Mathematical theorem problems, median value theorem for mathematical problems

The number system is a scientific method for people to count using symbols. There are many types of number systems, and the number systems commonly used in computers are: decimal, binary, and hexadecimal.

Binary numbers have two characteristics: they are composed of two basic numbers, 0,1, and the law of binary number operation is every two to one.

In order to distinguish it from other decimal numbers, binary numbers are usually written with a base number 2 at the bottom right of the number, or a b after the addition of a number.

For example, a binary number 10110011 can be written as (10110011)2, or 10110011b, or unmarked for decimal numbers. The data in the computer is represented by binary numbers because binary numbers have the following characteristics:

1) There are only two characters 0 and 1 in a binary number, which represent components with two different steady states. For example, there is no current in the circuit, and the current is represented by 1, and the absence of current is represented by 0. Similarly, the voltage in the circuit is high and low, and the transistor conduction and cut-off.

2) Binary number operation is simple, which greatly simplifies the structure of the arithmetic parts in the calculation.

The addition and multiplication operations of binary numbers are as follows:

To sum up, what you are talking about is just a representation of a number in binary system, not a theorem.

1. Points, lines, and angles.

The theorem of points: there is only one straight line after two points.

The theorem of points: the shortest line segment between two points.

Theorem of angles: Complementary angles of the same or equal angles are equal.

The theorem of angles: co-angles of the same or equal angles are equal.

Straight line theorem: At a point, there is only one and only one straight line perpendicular to a known straight line.

Straight line theorem: Of all the line segments connected by a point outside a line and points on a line, the perpendicular line segment is the shortest.

2. The theorem of the inner angle of the triangle.

Theorem: The sum of the two sides of a triangle is greater than the third side.

Corollary: The difference between the two sides of the triangle is less than the third side.

The sum of the inner angles of a triangle theorem: the sum of the three internal angles of a triangle is equal to 180°.

3. Geometric parallelism.

Parallel theorem: After a point outside the straight line, there is only one and only one straight line parallel to the straight line.

Corollary: If both lines are parallel to the third line, the two lines are also parallel to each other.

Prove the parallel theorem of two straight lines: the isotope angles are equal, and the two straight lines are parallel; The inner staggered angles are equal, and the two straight lines are parallel; The inner angles of the same side are complementary, and the two straight lines are parallel.

Inference of the parallel of two straight lines: two straight lines are parallel and the isotopic angles are equal; The two straight lines are parallel, and the internal staggered angles are equal; The two straight lines are parallel and complementary to the side inner angles.

4. Congruent triangle determination.

Theorem: The corresponding sides and angles of congruent triangles are equal.

Corner edge theorem (SAS): There are two triangles with equal sides and their angles to be congruent.

Corner-Edge-Corner Theorem (ASA): There are two corners and their edges corresponding to two triangles that are congruent.

Inference (AAS): There are two angles and the opposite side of one of the corners corresponds to two equal triangle congruences.

Edge-by-edge theorem (SSS): There are three sides corresponding to two equal triangles congruence.

Hypotenuse, right-angled edge theorem (HL): There is an hypotenuse and a right-angled edge corresponding to two equal right-angled triangle congruences.

Too much ......Menelaus's theorem, Seva's theorem, Simson's theorem, Ptolemy's theorem, Microkel's theorem, Pythagorean theorem, 9-point circle theorem,

Let f(x) give the original function f(x), 0,1)f(x)dx=f(1)-f(0)=2

According to the median value theorem, there is (0,1).

f（ ξ=f'（ ξ=[ f（1）-f（0） ]/（1-0）=2

For the unary quadratic equation: ax bx c 0, if there are real roots x1 and x2, liquid silver.

From Vedder's theorem: x1 x2 b a

x1·x2 Dress up C A

ax +bx+c (this is the one-time only equation of the second house, a, b, c are regarded as numbers) The sum of the two roots: x1 and x2 are two x1+x2=-(b a) x1*x2=c a (where a, b, c are the previous equations) refers to the absolute Wang Qiu Oh macro collision.

Vedic theorem, for a one-dimensional quadratic equation with two roots, let the two roots of hunger wax be rotten and slippery respectively, then the calendar infiltrates x1+x2=-(b a), x1*x2=c a

Unary quadratic equation Vedic theorem x1+x2=-b a x1*x2=c a