This is a sequence defined inductively through a0=a1=1 and ai=ai-1+ai-2, for i>1. The sequence of squares below is based on this sequence. The side of each square is the sum of the sides of the two squares preceding it. It can be proved that
For the sequence of areas, the above picture gives a visual proof of the equation:
![[alogo]](alogo.png){kind=small}
Fibonacci sequence ![[0_0]](Fibonacci_files/Fibonacci_0_0_0.png)
![[0_1]](Fibonacci_files/Fibonacci_0_0_1.png)
![[0_2]](Fibonacci_files/Fibonacci_0_0_2.png)
![[0_3]](Fibonacci_files/Fibonacci_0_0_3.png)
![[0_4]](Fibonacci_files/Fibonacci_0_0_4.png)
![[1_0]](Fibonacci_files/Fibonacci_0_1_0.png)
![[1_1]](Fibonacci_files/Fibonacci_0_1_1.png)
![[1_2]](Fibonacci_files/Fibonacci_0_1_2.png)
![[1_3]](Fibonacci_files/Fibonacci_0_1_3.png)
![[1_4]](Fibonacci_files/Fibonacci_0_1_4.png)
![[2_0]](Fibonacci_files/Fibonacci_0_2_0.png)
![[2_1]](Fibonacci_files/Fibonacci_0_2_1.png)
![[2_2]](Fibonacci_files/Fibonacci_0_2_2.png)
![[2_3]](Fibonacci_files/Fibonacci_0_2_3.png)
![[2_4]](Fibonacci_files/Fibonacci_0_2_4.png)
![[0_0]](Fibonacci_files/Fibonacci_1_0_0.png)
![[0_1]](Fibonacci_files/Fibonacci_1_0_1.png)