The golden section is a mathematical aesthetic problem that we contact more in our lives. With it, vivid colors are more colorful: architects have long known how to use the golden ratio. The pyramids of Egyptian Pharaoh Khufu built in 3000 BC and the Parthenon in Athens built in 432 BC all adopted this magical proportion, so its overall structure and its cooperation with the outside world are so harmonious and beautiful. Our current window sizes are generally made in accordance with the golden ratio. It is even more magical in the field of art. As we all know, the beautiful figure of the goddess Venus can be said to be perfect, and her up-and-down ratio is the golden ratio. Ballerinas stand on tiptoe to make the proportion of the human body more in line with the golden ratio. The painting "Saint Juram" was completed around 1483, and the rectangular frame of the painting also conforms to this excellent golden ratio.
The exact value of "golden ratio" is 0.6 1803398878. Students who have studied the quadratic equation of one variable can solve the equation X 2-X- 1 = 0, and one of its positive roots is. This figure is the golden ratio.
The absolute value of the difference between the first and second terms of a series and the golden section.
1 1.000000000000000000 0.38 19660 1 1250 105 152
2 0.500000000000000000 0. 1 18033988749894848
3 0.666666666666666667 0.0486326779 1677 18 19
5 0.600000000000000000 0.0 18033988749894848
8 0.625000000000000000 0.0069660 1 1250 105 152
13 0.6 153846 153846 15385 0.002649373365279464
2 1 0.6 190476 190476 19048 0.00 10 13630297724 199
34 0.6 176470588235294 12 0.000386929926365436
55 0.6 18 18 18 18 18 18 18 182 0.000 14782943 1923334
89 0.6 17977528089887640 0.000056460660007208
144 0.6 18055555555555556 0.00002 1566805660707
233 0.6 1802575 107296 1373 0.000008237676933475
377 0.6 18037 1352785 14589 0.000003 1465286 1974 1
6 10 0.6 18032786885245902 0.00000 120 1864648947
987 0.6 1803444782 168 1864 0.00000045907 17870 16
1597 0.6 180338 13400 125235 0.000000 1753497696 13
2584 0.6 18034055727554 180 0.00000006697765933 1
4 18 1 0.6 18033963 166706530 0.000000025583 1883 19
6765 0.6 1803399852 1803400 0.00000000977 1908552
10946 0.6 180339850 17357939 0.000000003732536909
177 1 1 0.6 18033990 175597087 0.00000000 1425702238
28657 0.6 1803398820532505 1 0.000000000544569797
46368 0.6 1803398895790200 1 0.000000000208007 153
75025 0.6 18033988670443 186 0.00000000007945 1663
12 1393 0.6 18033988780242683 0.000000000030347835
1964 18 0.6 18033988738303007 0.0000000000 1 159 184 1
3 178 1 1 0.6 18033988754322538 0.000000000004427689
5 14229 0.6 1803398874820362 1 0.00000000000 169 1227
832040 0.6 18033988750540839 0.00000000000064599 1
1346269 0.6 18033988749648 102 0.000000000000246747
2 178309 0.6 18033988749989097 0.000000000000094249
3524578 0.6 18033988749858848 0.000000000000036000
5702887 0.6 18033988749908599 0.0000000000000 1375 1
9227465 0.6 18033988749889596 0.000000000000005252
14930352 0.6 18033988749896854 0.000000000000002006
24 1578 17 0.6 18033988749894082 0.000000000000000766
39088 169 0.6 18033988749895 14 1 0.000000000000000293
63245986 0.6 18033988749894736 0.000000000000000 1 12
102334 155 0.6 1803398874989489 1 0.000000000000000043
165580 14 1 0.6 18033988749894832 0.0000000000000000 16
2679 14296 0.6 18033988749894854 0.000000000000000006
433494437 0.6 18033988749894846 0.000000000000000002
Did you find a pattern?
The ratio of odd-numbered items to even-numbered items is greater than the golden section number, and the ratio of even-numbered items to odd-numbered items is less than the golden section number.
When n tends to infinity, An/(An+ 1) is equal to the golden ratio.
It seems to prove that