Super Golden Result


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Super Golden Result

What is the supergolden sequence?

The supergolden sequence, also known as the Narayana's cows sequence, is a sequence where the ratio between consecutive terms approaches the supergolden ratio. The first three terms are each one, and each term after that is calculated by adding the previous term and the term two places before that.

What are the first values of the supergolden ratio?

The first values are 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595… ( OEIS:A000930 ). Many of the properties of the supergolden ratio are related to those of the golden ratio φ.

What are the algebraic conjugates of the supergolden ratio?

The supergolden ratio's algebraic conjugates are is 1. , the supergolden ratio ψ. When a square with the same side length as the shorter side of the rectangle is removed from one side of the rectangle, the sides resulting rectangle will be in a ψ 2 :1 ratio.

What is an example of a supergolden rectangle?

There is a supergolden rectangle that has the property that if a square is removed from one side, the remaining rectangle can be divided into two supergolden rectangles of opposite orientations. Another example is that both the golden ratio and the supergolden ratio are Pisot numbers .

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