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.
Hi Rachel. This is to continue our interesting discussion about a result with squares I'd thought I'd found in the Fibonacci sequence (see below). This time compare some of the sequence to the left as well as the right of 0 with a corresponding segment of the famous Lucas sequence:
Fibonacci: . . . 34 -21 13 -8 5 -3 2 -1 1 0 1 1 2 3 5 8 15 21 34 . . .
Lucas: . . . 47 -29 18 -11 7 -4 3 -1 2 1 0 3 4 7 11 18 29 47 . . .
The Lucas can be seen as resulting from swapping round two consecutive Fibonacci terms, from 2, -1 to -1, 2 while retaining the same addition rule as Fibonacci, adding two consecutive numbers to get the third as you go right. To the right in the Lucas we now have not just one but two integer squares, those of -1 and 2, namely 1 and 4, in the Lucas. Hmm? Well, let's do the Lucas swap elsewhere in the Fibonacci to be a bit more convincing. What about from 13, -8 to -8, 13 (and get a different sequence because we're keeping to the same addition rule)?
. . . -8 13 5 18 23 41 64 85 169
Do you think this result escapes the charge of triviality that I felt bound to level at my first attempt to hit the square? Do you feel it's twice as lovely? I do for the moment, but am always ready to reconsider.