Fibonacci numbers – Quanta Magazine https://www.quantamagazine.org Illuminating science Mon, 16 Sep 2024 14:10:47 -0400 en-US hourly 1 https://wordpress.org/?v=6.2 The Astonishing Behavior of Recursive Sequences https://www.quantamagazine.org/the-astonishing-behavior-of-recursive-sequences-20231116/ https://www.quantamagazine.org/the-astonishing-behavior-of-recursive-sequences-20231116/#respond Thu, 16 Nov 2023 15:20:25 +0000 https://www.quantamagazine.org/?p=132363 The post The Astonishing Behavior of Recursive Sequences first appeared on Quanta Magazine

]]> In mathematics, simple rules can unlock universes of complexity and beauty. Take the famous Fibonacci sequence, which is defined as follows: It begins with 1 and 1, and each subsequent number is the sum of the previous two. The first few numbers are: 1, 1, 2, 3, 5, 8, 13, 21, 34 … Simple, yes, but this unassuming recipe gives rise to a pattern of far-reaching significance, one that appears to be...

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]]> https://www.quantamagazine.org/the-astonishing-behavior-of-recursive-sequences-20231116/feed/ 0 Mathematicians Discover the Fibonacci Numbers Hiding in Strange Spaces https://www.quantamagazine.org/mathematicians-surprised-by-hidden-fibonacci-numbers-20221017/ https://www.quantamagazine.org/mathematicians-surprised-by-hidden-fibonacci-numbers-20221017/#respond Mon, 17 Oct 2022 13:44:13 +0000 https://www.quantamagazine.org/?p=119791 The post Mathematicians Discover the Fibonacci Numbers Hiding in Strange Spaces first appeared on Quanta Magazine

]]> Fourteen years ago, the mathematicians Dusa McDuff and Felix Schlenk stumbled upon a hidden geometric garden that is only now beginning to flower. The pair were interested in a certain kind of oblong shape, one that could be squeezed and folded up in very particular ways and stuffed inside a ball. They wondered: For a certain shape, how big does the ball need to be? As their results began to...

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]]> https://www.quantamagazine.org/mathematicians-surprised-by-hidden-fibonacci-numbers-20221017/feed/ 0 The Connoisseur of Number Sequences https://www.quantamagazine.org/neil-sloane-connoisseur-of-number-sequences-20150806/ https://www.quantamagazine.org/neil-sloane-connoisseur-of-number-sequences-20150806/#comments Thu, 06 Aug 2015 14:25:43 +0000 https://www.quantamagazine.org/?p=17993 The post The Connoisseur of Number Sequences first appeared on Quanta Magazine

]]> Neil Sloane is considered by some to be one of the most influential mathematicians of our time. That’s not because of any particular theorem the 75-year-old Welsh native has proved, though over the course of a more than 40-year research career at Bell Labs (later AT&T Labs) he won numerous awards for papers in the fields of combinatorics, coding theory, optics and statistics. Rather...

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]]> https://www.quantamagazine.org/neil-sloane-connoisseur-of-number-sequences-20150806/feed/ 16 How to Make Impossible Wallpaper https://www.quantamagazine.org/how-to-make-impossible-wallpaper-20130305/ https://www.quantamagazine.org/how-to-make-impossible-wallpaper-20130305/#comments Tue, 05 Mar 2013 16:26:35 +0000 https://www.quantamagazine.org/?p=3739 The post How to Make Impossible Wallpaper first appeared on Quanta Magazine

]]> At first glance, designing wallpaper can seem as simple as a kindergarten art project. Designers can start with any combination of colors and forms for the first small patch, and then just replicate it again and again in two independent directions. Depending on the patterns in the original patch, and the choice of the two directions, additional symmetries may emerge — for example...

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