For this year's celebrations of Pi Day on March 14th we bring you the shiniest of numbers! The golden ratio, $\phi$, has fascinated mathematicians for centuries. It arises from the Fibonnacci sequence! It appears in nature! And could it be the key to beauty? Or is that just a mathematical myth? Our favourite fact, and the real reason we chose it to celebrate Pi Day is that, like the number $\pi$, the golden ratio is an irrational number. But not just that, the golden ratio is the most irrational number there is – definitely something worth celebrating!
Happy Pi Day everyone!
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Maths in a minute: The golden ratio — We're very pleased to give you a very quick introduction to this very famous number!
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The life and numbers of Fibonacci — Find out how the golden ratio arises from rabbits and how it appears nature.
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Maths in a minute: Continued fractions — A quick explanation of why the golden ratio is the most irrational number of them all!
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Myths of maths: The golden ratio — The golden ratio has many amazing properties. But is it really a secret of nature and the epitome of beauty? Find out in this article and video from Chris Budd's lecture at Gresham College.
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Metallic numbers: Beyond the golden ratio — You've heard of the golden ratio but have you heard of the silver ratio? And all its other cousins called the metallic numbers? Read this article to meet the family!
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The fingernail problem and metallic numbers — A beautiful geometric problem opens the door to the world of metallic numbers.