# Fibonacci Sequence

• Oct 14th 2009, 11:13 PM
m.c
Fibonacci Sequence
"I thought about the origin of all square numbers and discovered that tthey arise out of the increasing sequence of odd numbers; for the unity is a square and from it is made the first square, namely 1; to this unity is added 3, making the second square, namely 4; if to the sum is added to the third odd number, namely 5, the third square is created, namely 9; an thus sums of consecutive odd numbers and a sequence of squares always arise together in order." -Fibonacci

1,3,5,7.... the sequence of odd numbers
1,4,9,16... the sequence of squares

I am confused and do not see the connection? Is there a formula that connects the relationship of odd numbers and squares?
• Oct 14th 2009, 11:47 PM
mr fantastic
Quote:

Originally Posted by m.c
"I thought about the origin of all square numbers and discovered that tthey arise out of the increasing sequence of odd numbers; for the unity is a square and from it is made the first square, namely 1; to this unity is added 3, making the second square, namely 4; if to the sum is added to the third odd number, namely 5, the third square is created, namely 9; an thus sums of consecutive odd numbers and a sequence of squares always arise together in order." -Fibonacci

1,3,5,7.... the sequence of odd numbers
1,4,9,16... the sequence of squares

I am confused and do not see the connection? Is there a formula that connects the relationship of odd numbers and squares?

Add up the odd numbers and you will see:

1 + 3 =

1 + 3 + 5 =

1 + 3 + 5 + 7 =