UN Secretariat Building
Another building to use the golden ratio in modern times is the UN Secretariat Building. The building was built according to the golden ratio: 10 floors to the ratio of the width of the building is 1: đťś‘ . As shown in Figure 5, we can see the golden ratio from the width of the entire building when comparing it to the height of every ten floors. There are four noticeable bands on its facade with ratio of 5, 9, 11 and 10 floors between them 9 .
fig. 5: UN Secretariat Building
Furthermore, the golden ratio extends into the interior of the UN Secretariat Building. As shown in the floor plan of figure 6, the hallway divides the floor at the golden ratio of the building’s cross-section. The central conference room is also in the shape of a golden rectangle 9 . In addition, the front entrance of the UN Secretariat Building also reveals the golden ratio as the large open framed areas to the left and right of the centre entrance area are golden rectangles, and the doors on the left and right side of the centre entrance are also golden rectangles 9 (as shown in figure 6).
fig. 6: Floor plan and front entrance of UN Secretariat Building
Le Corbusier, the architect of the UN Secretariat Building, designed the building based on mathematical proportions in human body. His objective was to apply the Fibonacci sequence and golden ratio to architecture with a range of harmonious measurements to suit the human scale. Richard Padovan who invented the Padovan sequence praised the building as “rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities.” 10 Although both Parthenon and the UN Secretariat Building were built using the golden ratio, they have different appearance. The Parthenon forms a spiral and has many golden rectangles in its design, whereas the UN secretariat building has only a few golden rectangles resembling the perfect human body, but without any spiral on it as it only goes straight up 10 . This shows that modern architects have different ideas from the old architects in their design and their ways of representing the golden ratio. Comparison between the Parthenon and the UN Secretariat Building
In the following sections, I will examine two other sequences: the terms in powers of two and root proportions.
Terms of Powers of Two
In mathematics, a power of two means a number of the form 2 where n is an integer, i.e. the result of exponentiation with two as the base and an integer n as the exponent. When the terms of power
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