MathDB

triangle, sides √(fibonacci #s)

Source: S&M 2002 3&4th Grade P2

May 15, 2021

geometryFibonacci

Problem Statement

The (Fibonacci) sequence

f_n

is defined by

f_1=f_2=1

and

f_{n+2}=f_{n+1}+f_n

for

n\ge1

. Prove that the area of the triangle with the sides

\sqrt{f_{2n+1}},\sqrt{f_{2n+2}},

and

\sqrt{f_{2n+3}}

is equal to

\frac12