Chapter VII Unary Linear Inequality (1 1 class hour)
7. 1 Inequality in Life (1 class hour)
7.2 Solving Set Inequalities (1 class hour)
7.3 Properties of Inequalities (1 class hour)
7.4 Solving linear inequality of one variable (2 class hours)
7.5 Solving one-dimensional linear inequality and solving problems (1 class hour)
7.6 One-dimensional linear inequality group (2 class hours)
7.7 Unary linear inequality, unary linear equation and unary linear function (2 class hours)
Review and summarize
Chapter 8 Grades (10 class hour)
8. 1 score (1 class hour)
8.2 the basic nature of the score (2 class hours)
8.3 Addition and subtraction of scores (1 class hour)
8.4 Fractional Multiplication and Division (2 class hours)
8.5 Fractional Equation (3 class hours)
Review and summarize
Chapter 9 Inverse Proportional Function (6 class hours)
9. 1 inverse proportional function (1 class hour)
9.2 Images and Properties of Inverse Proportional Function (3 class hours)
9.3 Application of Inverse Proportional Function (1 class hour)
Review and summarize
Chapter 10 Similarity of Graphics (14 class hours)
10. 1 Distance on the map and actual distance (1 class hour)
10.2 golden section (1 class hour)
10.3 Similar graphics (1 class hour)
10.4 Explore the conditions of triangle similarity (4 class hours)
10.5 the nature of similar triangles (2 class hours)
10.6 graphic similarity (1 class hour)
10.7 application of similar triangles (3 class hours)
Review and summarize
Chapter 11 Graphic Proof (1) (9 class hours)
1 1. 1 is your correct judgment (1 class)
1 1.2 reasoning (2 class hours)
1 1.3 proof (3 class hours)
1 1.4 reciprocal proposition (2 class hours)
Review and summarize
Chapter 11 Unit Testing
Chapter 12 Cognitive Probability (5 class hours)
12. 1 and other possibilities (1 class hour)
The probability under possible conditions is 12.2 (1) (2 class hours).
The probability under possible conditions is 12.3 (ii) (1 class hour).
Project learning: Is the game fair?
Review and summarize
In the next book in the eighth grade.
What exactly is the golden section of mathematics about? Divide a line segment into two parts so that the ratio of one part to the total length is equal to the ratio of the other part to this part. The ratio is [5 (1/2)- 1]/2, and the approximation of the first three digits is 0.6 18. Because the shape designed according to this ratio is very beautiful, it is called golden section, also called Chinese-foreign ratio. This is a very interesting number. We use 0.6 18 to approximate it, and we can find it by simple calculation:
1/0.6 18= 1.6 18
( 1-0.6 18)/0.6 18=0.6 18
This kind of value is not only reflected in painting, sculpture, music, architecture and other artistic fields, but also plays an important role in management and engineering design.
Let's talk about a series. The first few digits are: 1, 1, 2, 3, 5, 8, 13, 2 1, 34, 55, 89, 144 ... The characteristic is that every number is the sum of the first two numbers except the first two numbers (the numerical value is 1).
What is the relationship between Fibonacci sequence and golden section? It is found that the ratio of two adjacent Fibonacci numbers gradually tends to the golden section ratio with the increase of the series. That is f (n)/f (n-1)-→ 0.618. Because Fibonacci numbers are all integers, and the quotient of the division of two integers is rational, it is just approaching the irrational number of the golden ratio. But when we continue to calculate the larger Fibonacci number, we will find that the ratio of two adjacent numbers is really very close to the golden ratio.
This Fibonacci number not only starts from 1, 1, 2, 3, 5 ... Like this, if you choose two integers at will, and then sort by Fibonacci number, the ratio of the two numbers will gradually approach the golden ratio.
A telling example is the five-pointed star/regular pentagon. The pentagram is very beautiful. There are five stars on our national flag, and many countries also use five-pointed stars on their national flags. Why? Because the length relationship of all the line segments that can be found in the five-pointed star conforms to the golden section ratio. All triangles that appear after the diagonal of a regular pentagon is full are golden section triangles.
The golden triangle has another particularity. All triangles can generate triangles similar to themselves with four congruent triangles, but the golden section triangle is the only triangle that can generate triangles similar to itself with five congruent triangles instead of four congruent triangles.
Because the vertex angle of the five-pointed star is 36 degrees, it can also be concluded that the golden section value is 2Sin 18.
The golden section is approximately equal to 0.6 18: 1.
Refers to the point where a line segment is divided into two parts, so that the ratio of the length of the original line segment to the longer part is the golden section. There are two such points on the line segment.
Using two golden points on the line segment, a regular pentagram and a regular pentagon can be made.
More than 2000 years ago, Odox Sass, the third largest mathematician of Athens School in ancient Greece, first proposed the golden section. The so-called golden section refers to dividing a line segment with length L into two parts, so that the ratio of one part to the whole is equal to the ratio of the other part. The simplest way to calculate the golden section is to calculate the ratio of the last two numbers of Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 2 1, ... 2/3, 3/5, 5/8, 8/655.
Around the Renaissance, the golden section was introduced to Europe by Arabs and was welcomed by Europeans. They called it the "golden method", and a mathematician in Europe17th century even called it "the most valuable algorithm among all kinds of algorithms". This algorithm is called "three-rate method" or "three-number rule" in India, which is what we often say now.
In fact, the "golden section" is also recorded in China. Although it was not as early as ancient Greece, it was independently created by China ancient algebras and later introduced to India. After textual research. European proportional algorithm originated in China, and was introduced to Europe from Arabia via India, not directly from ancient Greece.
Because it has aesthetic value in plastic arts, it can arouse people's aesthetic feeling in the design of length and width of arts and crafts and daily necessities, and it is also widely used in real life. The proportion of some line segments in the building adopts the golden section scientifically. The announcer on the stage is not standing in the center of the stage, but standing on the side of the stage. The position at the golden section of the stage length is the most beautiful and the sound transmission is the best. Even in the plant kingdom, the golden section is used. If you look down from the top of a twig, you will see that the leaves are arranged according to the golden section law. In many scientific experiments, a method of 0.6 18 is often used to select the scheme, that is, the optimization method, which enables us to arrange fewer experiments reasonably and find reasonable western and suitable technological conditions. It is precisely because of its extensive and important application in architecture, literature and art, industrial and agricultural production and scientific experiments that people call it the golden section.
The golden section is a mathematical proportional relationship. The golden section is strict in proportion, harmonious in art and rich in aesthetic value. Generally, it is 0.6 18 in application, just as pi is 3. 14 in application.
The aspect ratio of a golden rectangle is the golden ratio. In other words, the long side of a rectangle is 1.6 18 times of the short side. The golden ratio and the golden rectangle can bring aesthetic feeling to the picture, which is pleasant. It can be found in many artistic and natural works. The Pasa Shennong Temple in Athens, Greece is a good example. Leonardo da Vinci's Vitruvian Man fits the golden rectangle. Mona Lisa's face also conforms to the golden rectangle, and The Last Supper also applies this proportional layout.
Mathematical golden section problem AC/BC=AB/AC
AC/(AB-AC)=AB/AC
AB(AB-AC)=AC^2
AC^2+ 10AC- 100=0
AC=5(√5- 1) cm.
BC=5(3-√5) cm
The golden section of math problems in grade three is very simple. You draw a line segment, locate its golden section, and then make a rectangle with the two divided line segments as side lengths.
Is there a golden section for junior middle school students to teach mathematics? If so, what grade is it? The second volume of the eighth grade, that is, the second day of junior high school
Chapter IV Similar Figures
2. The golden section
Please adopt it. Thank you.
Chapter 8 of Mathematics-Golden Section: blog. 163. /Ada g _ haha10/8/blog/static/239969602007620530871/
It is not easy to copy with pictures.
Solution to the golden section problem in mathematics: Let AP=X, then BP =10-X.
AP:BP=BP:AB, then AP*AB=BP? .
Namely: 10X=( 10-X)? ，X？ -30X+ 100=0。
b？ -4ac = 900-4 * 1 * 100 = 500。
∴x=(30√500)/2 =(30 10√5)/2 = 15 5√5。
Then AP= 15-5√5. (15+5√5 irrelevant, omitted)
∴BP= 10-X=5√5-5.
AP:BP =( 15-5√5)/(5√5-5)=(√5- 1)/2。
The mathematical golden section formula is long times short = the square of the middle length.
Golden section math problem (√5- 1)/2x-(3-√5)/2x=6
(2√5-4)/2x=6
(√5-2)x=6
x=(6√5- 12)/3
The golden section of mathematics in the second day of junior high school! Solution: Because point C is a point on the AB line, AB= 1, AC=(√5- 1)/2,
So BC =1-(√ 5-1)/2 = (3-√ 5)/2.
So AC: BC = (√ 5-1)/2: (3-√ 5)/2 = (√ 5-1)/(3-√ 5).
=(√5- 1)(3+√5)/(3-√5)(3+√5)=(√5+ 1)/2