Fibonacci polygons

Kübra Nair, Sümeyye Koca, Musa Demirci


There are many results giving geometric meaning of some algebraic state- ment or vice versa.  In this paper, we answer a question proposed by B. U. Alfred in the first volume of the Fibonacci Quarterly about the existence of Fibonacci quadrilaterals which are quadrilaterals with edge lengths being successive Fibonacci numbers.  We give a negative answer to this question in the case where the quadrilaterals are special convex quadrilaterals having 2 successive right angles, and extend it to Fibonacci pentagons and in general Fibonacci n-gons where n ≥ 6.  We show that without such a condition, it is always possible to construct a Fibonacci quadrilateral.

Tam Metin:



Alfred BU., Exploring Fibnacci Polygons, Fibonacci Quarterly, 1(3), 60, (1963).

Alfred BU., Exploring Geometric-Algebraic Fibonacci Patterns, Fibonacci Quarterly, 2(4), 318–319, (1964).

Harborth A. F., Kemnitz A., FibonacciTriangles. In: Bergum GE, Philippou AN, Horadam AF, editors, Applications of Fibonacci Numbers. Dordrecht: Springer, 129-132, (1990).


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