I'm glad we got the puzzle of the cards sorted out - at least we know what they are now though I haven't seen a Tombola set for years and doubt I've ever seen a Smorfia one.
When Sophie found the cards on her bed and then laid them out to work out what they might mean:
I stare at the numbers for a long time, willing myself to see some pattern in them, trying to remember patterns that meant something to Ely. I remember he liked the Fibonacci Sequence, prime numbers, the digits of pi, and palindromic numbers, but none of those seem to fit these numbers...
I thought perhaps the mathematically challenged ones among us (are you there Ginny?) might care to know a little more about the the numbers and sequences Ely liked.
Fibonacci Sequence : As anyone who has read Dan Brown knows the Fibonacci numbers were discovered in 1202 by the Italian, Leonardo di Pisa (or Fibonacci) regarded as the first original mathematical thinker since the Greeks.
The sequence is:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377... arrived at by adding each number to its immediate predecessor eg 13+8=21.
The sequence itself originally related scientifically to the breeding of rabbits and was the first example of applying maths to the reproduction of animals.
The ratio of each number to the one before it decreases rapidly at first, then levels out to approach the 'Golden Ratio' of 1.61803... The Golden ratio is evident in the proportions of the Parthenon which is an example of math in aesthetics.
Prime Numbers: Prime numbers are those numbers such as 2, 3, 5, 7, 11 which cannot be broken up into factors ie. they can only be divided by two numbers - the number 1 and themselves.
The Digits of Pi: Pi relates to the arithmetic of the circle referred to as the Quadrature of the Circle and was one of the three great math problems of antiquity (ca. 500 BC). Archimedes (ca. 287-212 BC),was the first to compute the value of Pi to three or more decimal places. Since 1500 mathematicans have been obsessed with increasing the number of decimal places for Pi and during the 20th century the Chudnowsky brothers built their own super-computer and calculated the value to about 8 thousand million decimal places. Subsequently Takayama's calculations increased the decimal places to about 38 thousand million. If written on a strip of paper Takayama's decimal places would stretch several times around the equator.
Curiously, if Ely was interested in patterns there are none to be found in the Digits of Pi because Pi is a transcendental number. Pi is one of a group of numbers which cannot be obtained from an algebraic equation and hence is said to 'transcend' algebra.
Palindromic Numbers: These are simply numbers which read the same either forwards or backwards i.e 12321. This is analogous to words or sentences such as this one attributed to Napoleon:
Able was I ere I saw Elba