Time Triangles - Omar Chishti

Ephemeral geometry.

11 September 2025 · 4 min read

Poster showing an abstract clock composed of overlapping triangles — **Figure 1.** Triangles representing each minute of the day on an abstract clock.

Introduction

This piece was born one afternoon as I studied the seconds ticking by on a wall clock, neatly marking off my mortal span in increments uniform and unrelenting. The clock possessed a stark black face, with plain hands and no numerals. Silver-grey tickmarks. It marks the passage of time in my childhood bedroom (or a recreation of it, a room of Theseus, essence intact through several moves) in Delhi, India. It had been ticking on in solitude for seven years since my last visit to India.

I imagined freezing a moment by tearing the second hand off the center post and propping it against the endpoints of the major hands to form a triangle – a flying buttress against entropy's march. The hour and the minute hand in their base positions defining an angle, with the second hand completing the shape. This flavour of operation, translating transience into a crystalline stasis, lies at the heart of several different projects I've worked on over the years.

Construction

Figure 2. Simplified animation depicting the central conceit of the time triangulation.

When I got around to capturing the idea with code, I abandoned the second hand and considered an elastic expanse of webbing between the major hands. The fabric of reality stretched between the defining termini. The animation above brings out the resemblance to watching a a sundial timelapse. Parametric generation of the triangles involved some trigonometry and modular arithmetic. I employed the golden ratio for the lengths of the hands.

The hour hand and the minute hand follow the golden ratio — **Figure 3.** Schematic for triangle construction.

I used a dashed dodecagon (12 sided polygon) to mark the boundary of the clock, with vertices marking each hour, inset within a circumscribing circle. I chose 07:00 for the illustrative example since 7 is my favourite single-digit number. The font for the numerals across my visuals is often Academy Engraved LET, while other labels are in Bodoni Small Capitals. This image incidentally also serves as the cover image for my digital diaries, which I take the time to typeset neatly and reflect on annually.

The series of triangles formed by the passage of an hour — **Figure 4.** Series of triangles formed by the passage of an hour.

There is a tactile quality to time represented in this manner. Layers of triangles stacked on top of each other, separable into discrete units. Each hour consists of 58 triangles and two lines (degenerate triangles). The set of 60 for a given hour maps bijectively to the set for any other, with the only difference being orientation and ordering. The transparency of the gradient fill means the ordering is visually preserved in the overlay.

**Figure 5.** Ten minutes along a timeline.

The linear timeline view takes the triangles from their original radial arrangement and lays them out sequentially. A prime motivating factor for this visual was to capture the concept and yield the tools/units to visualise timestamped data in a salient manner. I haven't yet completed the larger project, but I hope the radial/linear representations will work well for what I have in mind.

Close up of overlapping lines from main clock — **Figure 6.** Detail view of pattern traced out over the course of the day.

Over the course of a full twelve-hour cycle, the overlapping triangles trace out a complex pattern reminiscent of spirograph designs. The density of lines and convergence of shapes in certain regions reflects the cyclical nature of time and the repetitive motion of the clock hands. The dark background has a space-filling curve overlaid on it.1 The curve winds its way through the negative space, capable (at higher iterations) of transiting through every pixel on the canvas.

Sketch of similar concept on graph paper circa 2016 — **Figure 7.**Sketch of a concept along similar lines on graph paper (circa 2016).

The roots of this visual lie in a sketch I made years ago on graph paper, exploring similar ideas about time and geometry. Each of the three circles above was meant to contain a clock set to a different timezone.

Conclusion

``In the sunset of dissolution, everything is illuminated by the aura of nostalgia, even the guillotine.''
— Milan Kundera, The Unbearable Lightness of Being

I credit my teenage fondness for Kundera's novels to the author's meditations on memory and time. The past, the present, the future in an uneasy dance; causality blurred by the fallibility of recollection and the prophetic impulse of anticipation. ``Einmal ist keinmal'' — once is never. Nietzsche's eternal recurrence. I'd love to similarly smoothly incorporate philosophical underpinnings to my writing, but unfortunately tend to drop in references in a more haphazard manner and hope the odd indices suffice to acquaint the curious reader with my tangle of preoccupations.

Despite the general geometric austerity of this visual, within its central motif lies a whole life: every minute of every day from first breath to last captured ``in a network of lines that enlace, in a network of lines that intersect, on the carpet of leaves illuminated by the moon around an empty grave – what story down there awaits its end?''2

Notes

[1] In mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square (or more generally an n-dimensional unit hypercube).

[2] From Italo Calvino, If on a winter's night a traveler (1979). The novel's chapter titles form a continuous sentence when read in sequence.