Parallel Transformations: A Mathematical and Personal Lens of Singapore's Architecture

by Jessica Kudlacek

Singapore Life in Focus

For some, the word “transformations” might bring back memories of middle school Geometry or Algebra—often with a cringe. For me, though, it sparks my inner math nerd and a genuine love for the subject. While some hear “transformation” and think of deep, personal change, my mind jumps first to geometric figures shifting in position, size, or shape. That same fascination carries into my appreciation of art and photography, where simple 2D and 3D forms can become strikingly modern through patterns, silhouettes, light, shadows, and, of course, transformations. This series explores geometric transformations through architecture, while also inviting you to reflect on the parallels between mathematical and personal transformations—whichever lens you choose to view it through.

The four basic geometric transformations provide a surprisingly natural bridge to how we think about change in our own lives:

• Rotation: In geometry, rotation is when a figure turns around an axis without altering its size or shape. Beyond math, rotation can be seen as shifting our perspective—viewing a situation or relationship from another angle, and in doing so, uncovering something new or different.

• Reflection: A reflection flips a figure to create its mirror image, still unchanged in size or shape. On a more personal level, reflection invites us to pause, take stock, and be present with ourselves—a moment to mirror back and better understand where we are.

• Translation: A translation occurs when a figure slides or moves without changing its form. Likewise, in life we are always in motion—carried along by shifting circumstances, relationships, and emotions, with highs and lows of varying magnitudes and durations that move us forward in different ways.

• Dilation: Dilation stretches or shrinks a figure. In human terms, this might be the most impactful transformation: how we choose to respond when life expands or contracts around us. Do we shrink back, or do we stretch into growth—embracing challenges as opportunities for resilience, openness, and new learning? Recognizing this dynamic reminds us that transformation, much like dilation, is something we can shape and strengthen.

Esplanade

Jointly designed by DP Architects (Singapore) and Michael Wilford and Partners (UK), with Theatre Project Consultants leading the theatre design, the Esplanade has become one of Singapore’s most recognizable landmarks.¹ Initial criticism of its aesthetics faded after its opening, and locals affectionately nicknamed it “The Durian,” after the spiky tropical fruit. Its lightweight curved space-frames are fitted with triangular glass panels and champagne-coloured sunshades, balancing solar control with panoramic views. The result is a play of filtered light, shifting shadows, and textured surfaces by day, and a glowing lantern-like presence on the bay by night.²

Gateway Towers

The Gateway twin towers, designed by world-renowned I.M. Pei, is a 37-story office space that can easily be classified as an optical illusion from its trapezoidal shape and strikingly sharp, acute exterior angles. While at first glance may appear quite simplistic, Gateway East and Gateway West are anything short of mesmerizing. A change in the viewer’s position provides drastically different transformations, shifting between three-dimensional and two-dimensional appearances. Adding onto the illusion, the horizontal striped facade often merges both towers together, removing a sense of scale and inviting in the imagination.

The Hive

An architectural landmark by Heatherwick Studios, The Hive reimagines the modern university campus as a place of connection, innovation, and exchange. Its twelve tower-like stacks of classrooms blur traditional boundaries between teachers and students, interwoven with informal nooks, plant-filled balconies, and wide circulation areas that encourage interaction. At the heart of the building, a vast open atrium visually links the spaces together.³ Sixty-one textured concrete columns and curved façade panels, cast with innovative molds, create a handcrafted, clay-like appearance—underscoring the building’s tactile, human-centered design.⁴

Art & Science Museum

The Art & Science Museum is a key permanent attraction of the Marina Bay Sands Integrated Resort located at Bayfront Avenue. The largest private museum in Singapore, it focuses on the connections between art and science through hi-tech exhibits that push disciplinary boundaries. Designed by world-renowned architect Moshe Safdie, the ArtScience Museum’s flower-like geometry was accomplished with complex mathematical geometry. This demonstrates how the union of art and science can lead to the creation of something beautiful.⁵

Duo Towers

Led by German-born architect Ole Scheeren, this mixed-use high rise development is a showstopper in the Singapore skyline. Its honeycomb-patterned concave façades contrast with sheer vertical lines, casting bold shadows and rhythmic geometry. Titled ‘DUO’, the two towers are not intended to be conceived as autonomous objects, but defined by the spaces they create around them, framing a “new civic nucleus.” Named DUO, the project intentionally avoids being read as two standalone towers; instead, its identity is defined by the dynamic civic spaces created between and around the buildings—framing a new kind of “civic nucleus.” ⁶

References

1. https://www.dpa.com.sg/projects/esplanade-theatres-on-the-bay/

2. https://www.nlb.gov.sg/main/article-detail?cmsuuid=b356eaf1-8f27-47e3-b2ac-608fafe060aa

3. https://www.archdaily.com/607594/learning-hub-heatherwick-studio

4. https://cpgconsultants.com.sg/blog/projects/the-hive-learning-hub-nanyang-technological-university-of-singapore/ 

5. https://www.nlb.gov.sg/main/article-detail?cmsuuid=1e7ab7ab-3da2-443a-a26d-2358e64993f2

6. https://www.archdaily.com/295945/buro-ole-scheeren-unveils-duo-towers-in-singapore

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With a professional background in educational technology and a lifelong passion for creative pursuits, Jessica and her family moved to Singapore from Southern California. Jessica enjoys exploring Singapore from the lens of her camera, as well as other hobbies including running, tennis, and appeasing her inner “foodie."