1. A little knowledge of mathematical measurement
A little knowledge of mathematical measurement 1. Elementary school mathematical graphics and measurement knowledge points
(1) Rectangle 1. Characteristics: The six faces are all rectangles (sometimes two opposite faces are squares). The areas of the opposite faces are equal, and the lengths of the 4 opposite edges of the 12 edges are equal. There are 8 vertices. The lengths of the three edges that intersect at one vertex are respectively They are called length, width, and height. The edge where two faces intersect is called an edge. The point where three edges intersect is called a vertex. If you put the cuboid on the table, you can only see three faces at most. The total area of ??the 6 faces of the cuboid or cube, It is called its surface area. 2. Calculation formula s=2(ab ah bh) V=sh V=abh (2) Cube 1. Characteristics: The six faces are all squares. The areas of the six faces are equal and there are 12 edges. The edge lengths are all A cube with 8 equal vertices can be regarded as a special cuboid 2. Calculation formula S table = 6a? v=a? (3) Cylinder 1. Understanding of the cylinder The upper and lower surfaces of the cylinder are called the base. The cylinder has a curved surface called the side. The distance between the two bases of the cylinder is called the height. Further method: In practice, the materials used are much larger than the calculation The result is more. Therefore, when you want to retain the number, if the omitted digit is 4 or smaller than 4, you must advance it by 1 to the previous digit. This method of approximation is called the one-step method. 2. Calculation formula s Side = ch s table = s side s base * 2 v = sh/3 (4) Understanding of cones The base of a cone is a circle, and the side of the cone is a curved surface. The distance from the vertex of the cone to the center of the bottom is the height of the cone. Measure the height of the cone: First lay the bottom of the cone flat, place a flat plate horizontally on the top of the cone, and measure the distance between the flat plate and the bottom vertically. Expand the side of the cone to get a fan shape. 2 Calculation formula v= sh/3 (5) Sphere 1. Recognize that the surface of the sphere is a curved surface, which is called a sphere. A sphere is similar to a circle and has a center, represented by O. The line segment from the center of the sphere to any point on the sphere is called a sphere. The radius of , represented by r, each radius is equal. The line segment that passes through the center of the sphere and both ends are on the surface of the sphere is called the diameter of the ball, represented by d. Each diameter is equal, and the length of the diameter is equal to 2 times the radius, That is d=2r. 2 Calculation formula d=2r.
2. What basic knowledge should you know when you first learn surveying?
If you just learn surveying, it depends on whether you want to go into this major. If not, you only need to memorize some formulas and software. The operation and use of the instrument are fine.
But if you want to pursue this major and plan to study in depth for a living, it is recommended that you have a good foundation in mathematics. What we are exposed to is data, especially trigonometric functions and advanced mathematics. Of course, learn computers.
You need to know computer programming languages. Many software are very good, but are powerful and slow to run, and are not suitable for your engineering project. You need to write some small plug-ins and small software to help you calculate data.
Generally successful surveyors have good computers. Office software is also very necessary. The production of design documents and calculations using tables are all elementary things and require time to be thoroughly understood.
In short, when you first learn to measure, you must follow the teacher or master in a solid manner, do more, calculate more, and ask more questions. In actual production, all factors need to be taken into consideration. You cannot be stupid and have to be flexible and smart.
Keep in mind that 60 cents is long live and one more crime is needed to maximize economic benefits. There are many formulas in measurement, but when you understand the basic things, you will find that everything remains the same. The principle is to deal with mathematics, physics, etc. The key is that you must have a clear mind and must not be confused. ...Then I wish you success on this road.
Another key point is that you must be able to endure hardship! ! ! Give me the best, it’s not easy for me either. The writing is relatively general, Haihan.
3. What knowledge do you need to learn to measure?
Mathematical knowledge: As long as you know trigonometric functions and have junior high school mathematical knowledge, preferably high school mathematical knowledge
Measurement The books you need to learn professionally are:
Surveying (preferably published by Wuchai) mainly learns the basic knowledge of measurement,
Control measurement: mainly learns how to lay out control networks and complex How to calculate the control network
Engineering surveying: mainly learn how to measure and stake out. This book includes knowledge about setting out roads, houses, underwater surveys, etc.
You also need to buy a PC4850 or pc5800 for calculation This calculator can be programmed. With the basic knowledge of measurement, you can use the formulas of basic knowledge to program. After programming, you can directly calculate the results you want by simply entering the coordinates
4. Ask for some mathematics Little knowledge must be within 200 words. More than 100 words, or don’t answer
The Origin of Mathematical Symbols In addition to counting, mathematics also needs a set of mathematical symbols to express the relationship between numbers and numbers, numbers and shapes. Relationships. Mathematical symbols were invented and used later than numbers, but there are much more of them. There are more than 200 commonly used ones now, and there are more than 20 in junior high school mathematics books. They all have an interesting experience. For example, the plus sign once had a good Several types are now commonly used as "" numbers."" numbers evolved from the Latin "et" (meaning "and"). In the 16th century, the Italian scientist Tartaglia used the Italian word "più" (added) The first letter of (meaning) means plus, the cursor is "μ" and eventually it becomes "" sign. "-" sign evolved from the Latin "minus" (meaning "minus"), abbreviated as m, and then If the letter is omitted, it becomes "-". In the 15th century, the German mathematician Wei Demei formally determined: "" is used as a plus sign, and "-" is used as a minus sign. The multiplication sign has been used in more than a dozen ways, and is now commonly used. Two types. One is "*", which was first proposed by the British mathematician Ocutt in 1631; the other is "·", which was first pioneered by the British mathematician Heriot. The German mathematician Leibniz believes: " The * "sign resembles the Latin letter " In the 19th century, the American mathematician Odelay determined that "*" was used as a multiplication sign. He believed that "*" was "written with it slanted and was another symbol for increase. "÷" was originally used as a minus sign in continental Europe. It has been popular for a long time. Until 1631, the British mathematician Ocutt used ":" to express division or ratio, and others used "-" (division line) to express division. Later, Swiss mathematician Laha in his book "Algebra", It was only after mass discovery that "÷" was officially used as the division sign. In the 16th century, the French mathematician Viette used "=" to express the difference between two quantities. However, Lecauld, a professor of mathematics and rhetoric at the University of Oxford in the United Kingdom, thought: use Two parallel and equal straight lines are the most appropriate to represent the equality of two numbers, so the equal symbol "=" has been used since 1540. In 1591, the French mathematician Veda used this symbol extensively in rhombus. It was gradually accepted by people. In the 17th century, Leibniz in Germany widely used the "=" sign. He also used "∽" in geometry to express similarity, and "≌" to express congruence. Greater than sign "〉" and less than The symbol "〈" was created by the famous British algebraist Heriot in 1631. As for the three symbols ≯""≮" and "≠", they appeared much later. Braces "{ }" and square brackets "[ ]" were created by Wei Zhide, one of the founders of algebra. The origin and early development of mathematics: Mathematics, like other branches of science, developed through human social practice and production activities under certain social conditions. A kind of intellectual accumulation. Its main content reflects the quantitative relationships and spatial forms of the real world, as well as the relationships and structures between them. This can be confirmed from the origin of mathematics. The Nile River in ancient Africa, the Tigris River and the Euphrates River in Western Asia , the Indus River and Ganges River in Central and South Asia, and the Yellow River and Yangtze River in East Asia are the birthplaces of mathematics. Due to the need to engage in agricultural production, the ancestors of these areas began to control floods and irrigation, and measure the area of ????fields.
Accumulated rich experience in long-term practical activities such as product accumulation, calculating warehouse volume, calculating calendars suitable for agricultural production, and related wealth calculations, product exchanges, etc., and gradually formed corresponding technical knowledge and related mathematical knowledge.
5. Urgent need
Question: A train weighs 30 tons and a bridge can carry 20 tons. How did the train pass the bridge smoothly without taking any measures?
Answer: The driver’s bridge is short.
Interesting Math Trivia Did you know? Each of us carries several rulers with us. If the length of your "one arm" is 8 centimeters and the length of your desk is measured to be 7 inches, you will know that the length of the desk is 56 centimeters. If your steps are 65 centimeters long and you count the steps you take when you go to school, you can figure out how far it is from your home to school. Height is also a ruler. If your height is 150 centimeters, then if you hug a big tree and put your hands together, the circumference of the tree will be about 150 centimeters. Because everyone's arms are stretched out, the length between the fingertips and the height are approximately the same. If you want to measure the height of a tree, the shadow can also help you. You just need to measure the length of the tree's shadow and your own shadow. Because the height of the tree = tree shadow length * height ÷ human shadow length. why is that? You'll understand it once you learn proportions. If you are traveling and want to know how far away the mountain is from you, you can ask the voice to measure it for you. Sound can travel 331 meters per second, so if you shout at the mountain and watch for a few seconds, you can hear the echo. Multiply 331 the time it takes to hear the echo, and then divide it by 2 to calculate. Learning to use these rulers on your body will be very beneficial for you to calculate some problems. At the same time, it will also provide you with convenience in your daily life. You have to think about it! In winter, when the weather is cold and freezing, when cats and puppies sleep, they don’t lie down as we imagine, but like to curl up. So have you ever wondered why? Is it connected to mathematics? Let's first think about a familiar mathematical problem. The question is: How many different ways are there to build different cuboids using 12 small wooden cubes with an edge length of 1 cm? Through hands-on building and experimentation, 4 different building methods are obtained. Using the knowledge you have learned, you can know that the volumes of these four cuboids are equal, and their surface areas are: 50 (square centimeters), 40 (square centimeters), 38 (square centimeters), 32 (square centimeters), that is ( Figure 4) has the smallest surface area. This question shows a mathematical rule: when the volumes are equal, the more overlapping parts between small cubes, the smaller their surface area will be. According to this mathematical law, it is not difficult for us to realize that kittens and puppies like to curl up to sleep in winter. It is precisely under the condition that the volume remains unchanged, the overlapping parts of their bodies increase, thus reducing the surface area exposed to the outside, and also Even if the cold area is reduced, the heat emitted will also be reduced. Kittens and puppies curl up to sleep in winter to prevent cold and heat preservation.
6. Little knowledge about mathematics
For those primary school students with poor grades, learning primary school mathematics is very difficult. In fact, primary school mathematics is relatively basic knowledge. Many, as long as you master certain skills, it is relatively easy to master. In primary school, it is a period when good habits need to be developed. Paying attention to cultivating children's habits and learning abilities is an important aspect. So what are the skills for primary school mathematics?
1. Pay attention to listening in class and review in time after class.
The acceptance of new knowledge and the cultivation of mathematical abilities are mainly carried out in the classroom, so we must pay special attention to the classroom The efficiency of learning, looking for the correct learning method. In the classroom, we must follow the teacher’s ideas, actively formulate the following steps, think and predict the differences between the problem-solving ideas and the teacher. In particular, we must understand the basic knowledge and basic Learn skills and review them in time to avoid doubts. First of all, before performing various exercises, we must remember the teacher's knowledge points, correctly understand the reasoning process of various formulas, and try to remember rather than adopt "uncertain" Book reading ". Be diligent in thinking, try to use your brain to think about some problems, analyze the problem carefully, and try to solve the problem yourself.
2. Do more exercises and develop a good habit of solving problems.
If you want to learn mathematics well, you need to ask more questions and be familiar with the ideas for solving various problems. First, we will use the textbook topics as the standard and practice the basic knowledge repeatedly, and then find some extracurricular activities to help Develop ideas and practice to improve your analysis and master the rules of solving problems. For some easy-to-find questions, you can prepare a collection of wrong questions, write your own ideas to solve the problems, and develop a good habit of solving problems in your daily life. .Learn to concentrate highly, excite the brain, think quickly, enter the best state, and use it freely in the exam.
3. Adjust your mentality and treat the exam correctly.
First of all , the main focus should be on the basics, basic skills, and basic methods, because most tests are based on basic questions, and the more difficult questions are also based on basic questions. Therefore, the only way to adjust your learning mentality is to try to solve it with a clear mind. There is no question that is too difficult. Before the exam, you should practice the exercises more, broaden your mind, and improve the speed of doing the questions while ensuring the accuracy. For simple basic questions, you should be 20 points sure; it is rare; You should try your best to answer the questions correctly so that your level can be normal or extraordinary.
It can be seen that the skill of primary school mathematics is to do more exercises and master the basic knowledge. The other is the mentality. You cannot be timid before the exam. , it is very important to adjust your mentality. So you can follow these tips to improve your ability and enter the ocean of mathematics.
7. Second grade of elementary school, handwritten newspapers, small mathematics knowledge
In ancient times, people often needed to measure the length of objects, the size of fields, and the weight of objects in their daily lives. This gradually gave rise to length, area, weight (mass) and other quantities. concept.
When measuring length, people began to use a certain part of the body, such as one degree or one step. Later, some simple tools were invented to unify the standards of measurement.
Nowadays, there are various rulers, making measurement more convenient. 2. We know that *** the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 were originally invented by Indians. They were introduced to China in the late 13th century. People mistakenly believed that 0 was also invented by Indians.
In fact, there was no "0" when India first invented it. They wrote "204" as "2 4" with an empty space in the middle. They wrote 2004 as "2 4". How to distinguish how many zeros there are in the middle? ? In order to avoid confusion, use a dot "·" to represent it. 204 is written as "2·4". Isn't that confused with a decimal? It was not until 876 AD that "0" was determined.
However, our country had created "0" 1240 years ago. The zero in our country was "○" at that time. It was based on the missing character when writing. "□" was used to indicate the missing character. "0" meant that the number did not exist, or that the number was missing. There is no numerical value, and it is represented by "○". As people continued to count for a long time, it slowly developed and evolved, and was finally determined as today's "0".
Therefore, using "0" as zero is an outstanding contribution of ancient Chinese mathematicians. 3. It is one of the earliest regions with developed culture in the world.
It is located on both sides of the Nile River. Around 3200 BC, after nearly 800 years of struggle, the entire territory of Egypt was unified.
Because the Nile River flooded regularly, people wanted to measure the land after the river flooded, which gave rise to ancient Egyptian mathematics. Our current understanding of ancient Egyptian mathematics comes mainly from two books written in hieroglyphs.
One is the London version and the other is the Moscow version. The London Papyrus was originally discovered in the ruins of the ancient Egyptian capital. It was purchased by the Englishman Laint in 1858, so it is also called the Laint Papyrus.
Papyrus is an aquatic plant abundant in the Nile Delta. It is shaped like a reed. At that time, people could write by tearing its stems into thin slices layer by layer. This book is 550 centimeters long and 33 centimeters wide. It was written by the Egyptian monk Amesh. It was written around 1700 BC, which is about 3700 years ago.
The book is titled "A Guide to the Illumination of All Dark and Secret Things in Objects". The book is divided into three chapters: one is arithmetic, the other is geometry, and the third is miscellaneous topics; 85, presumably a practical calculation manual of the time. The Moscow original was acquired by a Russian collector in 1893 and transferred to the Moscow Museum in 1912.
It was written around 1850 BC. There are 25 questions recorded in the book. Unfortunately, the title of the book is missing and the title of the book is unknown.
In these two papyri, there are not only calculations of linear equations of one variable, but also the algorithm of Egyptian fractions at that time. In the application questions, issues such as grain, alcohol, animal feeding and grain storage are involved.
In particular, some calculation problems are very exciting. This shows that 4,000 years ago, people had already applied mathematics to solve practical problems in production and life.
4. Chinese people have always attached great importance to the philosophical value of "3" from ancient times to the present. When talking about people with "3", there are three emperors and three Sus; when talking about essays with "3", there are "trilogy" and "three words"; when talking about flowers and trees with "3", there are three treasures of the garden - ginkgo in the tree and peony in the flower. , Orchid in grass.
People also use "3" to study. For example, Zhu Xi, a philosopher in the Song Dynasty, believed that reading should be done in three ways: with the heart, with the eyes, and with the mouth.
Foreigners also attach great importance to "3". As early as the 5th century BC, the ancient Greek philosopher Pythagoras called "3" the perfect number because it embodies the "beginning, middle and end" and possesses divinity.
In ancient Greek and Roman mythology, the world is ruled by three great gods-the main god Jupiter, the sea god Neptune, and the underworld god Pluto. Jupiter held a three-pronged lightning bolt, Neptune held a trident, and Pluto held a three-headed dog.
There are also three legendary goddesses in Greek mythology: Fate, Vengeance and Grace. Ancient Westerners believed that the world is composed of three parts - earth, ocean, and sky; nature has three contents - animals, plants, and minerals; the human body has threefold nature - body, mind, and spirit; human beings need three kinds of knowledge. ——Theoretical, practical, and discerning; wisdom includes three aspects—thorough thinking, appropriate language, and fair behavior.
In modern times, many people’s sayings are still inseparable from “3”. The great French writer Hugo said: Human wisdom holds three keys: one opens mathematics, one unlocks letters, and one unlocks musical notes.
This means that smart people should learn mathematics, language and music well. The famous physicist Einstein summed up the three lessons for success: hard work, the right method and less empty words.
5. Encyclopedia of Mathematics: (1) Do you know? Our country is the first country in the world to use the rounding method for calculations. People have been using rounding for calculations about two thousand years ago.
(2) Among the four oceans in the world, the average water depth of the Pacific Ocean is about three times that of the Atlantic Ocean. The average water depth of the Pacific Ocean is 400 meters more than that of the Atlantic Ocean. The average water depth of the Indian Ocean is 103 meters less than the Pacific Ocean. What is the average water depth in the Atlantic, Pacific, and Indian Oceans? (3) Classmate Xiaodong is a young Internet user. He goes to the Internet every day to take a look.
Yesterday, he saw this information on the Internet: China discharges about 316 tons of sewage into the sea every second on average. The United States is twice as much as China, Russia is three times as much as China, and other coastal countries discharge into the sea. The sewage problem is 29 times that of China. 6. The origin of the name "mathematics" The ancient Greeks introduced names, concepts and self-thinking in mathematics, and they began to speculate how mathematics came into being very early.
Although their guesses were only jotted down, they almost occupied the field of thinking first. What the ancient Greeks jotted down became reams of articles in the 19th century and annoying platitudes in the 20th.
Among the existing information, Herodotus (484-425 BC) was the first person to start conjecturing. He talked only about geometry, and he may not have been familiar with general mathematical concepts, but he was sensitive to the precise meaning of land surveying.
As an anthropologist and a social historian, Herodotus pointed out that ancient Greek geometry came from ancient Egypt, where annual floods inundated the land for tax purposes. ,people.