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It can be found quite often in the literature that many well-known architects have employed either the golden rectangle or the Fibonacci rectangle in their works. On contrary, it is rare to find any specific reason for using them so often. Recently, Shekhawat (2015) proved that the golden rectangle and the Fibonacci rectangle are one of the best connected rectangular arrangements and this may be one of the reasons for their high presence in architectural designs. In this work we present an algorithm that generates n - 4 best connected rectangular arrangements so that the proposed solutions can be further used by architects for their designs. [ABSTRACT FROM AUTHOR]

It is often found in the literature that many researchers have studied or documented the use of golden rectangle or Fibonacci rectangle in architectural design. In this way, a lot of well-known architects in the history, knowingly or unknowingly, have employed either the golden rectangle or the Fibonacci rectangle in their works. Using some mathematical tools, this paper tried to approach one of the properties of the golden rectangle (or the Fibonacci rectangle) and its significance to architectural design, which could lead to state one hypothesis about why architects have used them so often. This work begins with an algorithm which constructs a Fibonacci rectangle and a golden rectangle. Then adjacency among the squares (which are arranged inside them) is defined, by considering each square as a room or an architectural space. At the end, using some tools of the graph theory, it has been proved that they are one of the best arrangements of squares (or rectangles) inside a rectangle, from the point of view of connectivity. [ABSTRACT FROM AUTHOR]