Birthday of Jacques Binet (1786) — The Formula in the Numbers

Jacques Philippe Marie Binet was born in Rennes on February 2, 1786. He is remembered chiefly for Binet's formula, which gives the nth Fibonacci number directly without computing all the previous ones: F(n) = (φⁿ − ψⁿ)/√5, where φ = (1+√5)/2 ≈ 1.618 is the golden ratio and ψ = (1−√5)/2 ≈ −0.618. That √5 in the denominator and two irrational numbers raised to integer powers always produce a perfect whole number is one of mathematics' quiet miracles. Binet also proved what is now called the Cauchy-Binet formula for matrix determinants, and worked extensively on matrix algebra decades before matrices were named.