{"product_id":"golden-ratio-earring-hoops-gold-vermeil","title":"golden ratio earring hoops | gold vermeil","description":"\u003ch2\u003eGolden ratio earring hoops | 18K gold vermeil\u003c\/h2\u003e\n\u003cp\u003eA hoop that closes on the one number both the mathematician and the botanist agree on. Gold suits the golden ratio for the obvious reason, but the better one is that gold catches light along a curve, and this curve is the point. For someone who has spotted the spiral in a sunflower head and never quite let it go.\u003c\/p\u003e\n\u003ch2 style=\"margin-top: 2em;\"\u003eThe Science Behind the Golden Ratio\u003c\/h2\u003e\n\u003cp\u003eThe golden ratio stayed a geometer's number for two thousand years, and then the physicists got hold of it. In 1992, Stéphane Douady and Yves Couder dropped ferrofluid droplets one at a time onto the centre of a dish of oil in a magnetic field. Each drop was repelled by the ones before it and drifted outward. Past a certain drop rate, the pattern organised itself: successive drops settled 137.5 degrees apart, the golden angle, and the dish filled with the same crossing spirals as a sunflower head, in consecutive Fibonacci numbers. No genes, no growth hormones, only repulsion and rate. It showed that phyllotaxis is not a rule plants obey but the least crowded arrangement anything can find when new elements keep arriving at a rotating edge. The number itself, φ = (1+√5)\/2, has the slowest-converging continued fraction of any irrational, which is exactly why 360°\/φ² spreads points out better than any other angle.\u003c\/p\u003e\n\u003ch2 style=\"margin-top: 2em;\"\u003eWho Wears It\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003emathematicians who teach continued fractions or the Fibonacci sequence\u003c\/li\u003e\n\u003cli\u003ebotanists and developmental biologists working on phyllotaxis\u003c\/li\u003e\n\u003cli\u003ephysicists who like their pattern formation experimental\u003c\/li\u003e\n\u003cli\u003eanyone who wants the precise version of the ratio, not the one from the design blogs\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2 style=\"margin-top: 2em;\"\u003eExplore Related Math and Physics Jewelry\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https:\/\/sciencejewelry1824.shop\/products\/golden-ratio-earring-hoops\"\u003eGolden ratio earring hoops | silver\u003c\/a\u003e\u003c\/li\u003e\n\u003cli\u003e\u003ca href=\"https:\/\/sciencejewelry1824.shop\/products\/golden-ratio-18k-gold-plated\"\u003eGolden ratio necklace | gold vermeil\u003c\/a\u003e\u003c\/li\u003e\n\u003cli\u003e\u003ca href=\"https:\/\/sciencejewelry1824.shop\/products\/pi-18k-gold-plated\"\u003ePi necklace | gold vermeil\u003c\/a\u003e\u003c\/li\u003e\n\u003cli\u003e\u003ca href=\"https:\/\/sciencejewelry1824.shop\/products\/mobius-ring-18k-gold-plated\"\u003eMobius strip necklace | gold vermeil\u003c\/a\u003e\u003c\/li\u003e\n\u003cli\u003e\u003ca href=\"https:\/\/sciencejewelry1824.shop\/products\/phi\"\u003ePhi necklace | silver\u003c\/a\u003e\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003csection class=\"product-faq\"\u003e\n\u003ch2 style=\"margin-top: 2em;\"\u003eFAQ\u003c\/h2\u003e\n\u003ch3 style=\"margin-top:1.75em;\"\u003eIs the spiral a true golden spiral?\u003c\/h3\u003e\n\u003cp\u003eIt is the classical construction: quarter-circle arcs drawn inside squares whose sides follow the Fibonacci sequence, the same drawing found in every textbook on the ratio. That construction approximates the true logarithmic spiral with growth factor φ closely enough that the two are indistinguishable at earring scale. The design is honest about which one it is.\u003c\/p\u003e\n\u003ch3 style=\"margin-top:1.75em;\"\u003eWhy does the golden angle show up in plants at all?\u003c\/h3\u003e\n\u003cp\u003eBecause 137.5 degrees is the angle that avoids alignment for longest. A rational angle would eventually place a new leaf or seed directly over an earlier one, wasting light and space. The golden angle is derived from the most irrational number there is, so no two elements ever line up along a radius. Sunflowers, pinecones and pineapples did not converge on it by coincidence. The 1992 droplet experiment showed that anything growing at a rotating edge will find the same angle.\u003c\/p\u003e\n\u003ch3 style=\"margin-top:1.75em;\"\u003eHow does gold vermeil hold up on hoops?\u003c\/h3\u003e\n\u003cp\u003eVermeil here is 2.5 microns of 18K gold over solid sterling silver, a thicker gold layer than standard plating. Hoops see little abrasion through the day, since nothing rubs against them. Clean with a soft dry cloth, and keep perfume, hairspray and cleaning products off the metal.\u003c\/p\u003e\n\u003ch3 style=\"margin-top:1.75em;\"\u003eWhat are the size, material and finding specs?\u003c\/h3\u003e\n\u003cp\u003e18K gold vermeil over a sterling silver core, 34 mm hoops on gold vermeil posts with ear nuts. Nickel-free and hypoallergenic, no chain. Free worldwide DHL Express in 1-5 business days, with all import duties and taxes covered. 30-day “Love It or Return It” returns.\u003c\/p\u003e\n\u003ch3 style=\"margin-top:1.75em;\"\u003eIs there a silver version?\u003c\/h3\u003e\n\u003cp\u003eYes. The same golden ratio hoops come in \u003ca href=\"https:\/\/sciencejewelry1824.shop\/products\/golden-ratio-earring-hoops\"\u003esterling silver\u003c\/a\u003e at the same 34 mm size on the same posts. Choose the finish the recipient already wears. Both versions carry the same design and the same meaning.\u003c\/p\u003e\n\u003c\/section\u003e","brand":"sciencejewelry1824","offers":[{"title":"Default Title","offer_id":56917328494978,"sku":"ER0057-GV","price":230.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1411\/4806\/files\/golden-ratio-earring-hoops-gold-vermeil.png?v=1789716983","url":"https:\/\/sciencejewelry1824.shop\/products\/golden-ratio-earring-hoops-gold-vermeil","provider":"sciencejewelry1824","version":"1.0","type":"link"}