Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Aesthetic Uses
It has been claimed that the ancient Egyptians knew the golden ratio because ratios close to the golden ratio may be found in the positio...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Alternate Forms
The formula can be expanded recursively to obtain a continued fraction for the golden ratio: and its reciprocal: Note that the suc...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Alternate Forms
The formula can be expanded recursively to obtain a continued fraction for the golden ratio: and its reciprocal: Note that the suc...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - A Startlingly Quick Proof Of Irrationality
Recall that we denoted the "larger part" by a and the "smaller part" by b, and concluded that This gives a startlingly quick proof tha...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Mathematical Uses
The number φ turns up frequently in geometry, in particular in figures involving pentagonal symmetry. For instance the ratio of a regula...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Definition
Two quantities are said to be in the golden ratio, if "the whole (i.e., the sum of the two parts) is to the larger part as the larger par...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Decimal Expansion
(sequence A001622 in OEIS) 1.6180339887 4989484820 4586834365 6381177203 0917980576 2862135448 6227052604 6281890244 9707207204 189391...   » Read the article