Page 23 - Module 1_Chapter 1_Mathematics in the Modern World

Mathematics in our World
13

E. Golden Ratio in Binet’s Formula for
Architecture Fibonacci Sequence

Some logo design also applies the Binet's formula is an explicit formula
th
golden ratio. used to find the n term of the Fibonacci
sequence. It is so named because it was
derived by mathematician Jacques Philippe

Marie Binet, though it was already known by
Abraham de Moivre.
Binet’s Formula:

n n
( 1 + √5 ) - ( 1 - √5 )
2 2
f =
n
√5

Example 3

Find the 2nd term of Fibonacci sequence
using Binet’s Formula?

Solution: Let n = 2, then

2 2
( 1 + √5 ) - ( 1 - √5 )
f = 2 2
2
√5

1 + 2√5 + 5 1 - 2√5 + 5
f = ( 4 )−( 4 )
2 √5

4√5
f = 4 = 1
2 √5

Supplementary Video

Watch the short movie highlighting the

Fibonacci Numbers.

Video link: https://vimeo.com/9953368

ZANNIE I. GAMUYAO, MSM
Assistant Professor 1 UNIT 1.2 The Fibonacci Sequence
Department of Arts and Sciences