The following pages are devoted to investigations by the author which have the pupose of unravelling fascinating new aspects of various number relationships. I start with several contributions on the Fibonacci Sequence.
 

Phi in the Sky
Recent Addendum

Extended Fibonacci Like Sequences (two-term case)

Fibonacci Extensions - Alternating Sequences

Fibonacci Extensions - Rotating Sequences

Remarkable Binary Connections

Further Point Series Connections

Alternating Point Sequences

N-Term Generalization of Fibonacci Sequence

General Formulae for Phi_n

Generalized Fibonacci Decimal Point Sequences

Generalized Fibonacci Binary Point Sequences

The 3-term Fibonacci-like Sequence: Lucas Equivalent

Extension of Interesting Fibonacci Result to 3-term Sequence

Extension of Interesting Fibonacci Result to 4-term Sequence

Extension of Interesting Fibonacci Result to 5-term Sequence

Implication of Expansion for 2-term Sequence

Generalization of Result to n-terms

Algebraic Expression for Phi₃

Interesting Result

Further N-term Generalization

Further N-term Generalization of Decimal Point sequences

Lucas Series:  Pythagorean Connections

Fascinating Pythagorean Result

Fibonacci Sequence and Complex Numbers

Pythagorean Triples, Fibonacci and Lucas Series

Another Interesting Result