A supergold section is an irrational number that is a real solution to the equation . This number is indicated by the Greek letter. and equal to 1.46557123187676802665 ... (sequence A092526 in OEIS ). This number is equal to
- .
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Sequence of Narayana Cows
The supergold section arises in the following problem, which is an analogue of the Fibonacci rabbit problem : “First, there is one young pair of cattle. Three months after birth, they can breed and from that moment breed each month, giving birth to a heterosexual couple. How many pairs will be through months? ”The solution to this problem is the so-called sequence of Narayana cows [1] , named after the 14th-century Indian mathematician. This sequence begins as follows:
- 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, ... (sequence A000930 in OEIS ).
The members of this sequence are calculated using the recurrence formula :
- ,
- Where , and .
Supergold section is the limit of the ratio of neighboring members of this sequence [2] .
Notes
- ↑ A000930 sequence in OEIS
- ↑ Tony Crilli. Mathematics: 50 Ideas You Need to Know About = 50 Mathematical Ideas you really need to know . - Phantom Press. - 209 p. - ISBN 9785864716700 .