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We prove that the Fibonacci groupF  ⁢   (  2  ,  n  ){F(2,n)}    for  n  odd andn  ≥  11{n\geq 11}    is hyperbolic. We do this by applying a curvature argument to an arbitrary van Kampen diagram ofF  ⁢   (  2  ,  n  ){F(2,n)}    and show that it satisfies a linear isoperimetric inequality. It then follows thatF  ⁢   (  2  ,  n  ){F(2,n)}    is hyperbolic.

Fibonacci groups 𝐹(2, 𝑛) are hyperbolic for 𝑛 odd and 𝑛 ≥ 11