Add new comment

Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
What do chocolate and mayonnaise have in common? It's maths! Find out how in this podcast featuring engineer Valerie Pinfield.
Is it possible to write unique music with the limited quantity of notes and chords available? We ask musician Oli Freke!
How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?
Was the mathematical modelling projecting the course of the pandemic too pessimistic, or were the projections justified? Matt Keeling tells our colleagues from SBIDER about the COVID models that fed into public policy.
PhD student Daniel Kreuter tells us about his work on the BloodCounts! project, which uses maths to make optimal use of the billions of blood tests performed every year around the globe.
A geometric sequence with a common ratio (or ratio constant) of 2 has the recurrence Sn=Sn1 + Sn1, 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=Sn1 + Sn2.
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=Sn1 + Sn3.
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.