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The classical Fibonacci sequence is defined so that the first two terms are each equal to 1, and each term after this is the sum of the two terms immediately before it. The golden ratio is the ratio of the longer to shorter side of a rectangle with the property that if we remove a square from the rectangle such that the remainder is also a rectangle, that the old and new rectangles are proportional. Johannes Kepler showed that if we take the sequence of ratios of consecutive Fibonacci numbers, the limit of this sequence is the golden ratio [5]. In this paper, we give a higher dimension extension of Fibonacci sequences and golden ratios and provide a connection between the two.

Relationships between Fibonacci-type sequences and Golden-type ratios