![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
A mathematical problem about golden section It is known that P and Q are the golden section points of line AB, and PQ = 2cm The answer is (root 5 + 4) / 2, but how is it calculated? I hope you can help me explain,
AP:PB:AB=1:K:K^2
PQ=PB-PA=AB[(K/K+1)-(1/K+1)]=AB*(K-1)/K+1=2
K is the golden section ratio
It can be worked out
The golden section
1. Given that the line segment AB = 1, points c and D are its two golden section points respectively, then the length of CD is ()
2. If the ratio between the bottom and the waist of an isosceles triangle whose vertex angle is 36 degrees is the golden ratio, then the triangle ()
1. Given that the line segment AB = 1, points c and D are its two golden section points respectively, then the length of CD is (0.34)
2. If the ratio between the bottom and the waist of an isosceles triangle with a vertex angle of 36 degrees is the golden ratio, then the triangle does not exist
RELATED INFORMATIONS
- 1. Please help solve the following math problem (about golden section). Thank you-- It is known that the length of AB is the following sign 10, and C is divided into two parts: AC = (five times of the following sign 2 - root sign 10) / 2, BC = (three times of the root sign 10 - five times of the root sign 2) / 2 Verification: C is the golden section of line AB (write the specific process)
- 2. Point C is the golden section point (AC > BC) of line ab. if AB = 2, then AC = 2___ (denoted by root)
- 3. How to judge the positive and negative of the root of an equation by Weida's theorem
- 4. If ax ` 2 + BX + C = 0 (a ≠ 0) has two roots, which are 2,3, then find the root of Cx ` 2 + BX + a = 0
- 5. It is known that the quadratic equation AX2 + BX + C = 0 with respect to X has no real roots. If a misinterprets the quadratic coefficients and obtains two of them as 2 and 4, and B misinterprets the sign of the quadratic coefficients and obtains two of them as - 1 and 4, then the value of 2B + 3CA is () A. 2B. 3C. 5D. -6
- 6. X1.x2 is x ^ 2 + X-2 = 0, X1 + x2 =?
- 7. According to the social needs, the municipal government held a hearing on the price of tap water and decided to adjust the price of tap water from April this year. Some information about the price of domestic water after adjustment is as follows: & nbsp; & nbsp; & nbsp; & nbsp; unit price of water consumption (M3) (yuan / m3) & nbsp; the part within 5M3 (including 5M3) 2 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; It is known that xiaojingjia and Xiaolei paid 19 yuan and 31 yuan respectively in May, and the water consumption of Xiaolei is 1.5 times of xiaojingjia's
- 8. 1. 2X + 3Y = 1,2,2 of X + y + 4 of X-Y = 4 3x-5y=68 4（x+y)-3(x-y)=12
- 9. `Mathematics is formulated by a quadratic equation of two variables It is known that the length of a railway bridge is 1400 meters. Now there is a train passing through the bridge. It takes 1 minute and 20 seconds for the train to get on the bridge. The time for the whole train to be completely on the bridge is 1 minute. Find the speed and length of the train`
- 10. In order to protect the ecological balance and green the environment, the state strongly encourages "returning farmland to forest and grass", and its compensation policy is shown in table (1). A farmer in Danjiangkou reservoir area actively responds to the call of "one river to send spring water to Beijing" put forward by our city to cooperate with the national "south to North Water Diversion" project, and undertakes to plant trees and grass on a hillside, and the compensation obtained by the state is shown in table (2) How many mu of trees and grass?
- 11. What is Fibonacci sequence?
- 12. The golden section ratio should be an expression with a root sign
- 13. Golden section ratio formula, the five, root five - 1 / 2, root five + 1 / 2
- 14. What does "golden section" mean?
- 15. Let P, Q, a and B be any four points, then PA Λ 2-pb Λ 2 = QA Λ 2-qb Λ 2 ＜ = > pq⊥ ab
- 16. It is natural and appropriate for the mathematics presenter to stand at the golden section of the stage when hosting the program When the stage was 20m, he asked how far to stand from the left end. Is it 12.36 or 7.64? It seems that we usually take 7.64 instead of 12.360. Why? He doesn't ask how far it is from the left end, why can't we take 12? Isn't it the golden section
- 17. When the host standing position P is the golden section point of stage AB, the sound effect is the best. So you think the distance of AP should be equal to () A. 10 m B.10 (root 5-1) m C.10 (3-root 5) m d.10 (root 5-1) or 10 (3-root 5) M
- 18. C is the golden section point of line AB, find the value of AC / BC
- 19. The golden section is 0.618 0.236 what else
- 20. What are the special numbers! Such as golden section! PI! What are the special numbers! Such as golden section point 0.618! PI 3.14 It's better to have all of them