Fibonacci sequence and Pi directly related

[Epsilon=One]

Is anyone aware if there is any merit to being able to directly relate the Fibonacci sequence to Pi as well as relating the sequence, directly and precisely, to the Golden Ratio (not converging terms)?

[senior_dog]

I am not aware of this. HAve you found a relation?

[Epsilon=One]

I am not aware of this. HAve you found a relation?Yes. The Brunardot Series (http://www.physicsmathforums.com/showthread.php?t=99) is the link.

The first four terms of any Brunardot Series (http://www.physicsmathforums.com/showthread.php?t=99) sequence beginning with a Natural integer (http://www.physicsmathforums.com/showthread.php?t=100) generates a Brunardot Ellipse (http://www.physicsmathforums.com/showthread.php?t=104) when the terms are respectively the perigee, soliton, vector, and apogee.

The first integer sequence of the Brunardot Series (http://www.physicsmathforums.com/showthread.php?t=99) gives the revised Fibonacci sequence (http://www.physicsmathforums.com/showthread.php?t=103) (rFs), 1, 0, 1, 1, 2, 3, 5, ... when the values of the first four terms of the rFs are the perigee, soliton, vector, and apogee of a Brunardot Ellipse (http://www.physicsmathforums.com/showthread.php?t=104), then the ellipse is a circle.

Also, of interest, if the soliton of the Brunardot Ellipse (http://www.physicsmathforums.com/showthread.php?t=104) is one, "1," the perigee is the Golden Ratio, Phi.

[hector berlioz]

elaborate in terms of pi

[Epsilon=One]

elaborate in terms of piI am not certain what you do not understand from my prior post.

Pi is related to the circle. The circle is a special ellipse (as is the straight line). All ellipses are defined by the Brunardot Series (http://www.physicsmathforums.com/showthread.php?t=99). The Fibonacci series (http://www.physicsmathforums.com/showthread.php?t=103) is a portion of the Brunardot Series (http://www.physicsmathforums.com/showthread.php?t=99); and, if the second term of a Brunardot Series (http://www.physicsmathforums.com/showthread.php?t=99) is one, "1," the first term is the Golden Ratio.