What rectangle did the ancients consider the most pleasing to the eye. And what is relationship (see below)?

Question

And what is relationship of the long side divided by the short side. And is this relationship found in natere? Where? What artist (most famous) used this relationship in his paintings? What is the matematical name for this?

Answer 1

It's name is the Golden Ratio. Two quantities are said to be in the Golden Ratio if the whole (that is, the sum of the two parts) is to the larger part as the larger part is to the smaller part. Mathematically, it's (a+b)/a = a/b

Our observations of the world are influenced by the rule of proportion, and the Golden Ratio can be considered a representation of the collective consciousness of humanity. For if we were to view nature from an altered state of consciousness, the proportion would also be altered.

In 1509, Luca Pacioli published the Divina Proportione, which explored not only the mathematics of the Golden Ratio, but also its use in architectural design. This was a major influence on subsequent generations of artists and architects. Leonardo Da Vinci drew the illustrations, leading many to speculate that he himself incorporated the Golden Ratio into his work. It has been suggested for example that Da Vinci's painting of the Mona Lisa employs the Golden Ratio in its geometric equivalents.

Da Vinci suggested that the human body has proportions close to the Golden Ratio. The Swiss architect Le Corbusier took this suggestion to an extreme, not only splitting the body's height at the navel into two sections in the Golden Ratio, but splitting those each again, at the knees and at the throat.

Answer 2

In Europe next rectangle is used for paper.
--- A4 has double area as A5.
--- A5 has double area as A6.
--- The area of an A0 is by definition 1 m2.
Suppose the two sides of an A4 are p and q. (Guess p>q).
When you fold it into two equal rectangles with sides q and p/2.
Now the demand is p / q = q / (p/2).
This can be simplified to p / q = V2 / 1
and probably, this is not what you ask, I guess. However it is a 'good looking' rectangle

The Golden Cut is what you are looking for most probably.
Choose a point C on the straight line AB. AC = p and CB = q
C gives the Golden Cut if
p / q = q / (p+q)
This can be simplified to p / q = {(V5) - 1} / 2
This is about 0.6180339 / 1 = 1 / 1.6180339
Mind the digits behind the decimal point in both numbers!

Answer 3

It seems you already know the answer to this, but here.

The ratio is 1.618. It exists all over nature, mainly in the chambered nautilus. Leonardo Da Vinci used it. It is known as the Fibonacci ratio, the PHI ratio, and the golden ratio.

I might be wrong though.

Answer 4

It's called geometry. A rectangle is just formed by combining two right triangles together. Artists have always used the rectangle as a form on their canvas. http://www.haberarts.com/rothko.htm
Also a good source or art, history and architecture.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html

Answer 5

why do you care?