Up to main page

2019: The Fibonacci Sequence


This year the code was based on the sequence of numbers ‒ a favourite of mine ‒ named after Leonardo of Pisa (c.1170 ‒ c.1250), usually referred to as Fibonacci, meaning “son of Bonacci”, who introduced the idea to Western European mathematics.

The Fibonacci sequence is defined by

Fn = Fn-1 + Fn-2

where

F0 = 0

and

F1 = 1

‒ so each number in the sequence is the sum of its two predecessors.

Fibonacci numbers occur in interesting ways. They are related to the angular arrangement of leaves around a stem. They have applications in computing and economics. The ratio between consecutive numbers tends to the “golden ratio”, (1+5)/2, as n increases; rectangles whose sides are in this ratio have been seen as aesthetically pleasing and have appeared in art and architecture.

Each number in the message represents its position in the sequence and thereby a single letter by the letter’s position in the alphabet. The sequence of these letters spell out the message. The relevant part of the sequence for the code is:


Fn

n

letter

0

0


1

1

A

1

2

B

2

3

C

3

4

D

5

5

E

8

6

F

13

7

G

21

8

H

34

9

I

55

10

J

89

11

K

144

12

L

233

13

M

377

14

N

610

15

O

987

16

P

1597

17

Q

2584

18

R

4181

19

S

6765

20

T

10946

21

U

17711

22

V

28657

23

W

46368

24

X

75025

25

Y

121393

26

Z


So, for example, the first number on the card, 21, is F8 and represents the eighth letter of the alphabet, H.

Unfortunately, since F1 = F2 = 1, there is an ambiguity in that A and B are both represented by the number 1. But the meanings should be clear from context: I don’t imagine anyone will think the season is Christmbs or that I have changed my name to Arian Aarker.

Front page

Front page of 2019 card

This translates as:

HAPPY CHRISTMAS

Inside page

Inside page of 2019 card

This translates as:

AND BEST WISHES FOR MMXX FROM BRIAN BARKER

There was no obvious way to encode digits using this code, so I couldn’t encode the new year in arabic numbers and had to use roman numerals instead.


Up to main page

Version 3: Revised 18 December 2019
Brian Barker