Lucas Numbers

The first ten Lucas numbers are –
1, 3, 4, 7, 11, 18, 29, 47, 76, 123

The sequence is made in the same way as for Fibonacci numbers. You get each number by adding together the two previous numbers –
1 + 3 = 4
3 + 4 = 7
4 + 7 = 11
– and so on.

If you take pairs of Lucas numbers and divide the higher by the lower you get almost the same number each time –
18/11 = 1.6363..
29/18 = 1.6111..
47/29 = 1.6206..
76/47 = 1.6170..
123/76 = 1.6184..
– the answer gets closer and closer to a number called the Golden Ratio which equals 1.6180339887. This is also true for Fibonacci numbers.

Based on the book Numbers: Facts, Figures & Fiction.