Add new comment


A geometric sequence with a common ratio (or ratio constant) of 2 has the recurrence Sn=Sn-1 + Sn-1, where n stands for the index in the sequence S.

The Fibonacci sequence with a ratio constant of roughly 1.618 (known as Phi) has the recurrence Sn=Sn-1 + Sn-2.

The Narayana's Cows sequence (OEIS A000930) with a ratio constant of roughly 1.4656 (call it Moo or the bovine ratio) has the recurrence Sn=Sn-1 + Sn-3.

And so on.

(2^0)+1 = 2^(0+1)
(Phi^1)+1 = Phi^(1+1)
(Moo^2)+1 = Moo^(2+1)

Each of these equations simply shifts the bracket pairs along, so what's unique about the one featuring the golden ratio is that all the numerical values are 1's. Maybe that's what makes it beautiful.

Filtered HTML

  • Web page addresses and email addresses turn into links automatically.
  • Allowed HTML tags: <a href hreflang> <em> <strong> <cite> <code> <ul type> <ol start type> <li> <dl> <dt> <dd>
  • Lines and paragraphs break automatically.
  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.

  • As COP28, the 2023 United Nations Climate Change Conference, kicks off we look at how maths can help understand the climate crisis.

  • How do you create dramatic film out of mathematics? We find out with writer and director Timothy Lanzone.

  • Mathematics plays a central role in understanding how infectious diseases spread. This collection of articles looks at some basic concepts in epidemiology to help you understand this fascinating and important field, and set you up for further study.

  • Find out why the formula we use to work out conditional probabilities is true!

  • We talk about a play that explores the fascinating mathematical collaboration between the mathematicians GH Hardy and Srinivasa Ramanujan.