Since17th century, the original geometry and algebra have been difficult to solve many new problems raised by production and natural science at that time, such as: how to find the instantaneous velocity and acceleration of an object? How to find the tangent of the curve and the length of the curve (planetary distance), the area swept by the vector diameter, the minimum value (such as perihelion, apohelion, maximum range, etc.). ), volume, center of gravity, gravity, etc.; Although Newton had made some achievements in logarithm, analytic geometry and infinite series before, he could not solve these problems satisfactorily or universally. The greatest influences on Newton at that time were Descartes' Geometry and Varis's arithmetica infinitorum. Newton unified various special methods for solving infinitesimal problems since ancient Greece into two algorithms: downstream calculus (differential) and countercurrent calculus (integral), which are embodied in the application of infinite polynomial equation in 1669, stream calculus and infinite series in 167 1, and infinite series in 1676. The so-called "flow" is an independent variable that changes with time, such as x, y, s, u, etc. The "flow number" is the speed of flow change, that is, the rate of change, writing, etc. There is a difference between the "differential rate" and the "variable rate" he said. At the same time, he first published his binomial expansion theorem in 1676. Newton discovered other infinite series and used them to calculate areas, integrals, solve equations and so on. 1684, Leibniz introduced and lengthened S as the symbol of calculus from the tangent study of curves, and the calculus founded by Newton was rapidly popularized in mainland countries.
The appearance of calculus has become another important branch in the development of mathematics besides geometry and algebra-mathematical analysis (Newton called it "analysis by the method of infinite polynomial equation"), and further developed into differential geometry, differential equation, variational method and so on, thus promoting the development of theoretical physics. For example, J Bernoulli of Switzerland seeks the solution of the steepest descent curve, which is the initial problem of variational method, and no mathematician in Europe can answer it within half a year. 1697, Newton overheard it one day, and it was solved in one fell swoop that night, and it was published anonymously in the Journal of Philosophy. Bernoulli said in surprise, "I recognized the lion from this claw."
(2) Newton's achievements in optics.
Newton's optics is another classic of science (1704). The subtitle of the book is "Papers on Reflection, Refraction, Bending and Color of Light", which reflects his optical achievements.
The first is geometric optics and color theory (prism spectrum experiment). From 1663, the lens was ground and the telescope was made by ourselves. In a letter to the Royal Society, he reported: "I made a triangular glass prism at the beginning of 1666 to test the famous color phenomenon. To this end, I darkened the room ... "Then he described in detail the prism dispersion experiment he conducted by opening a small hole to introduce sunlight. From Aristotle to Descartes, the color theory of light holds that white light is pure and uniform, which is the true color of light. "Colored light is a variant of white light. Newton carefully noticed that sunlight is not the five colors that people used to say, but between red, yellow, green, blue and purple, and there are intermediate colors such as orange and indigo. Strangely, the prism is not round but oblong, and then he tested the effects of "parts with different thicknesses of glass", "windows with different sizes", "putting the prism outside and then passing through the hole" and "uneven or occasionally irregular glass". Put the two prisms upside down to "eliminate the influence of the first prism"; Take "the light from different parts of the sun, see what kind of influence it will have in different incident directions"; And "calculate the refractive index of each color light" and "observe whether the light will move along the curve after passing through the prism"; Finally, a "decisive experiment" was made: monochromatic light was taken out of the ribbon formed by the prism through the small hole on the screen, and then projected onto the second prism to obtain the refractive index of nuclear color light (then called "refractive index"), thus it was concluded that "white light itself is a non-uniform mixture of colored lights with different refractive indexes". This amazing conclusion overturns the previous theory and is the result of Newton's careful observation and repeated experimental thinking.
In the process of studying this problem, Newton also affirmed that neither galileo telescope (concave lens or convex lens) nor Kepler telescope (two convex lenses) can avoid chromatic aberration caused by objective lens dispersion. He found that a carefully polished metal mirror can be magnified 30 ~ 40 times as an objective lens. 167 1 year, he sent this mirror to the royal society for preservation. Up to now, the giant astronomical telescope still adopts Newton-like basic structure. Grinding and polishing precision optical mirrors by Newton method is still the main means of optical processing in many factories.
The second part of optics describes various experiments of Newton's ring phenomenon when light shines on stacked convex lens and flat glass. He did all the experiments that modern experiments can think of and made accurate measurements, except for the reason why the ring came into being. He explained the interference phenomenon as "burst" or "coincidence" in light propagation, that is, it is periodic, sometimes "easy to reflect" and sometimes "easy to transmit". He even measured the size of this equal interval For example, there is a burst interval of colored light between yellow and orange that is 1/89000 inches (currently it is 2854 × 10-65438).
The third part of optics is "kink" (he thinks that light is absorbed), that is, diffraction and birefringence experiments and his 3 1 topic. These diffraction experiments include more than 10 experiments, such as hair, leaves and monochromatic narrow beam "light band" (now called diffraction pattern) formed by sharp splitting. Newton has reached the door of an important discovery, but missed it. His 3 1 question is very enlightening, which shows that Newton did not make absolute affirmation before the experimental facts and physical thoughts matured. In the first and second chapters of Optics, Newton regarded light as a material flow, that is, a group of particles with different speeds and sizes emitted by a light source. In birefringence, he assumes that these light particles are oriented and anisotropic. Because the wave theory at that time could not explain the straight-line progress of light, he tended to the particle theory, but he thought that particles and waves were hypothetical. He even thinks that the existence of ether is unfounded.
In fluid mechanics, Newton pointed out that the viscous resistance of fluid is directly proportional to the shear rate, and this resistance is directly proportional to the separation speed between parts of liquid. Those that conform to this law (such as air and water) are called Newtonian fluids.
In terms of heat, Newton's cooling law is that when the surface of an object forms a temperature difference with its surroundings, the heat lost per unit time and area is directly proportional to this temperature difference.