magic ratio

the golden ratio-------most amazing!

u even cannot imagineofanaturalnumber that definesall the beauty of world.....theTAJ MAHAL,PYRAMIDS,MONALISA,GREAT WALLOF CHINA,ANGELINA JOLIE,NATURAL BEAUTY.........all these can b defined with the helpof a a ratio ....1.6180339...

Think of any two numbers. Make a third by adding the first and second, a fourth by adding the second and third, and so on. When you have written down about 20 numbers, calculate the ratio of the last to the second from last. The answer should be close to 1.6180339887...

The appeal of the divine proportion to the human eye and brain has been scientifically tested. Dozens of psychological tests, beginning with those of Gustav Fechner in the 19th century, have shown that, when subjects are presented with a range of rectangles, they invariably pick out as most pleasing ones whose sides are in the golden ratio

But the most surprising thing is that a number deemed aesthetically pleasing by human beings also crops up in nature and science. Take the arrangement of leaves on the stem of a plant. As each new leaf grows, it does so at an angle offset from that of the leaf below. The most com mon angle between successive leaves is 137.5 - the golden angle. Why? Because 137.5 = 360 - 360/G, where G is the golden ratio. Why does the golden ratio play a role in the arrangement of leaves? It's all down to the "irrationality" of the number. Irrational numbers are ones that cannot be expressed as the ratio of two whole numbers - for instance, 5/2.

Take a look at the diagram above. Notice that it is made up solely of squares, yet the overall image is a rectangle. This rectangle, if you measure it, has the magic ratio of 1.618. Also if you look at the curved lines within each of the squares you will notice that these are infact quarter circles, but, as a whole you would be forgiven for thinking that they look like the cross section of a sea shell. And you'd be right, for this is the same as the growth rate of the beautiful Nautilus Sea Shell - i.e. 1.618.Take a look at the diagram below. Notice that it is made up solely of squares, yet the overall image is a rectangle. This rectangle, if you measure it, has the magic ratio of 1.618. Also if you look at the curved lines within each of the squares you will notice that these are infact quarter circles, but, as a whole you would be forgiven for thinking that they look like the cross section of a sea shell. And you'd be right, for this is the same as the growth rate of the beautiful Nautilus Sea Shell - i.e. 1.618.

Some studies of the Acropolis, including the Parthenon, conclude that many of its proportions approximate the golden ratio. The Parthenon's facade as well as elements of its facade and elsewhere can be circumscribed by golden rectangles.[12] To the extent that classical buildings or their elements are proportioned according to the golden ratio, this might indicate that their architects were aware of the golden ratio and consciously employed it in their designs. Alternatively, it is possible that the architects used their own sense of good proportion, and that this led to some proportions that closely approximate the golden ratio. On the other hand, such retrospective analyses can always be questioned on the ground that the investigator chooses the points from which measurements are made or where to superimpose golden rectangles, and that these choices affect the proportions observed.

The geneology of the bee is a pattern. This pattern is the result of parthogenesis, the development of an unfertilized egg into an adult animal without fusion with sperm. The queen bee mates only once. She can then produce either unfertilized eggs or fertilized eggs. The unfertilized eggs become male drones, while the fertilized eggs become female workers or queens. In other words, a female bee has two parents, and a male bee has only one parent; a female. Female bees reproduce by parthenogenesis during the spring and summer. In the fall, the eggs produce both males and females. These insects mate, and the females produce fertilized eggs that hatch in the spring.
Family Tree of Drone Bee He had 1 parent, a female. He has 2 grand-parents, since his mother had two parents, a male and a female. He has 3 great-grand-parents: his grand-mother had two parents but his grand-father had only one. The total of all the males and the total of all the females that make each generation forms an overlapping Fibonacci series repeated twice; One for males and one for females
great- great, great gt,gt,gt grand- grand- grand grandNumber of parents: parents: parents: parents: parents:of a MALE bee: 1 2 3 5 8of a FEMALE bee: 2 3 5 8 13