From 7520d3e539694f053614ed9e8e1fd3bf980338c7 Mon Sep 17 00:00:00 2001 From: jxu <7989982+jxu@users.noreply.github.com> Date: Thu, 17 Apr 2025 14:03:29 -0400 Subject: [PATCH 1/2] Fibonacci: Cassini's identity proof sketches --- src/algebra/fibonacci-numbers.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/src/algebra/fibonacci-numbers.md b/src/algebra/fibonacci-numbers.md index 22403419a..7c805a629 100644 --- a/src/algebra/fibonacci-numbers.md +++ b/src/algebra/fibonacci-numbers.md @@ -22,6 +22,8 @@ Fibonacci numbers possess a lot of interesting properties. Here are a few of the $$F_{n-1} F_{n+1} - F_n^2 = (-1)^n$$ +This can be proved by induction. A one-line proof due to Knuth comes from taking the determinant of the 2x2 matrix form below. + * The "addition" rule: $$F_{n+k} = F_k F_{n+1} + F_{k-1} F_n$$ From 06d6a835e50e0d66de3c817a322eb292e69d23d5 Mon Sep 17 00:00:00 2001 From: Michael Hayter Date: Mon, 21 Apr 2025 21:11:00 -0400 Subject: [PATCH 2/2] Update fibonacci-numbers.md Try indentation. --- src/algebra/fibonacci-numbers.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/algebra/fibonacci-numbers.md b/src/algebra/fibonacci-numbers.md index 7c805a629..176a73600 100644 --- a/src/algebra/fibonacci-numbers.md +++ b/src/algebra/fibonacci-numbers.md @@ -22,7 +22,7 @@ Fibonacci numbers possess a lot of interesting properties. Here are a few of the $$F_{n-1} F_{n+1} - F_n^2 = (-1)^n$$ -This can be proved by induction. A one-line proof due to Knuth comes from taking the determinant of the 2x2 matrix form below. +>This can be proved by induction. A one-line proof by Knuth comes from taking the determinant of the 2x2 matrix form below. * The "addition" rule: