The document discusses the Fibonacci sequence and how it appears in nature. It describes the Fibonacci sequence as a number pattern where each number is the sum of the two preceding ones, starting from 0 and 1. This sequence is found in aspects of plant growth like the number of petals in flowers. The ratio of numbers in the sequence are also seen in spirals formed in nature. The Fibonacci sequence and its properties are currently being studied for applications in modeling physical systems.
2. When there is a staircase with three steps how many ways can
you reach the top?
Case a Case b Case c
3. There is a staircase, number of ways one can reach
Zero step –1
First step -1
Second step –2
Third step –3
Fourth step - 5
When we observe……..
1 1 2 3 5 8 13 ………..
4. The number pattern is known as the Fibonacci sequence.
1 1 2 3 5 8 13 21 34 55
7. On many plants, the number of petals is a Fibonacci
number:
Buttercups have 5 petals; lilies and iris have 3 petals;
some delphiniums have 8; corn marigolds have 13
petals; some asters have 21 whereas daisies can be found
with 34, 55 or even 89 petals.
13 petals: ragwort, corn marigold, cineraria, some daisies
21 petals: aster, black-eyed Susan, chicory
34 petals: plantain, pyrethrum
55, 89 petals: michaelmas daisies, the asteraceae family.
Some species are very precise about the number of
petals they have - e.g. buttercups, but others have petals
that are very near those above, with the average being a
Fibonacci number.
8. A Fibonacci word is a specific sequence of binary digits. The Fibonacci
word is formed by repeated concatenation in the same way that
the Fibonacci numbers are formed by repeated addition.
Fibonacci based
constructions are currently
used to model physical
systems with aperiodic order
such as quasicrystals. Crystal
growth techniques have
been used to grow Fibonacci
layered crystals and study
their light scattering
properties