This is not really a problem or question, just an announcement of something you might think is interesting or pretty. I have just added to my website (https://home.comcast.net/~stuartmanderson) a short paper illustrating how to fit a smooth curve through the Fibonacci sequence. Of course, you could fit arbitrarily many smooth curves through a discrete point sequence, but this one is analytic. It oscillates between the (rescaled) graphs of cosh(x) and sinh(x) with the points of tangency giving the Fibonacci sequence.

Although this is not a "deep" result by any means, it produces a pretty graph connecting hyperbolic trig functions to this well-known sequence. You can also see how to do the same thing for any linear recursive sequence, although the results are not likely to be so pleasing. Is anyone game to try applying this technique to your favorite recursive sequence and producing other interesting graphs?

--Stuart Anderson

Even in 3d?

https://members.aol.com/kwpapke/Binet3D.html