{"product_id":"golden-ratio-rectangles-1","title":"Golden Ratio Rectangles 01","description":"\u003cp\u003e\nOne of the fascinations of working with shapes based on the golden ratio is the way things nest together in such harmonious ways. This rectangle is a case in point.\n\nTake a rectangle where the relationship between the sides is the strange value called ‘the golden ratio’. If you want to work it our for yourself, it’s the ratio of a\/b where a\/b = (a+b)\/a. It’s not difficult to solve that equation and come up with a value involving the square root of 5 but Instagram comments don’t sit comfortably with maths notation. It’s a number that can’t be expressed exactly but it’s around 1.618 and is labelled ϕ. What’s special about the golden ratio is that 1\/ϕ = ϕ-1 (~0.618) and consequently ϕ*0.618 = 1.\n\nSo the short side of the rectangle is ~0.618 the length of the long side. The smaller rectangles have sides which relate in the same way but their long side is ~0.618 times the length of the short side of the big rectangle.\n\nThat done, all that remains is to fit together combinations of the smaller rectangles.\n\nThere will always be a couple of squares left somewhere in the mix but the interesting thing is that every side length within the design is related in some way to every other by the golden ratio, the foundation of the Fibonacci sequence.\n\nExtra tags: mathematics, maths, geometry\u003c\/p\u003e","brand":"d\/dx art","offers":[{"title":"Default Title","offer_id":58790020120959,"sku":"v2-shell-6832","price":28.79,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/myarthaus.com\/products\/golden-ratio-rectangles-1","provider":"Arthaus","version":"1.0","type":"link"}