Fibonacci Sequence And Hyperbolic Trigonometric Functions

Transcript

This is a mathematic paper about the hyperbolic functions and their connection with Fibonacci sequence. 1st we define the hyperbolic functions and we compose the sech(arcsinh(x)) infinite ammount of times. We get a continued fraction formula. In the second chapter we define the Fibonacci sequence and number phi in order to connect these two sections in the 3rd chapter, where we try to prove that cosh(arcsinh(sech(...(x)...))) =sqrt(phi). By integration and using the elliptic integrals we are very close to prove this proposition but to do this we will need 2 new theorems about functions of two variables, one of which takes values from a convergent sequence.