Golden ratio

approximately 1.618033989. It is also known as the Divine Ratio,

the Golden Mean, the Golden Number, and the Golden Section.

a unique sequence of integers, starting with 1, where each

element is the sum of the two previous numbers. For example: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.

Sequence is an infinite sequence, which means it goes on

for ever, and as it develops, the ratio of the consecutive terms converges (becomes closer) to the Golden Ratio, ~1.618. For example, to find the ratio of any two successive numbers, take the latter number and divide by the former. So, we will have: 1/1=1, 2/1=2, 3/2=1.5, 5/3=1.66, 8/5=1.6, 13/8=1.625, 21/13=1.615.

Even though we know it approaches this one particular constant,

we can see from the graph that it will never reach this exact value.

MB
Draw a circle with the center of M, radius of

MB
Expand the DC until it meets with the circle. The intersection is one vertex of the rectangle
Complete the rectangle

is an isosceles triangle such that the ratio of the

hypotenuse a to base b is equal to the golden ratio. From the above figure, this means that the triangle has vertex angle equal to

pattern, where the first level has one "branching" (the trunk),

the second has two branches, than 3, 5, 8, 13 and so on. Also, the spacing of leaves around each branch or stalk spirals with respect to the Golden Ratio.

(the part of the flower that is not the petal)

that protected the bud are outermost, followed by the 5 outer green petals and an inner layer of 5 more paler green petals.

 

Fibonacci Numbers. The examples are that the buttercup has 5

petals, delphiniums has 8 petals, ragwort has 13 petals, aster as 21 petals, plantain has 34 petals, and asteraceae family has 55 petals, and some of them have 89 petals.

plastic surgeon, has used the golden section and some of

its relatives to make a mask that he claims that is the most beautiful shape a human face can ever have, it used decagons and pentagons as its function that embodies phi in all their dimensions.

a golden rectangle. There is also a Golden Ratio in

the height to width of the center two teeth. And the ratio of the width of the two center teeth to those next to them is phi. And, the ratio of the width of the smile to the third tooth from the center is also phi.

impact on art, influencing artists' perspectives of a pleasant art

piece. Da Vinci, a sculpture, a painter, an inventor and a mathematician, was the first one who first called Phi the Golden Ratio.

to the ratio of the width of her forehead compared

to the length from the top of her head to her chin.

in several places, appearing in both the ceiling and the

position where the people sit.

Ratio is the length from the front head to the

ear opening compared with the length from the forehead to the chin. The second one appears in the ratio of the length from the nostril to the earlobe compare with the length from the nostril to the chin.

ancient architecture. Not only did the ancient Egyptians and Greeks

know about the magic of Golden Ratio, so did the Renaissance artists, who used the Golden Ratio in the design of Notre Dame in between the 12th and 14th centuries.

height, and the height from the vertex to the center

create a right triangle.

Ratio in many of the proportions.

the building compared with the height of every ten floors

is a Golden Ratio.

perfection. Ancient Greeks considered that the world can’t be without

laws of harmony and the searching of harmony is the way of learning the world.Golden ratio makes an impression of harmony and beauty. That’s why sculptors, architects and artists use golden ratio in their works.