{"product_id":"modular-circles-mc0003","title":"Modular Circles MC0003","description":"\u003cp\u003eMark points evenly around a circle, number them, and join each one by a straight line to the point at three times its number, wrapping around when the count runs past the total. Every line is straight. No curve is drawn at any stage.\u003c\/p\u003e\n\u003cp\u003eA nephroid emerges: two cusps, kidney-shaped, the curve traced by a point on a circle rolling around another circle exactly twice its size. It is the shape of the bright caustic that forms when parallel light reflects off the inside of a cylinder, which is why it turns up in a coffee cup and in the reflections inside a wedding ring.\u003c\/p\u003e\n\u003cp\u003eThe relationship between multiplier and curve is exact and simple: the number of cusps is always one less than the multiplier. Two gives a cardioid with one cusp, three gives this, four gives three cusps, and the sequence continues indefinitely. Each is an epicycloid, arrived at without anything rolling.\u003c\/p\u003e\n\u003cp\u003eWhat the construction demonstrates is that curvature can be emergent. The cusps are not drawn, not calculated, and not present in any individual line. They are a property of the whole family of lines, and of nothing within it.\u003c\/p\u003e\n\u003cp\u003ePart of the Signature series of mathematical art prints.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (70 × 70 cm | 28 × 28 in)","offer_id":46883866804385,"sku":"AXS-MODC-0003-S-700x700-AM-WHT","price":70.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (100 × 100 cm | 40 × 40 in)","offer_id":46883866837153,"sku":"AXS-MODC-0003-S-1000x1000-AM-WHT","price":120.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/axisophy-modular-circles-mc0003-art-print-700mm-mockup.jpg?v=1786708434","url":"https:\/\/axisophy.com\/products\/modular-circles-mc0003","provider":"Axisophy","version":"1.0","type":"link"}