Question 1: What did Newton invent? Among all Newton's scientific contributions, mathematical achievements occupy a prominent position. The first creative achievement in his mathematical career was the discovery of binomial theorem. According to Newton's own recollection, he discovered this theorem when he tried to modify his series of finding the area of a circle while studying Dr. Wallis' arithmetica infinitorum in the winter of 1664 and 1665.

Descartes' analytic geometry maps the functional relationship describing motion to geometric curves. Newton found a new way out under the guidance of his teacher Barrow and on the basis of studying Descartes' analytic geometry. The speed at any moment can be regarded as the average speed in a small time range, which is the ratio of a small distance to a time interval. When this small time interval is reduced to infinity, it is the exact value of this point. This is the concept of differentiation.

Derivation is equivalent to finding the tangent slope of the relationship between time and distance at a certain point. The distance traveled by a variable-speed moving object in a certain time range can be regarded as the sum of the distances traveled in a very small time interval, which is the concept of integration. Integration is equivalent to finding the area under the curve of time and speed. Newton established calculus from these basic concepts.

The establishment of calculus is Newton's most outstanding mathematical achievement. Newton founded this mathematical theory, which is directly related to physical concepts, in order to solve the problem of motion. Newton called it flow counting. Some specific problems it deals with, such as tangent problem, quadrature problem, instantaneous velocity problem, maximum and minimum value of function, have been studied before Newton. But Newton surpassed his predecessors. He synthesized the scattered conclusions in the past from a higher angle, unified various skills of solving infinitesimal problems since ancient Greece into two common algorithms-differential and integral, and established the reciprocal relationship between these two operations, thus completing the most critical step in the invention of calculus, providing the most effective tool for the development of modern science and opening up a new era of mathematics.

Newton did not publish the research results of calculus in time. He may have studied calculus earlier than Leibniz, but Leibniz adopted a more reasonable expression, and his works on calculus were published earlier than Newton.

Between Newton and Leibniz, when arguing about who is the founder of this subject, it actually caused a blatant * * *, which lasted for a long time among their respective students, supporters and mathematicians, resulting in a long-term opposition between European continental mathematicians and British mathematicians. British mathematics was closed to the outside world for a period of time, limited by national prejudice, and too rigidly adhered to Newton's "flow counting", so the development of mathematics fell behind for a whole hundred years.

It should be said that the establishment of a science is by no means a person's achievement. It must be completed by one person or several people through the efforts of many people and the accumulation of a large number of achievements. The same is true of calculus, which was independently established by Newton and Leibniz on the basis of predecessors.

1707, Newton's algebra lecture notes were compiled and published, named "General Arithmetic". He mainly discussed the basis of algebra and its application in solving various problems. This book states the basic concepts and operations of algebra, explains how to turn various problems into algebraic equations with a large number of examples, and deeply discusses the roots and properties of equations, thus achieving fruitful results in equation theory. For example, he draws the relationship between the roots of equations and their discriminant, and points out that the power sum of the roots of equations can be determined by using the coefficients of equations, that is, Newton's power sum formula.

Newton contributed to both analytic geometry and synthetic geometry. In Analytic Geometry published by 1736, he introduced the center of curvature, gave the concept of closed line circle (or curve circle), and put forward the curvature formula and the curvature calculation method of curve. And summed up many of my own research results into a monograph "Counting Cubic Curves", which was published in 1704. In addition, his mathematical work involves numerical analysis, probability theory, elementary number theory and many other fields.

1665, Newton, who was only 22 years old, discovered the binomial theorem, which is an essential step for the all-round development of calculus. The binomial theorem holds that energy is discovered by direct calculation.

The simple result is generalized to the following form.

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Binomial series expansion is a powerful tool to study series theory, function theory, mathematical analysis and equation theory. Today, we will find that this method is only applicable to the case where n is a positive integer. When n is a positive integer of 1, 2,3, ... and the series ends with a positive number ... >; & gt

Question 2: What did scientist Newton invent 1-3 Newton's three laws of kinematics?

law of universal gravitation

Reflecting telescope was invented.

6 Law of Conservation of Momentum

law of conservation of angular momentum

8 binomial theorem

Newton's identity

10 calculus

1 1 dispersion of light

(1) Newton's Mathematical Achievements

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 equations"), and further developed into differential geometry, differential equations, variational methods, etc., 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 paw."

(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.

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Question 3: What did Newton invent? Newton invented the reflecting telescope, and made the prototype of the triboelectric generator with glass balls. Put forward the law of universal gravitation and the three basic laws of object motion (Newton's three laws), invented calculus with Leibniz, and discovered the dispersion principle of light.

Question 4: What did Newton invent? Law of universal gravitation: there is gravitation between two objects, which is inversely proportional to the square of the distance and directly proportional to the product of the mass of the two objects;

Newton's first law: under any circumstances, all objects always keep still or move in a straight line at a constant speed when they are not affected by external forces;

Newton's second law: the acceleration of an object is directly proportional to the resultant force acting on the object and inversely proportional to the mass of the object, and the direction of acceleration is the same as that of the resultant force;

Newton's third law: a pair of forces acting on two objects, with opposite directions and equal magnitude, act on the same straight line and act on two different objects.

Question 5: What did Newton invent? Newton discovered the gravity of the earth.

Question 6: What did Newton invent? It's discovery, not invention.

1. Newtonian mechanics is based on Newton's three laws of motion.

2. Discover the law of universal gravitation.

3. Establish the basis of planetary law theory.

4. Devote to the study of Mitsubishi mirror dispersion and invent reflective telescope.

5. Discover the binomial theorem of mathematics and the calculus method.

6. The origin of modern atomic theory