What is rabbit sequence?

Rabbit sequence is Fibonacci sequence. The inventor of Fibonacci sequence is Italian mathematician Leonardo Fibonacci. He was born in 1170 AD and died in 1240. His native place is probably Pisa. He was called "Leonardo of Pisa" in 1202, He was the first European to study mathematical theories in India and Arabia. His father was appointed as a diplomatic consul by a business group in Pisa, and was stationed in what is now Algeria, Leonardo was able to study mathematics under the guidance of an Arab teacher. He also studied mathematics in Egypt, Syria, Greece, Sicily and Provence
Fibonacci sequence refers to such a sequence: 0,1,1,2,3,5,8,13,21
This sequence starts from the third term, and each term is equal to the sum of the first two terms. Its general term formula is: (1 / √ 5) * {[(1 + √ 5) / 2] ^ n - [(1 - √ 5) / 2] ^ n} [√ 5 denotes radical 5]
It's interesting that the general formula of such a series of numbers is expressed by irrational numbers
[the sequence has many wonderful properties]
For example, as the number of items in a sequence increases, the ratio of the former to the latter approaches the golden section of 0.6180339887
Another property is that, starting from the second term, the square of every odd term is one more than the product of the preceding and the following two terms, and the square of every even term is one less than the product of the preceding and the following two terms
If you see a question like this: someone cut an 8 * 8 square into four pieces and put it together into a 5 * 13 rectangle, pretending to be surprised to ask you: why 64 = 65? In fact, it uses the property of Fibonacci sequence: 5, 8 and 13 are the three adjacent terms in the sequence. In fact, the area difference between the front and the back is 1, but there is a slender slit in the back picture, It's not easy for ordinary people to notice
If you pick any two numbers as the starting point, such as 5, - 2.4, and then add the two terms to form 5, - 2.4, 2.6, 0.2, 2.8, 3, 5.8, 8.8, 14.6 You will find that with the development of the sequence, the ratio of the two terms is closer to the golden section, and the difference between the square of a term and the product of the two terms also alternates by a certain value
The nth term of Fibonacci sequence also represents the number of all subsets in the set {1,2,..., n} that do not contain adjacent positive integers

Derivation of sin (sin (SiNx))

Let u = SiNx, u '= cosx
Let v = sin (SiNx) = sinu, V '= COSU * u' = cos (SiNx) * cosx
y=sin(sin(sinx))=sinv,y'=cosv*v'=cos(sin(sinx))*cos(sinx)*cosx

Knowledge summary of physics chapter 3-4 in Volume 1 of Grade 8

Chapter 4 thermal phenomena
Temperature and thermometer: temperature: the degree of heat and cold of an object is called temperature
Thermometer: an instrument used to measure temperature
Regulation of 2 ℃ temperature: the temperature of ice water mixture is 0 ℃, which is the temperature of boiling water under standard atmospheric pressure
The temperature is 100 ℃. Between 0 ℃ and 100 ℃, it is divided into 100 equal parts, and each part is 1 ℃
*The unit of temperature in centigrade is centigrade, expressed in centigrade
Absolute zero: the lower limit of temperature in the universe is - 273 ℃, which is called absolute zero
Thermodynamic temperature: the temperature starting from absolute zero is called thermodynamic temperature. Unit: Kelvin K
5. The conversion between thermodynamic temperature and centigrade temperature: T = t + 273k, t = t-273 ℃
6 temperature range of thermometer: 35 ℃ - 42 ℃
Structural features: the volume of the glass bubble is larger than that of the glass tube, and there is a special hole above the glass bubble
It can prevent the rising mercury from falling back into the glass bubble automatically
Minimum unit: 0.1 ℃
Note: before each use, the mercury in the glass tube should be dropped to the glass bubble
Attention should be paid to the use of temperature
Choose the right thermometer
2 look at the minimum scale value of temperature 2 look
3. When measuring, the glass bubble of the thermometer shall be in full contact with the object to be measured and shall not leave the object to be measured,
Wait until the indication of the thermometer is stable before reading
When measuring, the glass bulb of the thermometer should not touch the wall and bottom of the container
When reading, the line of sight should be level with the upper surface of the liquid column
Change of state: the process by which a substance changes from one state to another
The three states of matter: gas, liquid and solid
The standard for distinguishing crystal from non crystal is that crystal has a fixed melting point, while non crystal has no fixed melting point
The common crystals are: ice, salt, naphthalene, various metals, Haibo, quartz, etc
Common non crystal are: rosin, glass, wax, asphalt, etc
Melting: the process by which a substance changes from a solid to a liquid. It absorbs heat
Solidification: the process by which a substance changes from a liquid to a solid state. Heat is released
Melting point: the temperature at which a crystal melts is called melting point. Freezing point: the temperature at which a liquid solidifies into a crystal
The melting point and freezing point of the same substance are equal
There are three distinct sections in the melting curve: solid heating section, melting section and liquid heating section
The material in the melting section may be solid, liquid or mixed
Vaporization: the process by which a substance changes from a liquid state to a gaseous state. Liquefaction: the process by which a substance changes from a gaseous state to a liquid state
There are two kinds of vaporization: evaporation and boiling. Vaporization should be endothermic and liquefaction exothermic
The difference between evaporation and boiling is: 1 evaporation takes place at any temperature and boiling takes place at a certain temperature
2. Evaporation takes place on the surface of the liquid, and boiling takes place on the surface and inside of the liquid
3 evaporation is a slow vaporization phenomenon, boiling is intense
Evaporation reduces the temperature of itself and the surrounding objects, and has the effect of refrigeration. The temperature remains unchanged (equal to the boiling point) during boiling
The three factors that affect evaporation are: 1 the temperature of the liquid 2 the surface area of the liquid 3 the surface area of the liquid
The flow of air in the air
Boiling point: the temperature at which a liquid boils. Boiling conditions are: 1 to reach boiling point, 2 to continue to absorb heat
Sublimation: the process in which a substance changes directly from a solid state to a gas state: sublimation is endothermic
Condensation: the process in which a substance changes directly from a gaseous state to a solid state. Condensation is exothermic
In the change of state of matter, the softer the matter is, the more it absorbs and the harder it releases

Find the rules: white, black, white, black, white, black, black, white, black How many white balls are there in the first 2005 balls/

The groups are as follows
(white, black), (white, black), (white, black), (white, black)
The number is 2 + 3 + 4 + 5 + +n
Sn=n(2+n)/2=2005
n=62.3

What is the cubic power of (- 3) - 3 times the fourth power of (- 3)

Original form
=-27-3×81
=-27-243
=-270

Sixth grade mathematics book Volume I PEP exercise 5... 6 questions
Join the equations with the same number, 15 out of 22 times 2 out of 5 times 5 out of 2, 5 out of 5 times (1 + 1 out of 2) 1 out of 3 times 3, 11 out of 6 times 5 out of 4, 9 out of 100 times 9 out of 100, 6 out of 5 times 1 out of 12 times 3

The answers are 15 / 22, 15 / 22 and 3 / 10, respectively

Judgment. 1. The product of two prime numbers must be composite. 2. The sum of two prime numbers must be even

1. The product of two prime numbers must be a composite number
2. The sum of two prime numbers must be even

How many jin is a liter of oil?

Generally, there are too many kinds of oil if 1 liter = 2 jin. Check the density

Algebra formula in the second semester of junior one
Various formulas

Square difference: A2-B2 = (a + b) (a-b)
Complete square: (a + b) 2 = A2 + 2Ab + B2 (a-b) 2 = a2-2ab + B2
Cross multiply
a+b=b+a
a*b=b*a
ab+ac=a(b+c)

The diameter of a certain cell existing in the organism is about 0.0000125m. This kind of cell is arranged in a straight line from head to tail, and each cell is up to 1cm

Let's have X cells
0.0000125m = 0.00125cm
The equation is 0.00125x = 1
x=1÷0.00125
x=800
A: it takes 800 cells in a row to reach 1 cm

What is rabbit sequence?