and the unit of angle is degrees. On the surface, they are completely irrelevant. However, why are they all divided into small units with the same names as parts and seconds? Why do they all use hexadecimal? When we study it carefully, we will know that these two quantities are closely related. It turns out that ancient people had to study astronomy and calendars because of the needs of productive labor, which involved time and angle. For example, to study the change of day and night, it is necessary to observe the rotation of the earth, where the angle of rotation is closely related to time. Because the calendar needs high precision, the unit of time "hour" and the unit of angle "degree" are too large, so we must further study their decimals. Both time and angle require its decimal units to have the properties of 1/2, 1/3, 1/4, 1/5, 1/6, etc. Can be an integer multiple of it. The unit of 1/60 has exactly this property. For example: 1/2 equals 30 1/60, 1/3 equals 20 1/60, 1/4 equals 15 1/60 ... Mathematics. The unit of 1/60 of1is called "second", which is indicated by the symbol "". Time and angle are expressed in decimal units of minutes and seconds. This decimal system is very convenient in representing some numbers. For example, 1/3, which is often encountered, will become an infinite decimal in decimal system, but it is an integer in this carry system. This hexadecimal decimal notation (strictly speaking, the sixty abdication system) has been used by scientists all over the world for a long time in the astronomical calendar, so it has been used until today.
Goldbach conjectures that Goldbach C. (1690.3.18 ~1764.438+01.20) is a German mathematician. In the letter 1742 to Euler on June 7th, Goldbach put forward a proposition that any odd number greater than 5 is the sum of three prime numbers. But how can this be proved? Although the above results are obtained in every experiment, it is impossible to test all odd numbers. What is needed is general proof, not individual inspection. "Euler wrote back and put forward another proposition: any even number greater than 2 is the sum of two prime numbers. But he also failed to prove this proposition. Now, these two propositions have been collectively called Goldbach conjecture for more than 200 years. Although many mathematicians have worked hard to solve this conjecture, it is still a proposition that has not been positively proved or refuted.
That's enough. Choose for yourself.