Modular Circles MC0004

Number a set of points spaced evenly around a circle, then join each to the point at four times its number, counting round again whenever the total is exceeded. The construction uses straight lines exclusively.

Three cusps appear. The curve is an epicycloid - the path traced by a point on the rim of a circle rolling around the outside of another - and this particular one, with three cusps, is close kin to the deltoid that Euler studied in 1745 while working on a problem in optics.

The rule holds throughout the series: cusps are always one fewer than the multiplier. What changes as the multiplier climbs is not the principle but the density. At four the structure is still legible as a single closed curve. Higher multipliers begin to fill the circle with overlapping envelopes until the individual shape gives way to texture.

The whole thing was once a schoolroom exercise done with pins and thread, which is worth remembering when looking at it: every intersection here could in principle have been placed by hand.

Part of the Signature series of mathematical art prints.

Signature is a collection of mathematical, scientific and infographic visualisations - prime number distributions, evolutionary trees, geological timescales, and other structures that become something unexpected when rendered at print scale.

Each piece begins as a data-driven computational process and is developed into a finished artwork through a combination of custom code and design refinement. The aim is not to illustrate mathematics but to make the underlying structures visible - to find the image that was always inside the data.

The series draws on fields including number theory, evolutionary biology, palaeontology, topology, and information design.

All prints are produced to order on 250gsm archival matte paper using pigment-based inks, chosen for colour accuracy and long-term stability.

Each print is rolled in acid-free tissue and shipped in a rigid cardboard tube, sealed for moisture protection, ready for framing on arrival.

Large · 70 × 70 cm · 28 × 28 in

XLarge · 100 × 100 cm · 40 × 40 in

UK: Free · 3-5 working days

Europe: €8.50 · 3-7 working days · No customs charges

USA & Canada: $8.95 / $12.00 CAD · 5-10 working days

Australia: $14.00 AUD · 5-10 working days

Rest of World: £14.95 · 7-14 working days

All prints are produced to order and dispatched within 1-3 working days. Orders placed before 5pm GMT ship the same day. You'll receive tracking information by email once dispatched.

Orders outside Europe may be subject to local customs charges on delivery - these are the responsibility of the recipient.

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Returns accepted within 30 days. Email returns@axisophy.com with your order number and we'll provide return instructions.

Return postage is the customer's responsibility except where the print arrives damaged or there's been an error - in which case we'll arrange a replacement or refund immediately, no return needed.

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