Mathematics is typically pervasive under the software hood – in this case, matrix algebra applied to a pixel grid. This transparency comes at a price. As a result, in our software-saturated design environments the formulated syntax of mathematics is all too easily amalgamated with the functionality of digital tools, which mathematics enable – but also predate by thousands of years. On a personal level, mathematics is likely to summon memories of hard graft, frustration and perhaps even of failure. Mathematics is a deeply abstract discipline, and as such it is easily misunderstood. Fdecomite, Third Stellation of Cuboctahedron

A cuboctahedron, also known as a dymaxion according to Buckminster Fuller, is a uniform polyhedron with a specific number of faces. Far from being a bonus or a side-effect, architectural geometry is a discipline in its own right, forming a long and complex continuum subdivided into distinct historical segments with vastly different instrumental priorities. While our design culture has firmly embraced the innovations of computing, it has decidedly less time for the formulated thought lying at the very root of the breakthrough. Architecture and Mathematics have constantly balanced between two extremes: an experiential dimension often imbued with contemplative connotations, and the quest for operative techniques that do not necessarily present a spatial meaning. D-1 n:=0.. Design software and numerical fabrication machinery have recast the traditional role of geometry in architecture and opened it up to the wondrous possibilities afforded by topology, parametric surface design and other areas of mathematics. D – 1

m + І ■ n 1 + і

Іт’п:=^Л Г

(1 + i>

f { z) := 1.4 • z • exp Зі • n • (I z I )2 D-1 D-1

Q2> f ( (I) ) *

2 2 rd ( x) := f loor(x + .5)

F2m’ n S1rd(Re(Q2m) „)) , rd(lm(Q2m> n))

SI

F2

Figure 3. George L Legendre, Self Portrait As Photoshop Filter, 2006

The mapping rotates the complex coordinates of a pixel by an amount proportional to the square of its distance from the origin to produce a swirl. Critically for designers (at first glance at least), the instrumentality of computation seems easier to grasp than that of mathematics, which good design software will render ‘transparent’ anyway. level functionality of design computing that has ultimately smothered it. — Antoine Picon, ‘Between Intuition and the Quest for Operative Techniques’, public lecture, Symposium on ‘Mathematics in Space’, Harvard Graduate School of Design, 5 March 2010

Over the past 15 years, architecture has been profoundly altered by the advent of computation and information technology.