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The ratio of the shorter side of the rectangle to the longer side is the same as the ratio of the longer side to the sum of the two sides. And that ratio is the Golden section.
A golden rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1:1.618. A 3x5 card has side lengths of 3 inches by 5 inches, which do not match the golden ratio. Therefore, a 3x5 card is not a golden rectangle.
In italy, the Pantheon, however has the golden ratio. Its pillars below the roof is a rectangle, the golden rectangle, on the roof (top part) is a triangle, the golden triangle.
It is considered that a shape, eg. Rectangle, with the golden ratio looks "most pleasing to the eye".
A golden rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1:1.618. Some whole number pairs of side lengths that approximate a golden rectangle include 1:2, 2:3, 3:5, 5:8, and so on. These pairs get closer to the golden ratio as the numbers increase.