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RECONCILING HIGH-RISE LIVING AND THE SUN 25

disseminated by Alexander et al. in A Pattern Language 4
and also with concern as to the numbers and the pro-
portions in Le Nombre Plastique by van der Laan 5 based
on the theories of Pythagoras and his definition of 7
notes of the octave, and particularly on his 3-4-5 triangle,
which governs three dimensional space as the golden
rectangle 6 governs two dimensional space. It is a finite
space rationally thought out, surrounded by convex 7
surfaces at the scale of the meter, created by man and
built for his soul, his spirit and his senses, at the center
of the converging space of the universe, upon which it
impacts but little. It masters, in an invisible and impla-
cable manner, the volumes at the heart of the physical
environment of nature and restrains liberty of design.

4 Christopher Alexander et al., A pattern language, Oxford, Oxford
University Press, 1977.

5 Dom Hans van der Laan, Le Nombre plastique, quinze leçons sur l’or-
donnance architectonique, Leiden, E.J. Brill, 1960; φ3 = φ +1

6 φ² = φ +1

7 These surfaces are characterized by a positive Gaussian curvature.
Take a paper hexagon formed by six equilateral triangles on a flat
surface, take away one triangle and move the others so that they
touch the borders of the empty space left by the triangle that has
been removed. You will form a “Chinese hat,” a convex surface that
is nothing other than the superior or inferior part of the icosahed-
ron. This surface corresponds to a universe in which human thought
is central. Now cut one radial side of two adjacent triangles of
another hexagon and force between them an additional equilateral
triangle of paper: you will have formed a “leaf of lettuce”, a surface
with a negative Gaussian curvature that does not close the space, an
undulating, concave surface. The plan and its hexagon, with its zero
Gaussian curvature, separates the surfaces with positive and nega-
tive curvatures: they form “the middle kingdom”, an abstract space.