The Fibonacci sequence can be used to determine the golden ratio. If you divide a term in the sequence by its predecessor, at suitably high values, it approaches the golden ratio.
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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.
Golden ratio can be traced back to as early as 2500 BC. The Great Pyramid of Giza is an example of the golden ratio. the side is 612.01. and the half of the base is 377.9. 612.01/ 377.9= 1.61950... its approximately the measurement of the golden ratio. Another example is the Parthenon.
There are both golden triangles and golden rectangles. In order to be considered golden the ratio must be the same as the sum of the longest side to the other two sides.
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.