Number nine dream.

Cecil Balmond's show at Louisiana reveals the inventive engineering power behind the throne of starchitecture.

Almost ten years ago Arup structural engineer Cecil Balmond published his first book. Entitled enigmatically Number 9: The Search for the Sigma Code, it revealed a passion for number theory linked with the discovery of beautiful patterns entirely untypical for the engineering profession. Overnight it bestowed Balmond with the aura of a mystic creator of fascinating structures, the true spirit behind superstar projects such as Koolhaas' Kunsthal, Siza's Portuguese Pavilion (AR July 1998) or Libeskind's unrealised Spiral extension to the Victoria & Albert Museum. Since the late '90s, Balmond has further established his reputation as a beguiling magus of structure, forces, pattern and numbers. Anish Kapoor's installation Marsyas at the Tate Modern, Toyo Ito's Serpentine Pavilion (AR September 2002) and Koolhaas' CCTV headquarters in Shanghai are just some of the striking structural interventions where Balmond explores what he calls the 'Informal'. Sudden twists and turns, hybrid and juxtaposed forces as well as an inimitable feeling for local space and atmosphere. 'Informal' also became the title of his second book in 2002.

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For a new series of exhibitions on leading edge architecture, Denmark's Louisiana Museum has, intriguingly, singled out Balmond to go first. Very much like his poetic reading of architectural structure the show is far from being an iterative display of projects; rather it develops the musical principle of theme and variation. A curved corridor introduces the six principal phenomena that have occupied Balmond's curiosity and imagination over the years: numbers, geometry, proportion, evolutionary form, time and equilibrium. You get a very personal introduction into mathematical, geometric and, indeed, the natural marvels of the universe. No cross reference is too remote, be it the monochord demonstrating the numeric order of music or the aesthetics of dome structures and catenaries developed by Frei Otto.

Each of these educational chapters provided Balmond with decisive clues to 'crack the code' of contemporary architecture as defined by a rational adherence to the Cartesian dogma of the right angle or the more current exuberant proliferation of blobs. Instead of desperately trying to 'engineer' wilful architectural shapes, Balmond reverts in his mathematical analysis of architecture to rhythmic pulse, natural harmonies or the aesthetic of algorithms.

The second space, entitled 'Fractal', reveals the behaviour or non-linear structure or how the hitherto didactic explanations of Balmond's inspiration and methodology come to life. It's a moving, or rather a dancing universe, projected on black walls in the dark space. For example, the Penrose aperiodic tiling discovered by American mathematician Robert Ammann, which Balmond adopted for the facade of Libeskind's Spiral, multiplies and divides endlessly in front of your eyes. Each wall of the square room is filled with a large projection that displays the dynamic forces of Informal. The middle is dominated by a white illuminated pinnacle of what would have been the top of the Spiral, a reminder that Balmond is dealing with actual architectural form and not just the theoretical beauty of underlying formulae.

The third, double-height exhibition space provides a stage for Balmond's three-dimensional models of individual projects. Each displays a wealth of inspiration from diverse sources--music, mathematics, fractals, algorithms or numerology. Most of the projects were designed with the now famous Advanced Geometry Unit (AGU), the specialist multidisciplinary engineering cabal set up by Balmond within Arup in 2000. No longer made up of ordinary squares, triangles, circles, geometry is transformed into an erratic puzzle and the tension becomes visible, stretched to the point of collapse or twist. The Pedro and Ines Footbridge in Coimbra (AR February 2007), for instance, shifts sideways at exactly the moment of greatest suspension and thus the two halves support each other. The bridge is a perfect interplay of the forces and proportions where constructive and aesthetic principles are stretched to the utmost. Here Cecil Balmond the designer dramatically trumps Cecil Balmond the engineer. Hani Rashid of Asymptote, the subject of the next exhibition in this series in 2009, has a hard act to follow.

The Frontiers of Architecture I: Cecil Balmond, Unfolding New Dimensions, Louisiana Museum of Modern Art, Denmark, 22 June-21 October. www.louisiana.dk