As early as 65,438+05,000 years ago, human beings have been able to describe the images of people and animals quite realistically. This is the earliest evidence of the germination of graphic consciousness. Later, it gradually began to pursue circles and straight lines, thus becoming the earliest prototype of mathematical graphics. In daily life and production practice, counting consciousness and counting system have gradually emerged. Humans have explored a variety of counting methods, including knotting with ropes at first, counting with stones, and further expressing language points with symbols, and gradually developing into the numbers we use today. When graphic consciousness and counting consciousness develop to a certain extent, measurement consciousness appears.
This series of development and evolution has gradually formed a complete mathematical discipline that we are familiar with today, including arithmetic, geometry, algebra, trigonometry, calculus, statistics and probability (in fact, it was originally for people to study gambling) ... and so on, and it is still developing.
Since the age of ignorance, human beings have been able to identify the number of things. Primitive people first noticed the difference in quantity between one sheep and many sheep, one wolf and a whole group of wolves in production activities such as gathering and hunting. By comparing a sheep with many sheep, a wolf with a whole group of wolves, they gradually saw something between a sheep, a wolf, a fish, a tree and so on (that is, their oneness).
Ancient counting methods:
1. Finger counting: use ten fingers of both hands. Aristotle pointed out that the decimal system is widely used.
It's just that most of us are born with 10 fingers.
2. Counting stones: Small stones are placed on the ground, but the counted piles are difficult to keep for a long time.
3. Make a knot number: tie a knot on the rope to indicate the number of things. For example, if you hunted five sheep today, would you
It is represented by tying five knots on the rope; If we meet again in three days, we will tie three knots on the rope and untie one knot a day. Wait a minute.
In ancient times (BC 1500 years ago), the Incas in Peru tied a knot on a rope to record the harvest.
There is a saying in the ancient Chinese literature "Zhouyi Xiexia" called "tying knots to rule the ancient times", that is, making a settlement or remembering knots.
This method of knotting and counting not only existed in ancient times, but also has been used by some ethnic groups. Song people said in a book: "Tatars have nothing to say. Every time they send troops, they make promises, which makes people eager for sparks." This is to send his troops by tying knots to convey the number of people to be transferred.
Others, such as Tibetans and Yi people, have written characters, but they still use this method for a long time among illiterate people. Minzu University of China has a pair of knots of Gaoshan nationality, which are composed of two ropes: each rope has two knots, and then the two knots are tied together.
4. notation: 1937 A wolf cub was found in Vestanis (Moravia) 400,000 years ago.
Limb bone, 7 inches long, with 55 deep notches on it. This is the earliest data found to be counted by the gap method. To this day, in some parts of Europe, Asia and Africa, there are still some shepherds who count their livestock with the scores on sticks.
It was not until about 5000 years ago that the writing and counting system finally appeared. We introduce several early counting systems of ancient civilizations (in chronological order).
1. hieroglyphics of ancient Egypt (about 3400 BC)
2. Babylonian cuneiform (about 2400 BC)
3. China Oracle Bone Inscriptions Numbers (about 65438 BC+0600 BC)
4. Greek Attica Numbers (about 500 BC)
5. China plans to calculate figures (about 500 BC)
6. Indian Brahmin Numbers (about 300 BC)
7. Maya numbers (? )
However, Arabic numerals are widely used in modern times. In fact, these Arabic numerals were not invented by Arabs, but originated in ancient India. Later, it was mastered, improved and spread to the west, and westerners called it Arabic numerals. Later, the whole world recognized this statement.
Just like the formation of the concept of numbers, the initial geometric knowledge of human beings germinated from the intuition of shapes. For example, people of different races have noticed the image difference between the full moon and the tall and straight pine trees. Geometry is based on the summary of this "shape" extracted from nature. For example, a plane is just a plane, and a straight line is an elongated rope. The original meaning of hypotenuse (hypotenuse, chord) comes from Greek and is "tension". Similarly, a series of geometric concepts such as triangle, circle, square and rectangle also come from people's observation and practice.
In different regions, the source and direction of this practice of geometry are different.
1. Ancient Egyptian geometry: Herodotus, an ancient Roman historian, pointed out that Egypt's geometry was "Ni"
Gift of Luohe. The annual Nile flood washed away someone's land, so he had to go.
The Pharaoh reported the losses suffered. Pharaoh will send someone to measure the lost land and then reduce the tax accordingly. In this way, geometry came into being and developed. This person in charge of measuring things has a special name, called "Si Rope".
2. Babylonian geometry: it is also derived from the actual measurement, and its important feature is the arithmetic nature.
As early as 1600 BC, they were familiar with the area calculation of rectangles, right triangles, isosceles triangles and some trapeziums.
3. Ancient Indian geometry: Its origin is closely related to religious practice, and it was formed from the 8th century BC to the 5th century BC.
Rope Sutra is a record of geometric problems and their solving rules in altar and temple buildings.
4. Ancient geometry of China: its origin is more related to astronomical observation. China's earliest mathematical classic "Zhou"
The Book of Calculations (written at the latest in the 2nd century BC) is actually a book on the mathematical methods used in astronomical survey in the early years of the Western Zhou Dynasty.