Mathematics is a subject that gives people wisdom and intelligence. In the world of mathematics, we can explore mysteries we didn't know before, and in the process, we become wise and intelligent. Because I chose liberal arts before, I didn't come into contact with the knowledge of crisis points until I went to college and began to explore calculus. Now I can say that I know a little. During this period, I learned the beauty of calculus and the power of new gravity.
But the process of learning calculus is difficult and arduous. At the same time, I also understand that mathematics is a way to seek well-known axioms, including clearly expressing the meaning of the concepts to be discussed and accurately expressing the postulate as the basis of reasoning. People with extremely strict logical thinking ability draw conclusions from these definitions and postulates.
At the same time, mathematics is a science that needs creativity, and the creative power of mathematics often comes from life. Conversely, these creative achievements of mathematics often act on all aspects of life.
Such as business and financial affairs, navigation and calendar calculation, the construction of bridges, dams, churches and power supply, the design of combat weapons and fortifications, and many human needs. At the same time, mathematics can give the most satisfactory solution to these problems.
In our rapidly developing society, there is no doubt that mathematics is regarded as a universal tool. Calculus does exist in our daily life, but we lack the spirit of being good at discovery.
For example, we are planting flowers, and there is too much water in the vase, so we should pour out some water. This is the formula in life. The question is: how much do we have to tilt the bottle to pour out half the sediment? This is calculus, which comes in handy. Suppose the longitudinal section of the vase is a parabola y = ax 2 (a >; 0) First, calculate the volume of the bottle when it is full of water, and use an integral. The result is equal to v = π H2/(2a); Step 2: Assuming that the tilt angle is α, just pour out half of the water, re-establish the coordinate system so that the symmetry axis of the bottle is Y axis and the ray perpendicular to the symmetry axis of the bottle is X axis, and then restore the coordinate system to the conventional upright figure. At this time, the cross-sectional image of the water in the bottle is the common part of the parabola and the straight line where the water surface is located. Note that the angle between the straight line of the water surface and the X axis is exactly the inclination angle α mentioned in the title (as shown in the original picture, the inclined horizontal plane is parallel to the X axis at this time, so the angle between the water surface and the symmetry axis of the bottle is 90-α, that is, in the new coordinate system, the angle between the straight line of the water surface and the Y axis is also 90-α, so the angle between it and the X axis is α).
So we can set the linear equation as y=tanα*x+b, and assume that the intersection of the straight line and the parabola is A(x0, y0), B(sqrt(h/a), h) (left a, right b) (the ordinate of point b is obviously equal to the height h of the bottle). Firstly, the intercept b of a straight line is obtained by using the coordinates of point b, and then the coordinates of point a can be obtained by using the equation of straight line and parabola. The third step is to find the volume of water in the bottle at this time. The image can be divided into two parts, one is the intersection of a straight line y=y0 and a parabola, and the other is the intersection of a straight line y=y0, a straight line y=tanα*x+b and a parabola y = ax 2 (a > 0). The volume of the first part is v1= ∫ π * (x 2) dy = ∫π * y/ady (the upper and lower integral limits are 0 and y0); The volume of the second part is v2 = ∫ π * (sqrt (y/a)-(y-b)/tan α)/2) 2dy (the upper and lower integral limits are y0 and h); Therefore, according to: v1+v2 = v/2 = π * H2/(4a) = ∫ π * y/ady (the upper and lower integral limits are 0 and y0)+∫π*(sqrt(y/a)-(y-b)/tan.
This is that mathematics is closely related to life. If mathematics can't be closely linked with life, then mathematics will become empty and powerless. The famous mathematician Russell once said, "If we treat him correctly, mathematics will have ... supreme beauty-just like the beauty of a statue, it is a cold and serious beauty, a subtle beauty of every stone and our nature. Without the ornate decoration of painting or music, these coals can be pure and sublime, and can reach the perfect state that only the greatest art can strictly show.
A kind of spiritual pleasure, a kind of spiritual excitement, and a kind of consciousness higher than human beings are the standards of perfection and beauty, which can be obtained in poetry and mathematics. "This shows that a great man saw the hidden charm of mathematics, because he has a pair of eyes that are good at discovering beauty. Besides creativity and discovery, imagination can also sublimate mathematics in our minds.
After studying mathematics for a long time, I show off that all kinds of mathematics have a long history and are unfathomable. He leads the way forward. Hankel said: Mathematics is advancing freely along its own path, not because it has various licenses that are not bound by law, but because mathematics has a freedom that is determined by its essence and consistent with its existence. It is useless that mathematics is unique and indispensable in life, and without it, the level of science and technology will go backwards.
This is not grandstanding, it is an affirmation of the high-tech subject of mathematics, which cannot be denied. Mathematics is not the discoverer of laws, because it is not induction.
Mathematics is not the founder of theory, because it is not a hypothesis. But mathematics is indeed the judge and master of laws and hypotheses, because both laws and hypotheses should show their opinions to mathematics and then wait for the judgment of mathematics.
Without mathematical recognition, laws can't work and theories can't be explained. Mathematics (from mathematical culture) is very important. Life is inseparable from mathematics, and so is the development of national defense and scientific and technological progress.
In distant ancient times, China was ahead of the world, because the industrious people at that time had discovered mathematical calculation and "Nine Chapters of Arithmetic" ... these were arguments left over from history. The strength of a country is inseparable from the accurate calculation of mathematics.
2/kloc-today in the 20th century, China has stood proudly among the nations of the world. In order to improve its international status, we must firmly develop and study mathematics.