1. 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?

2. 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 =