Exploring Ruby Algorithms for Fibonacci Numbers
이 기사는 루비(Ruby) 언어를 활용한 피보나치 수열 계산 알고리즘들을 심층적으로 탐구한다. 기본 재귀 알고리즘의 비효율성, Binet 공식의 상수 시간 계산법과 그 한계, BigDecimal과 Rational을 이용한 정밀도 개선 방법, 꼬리 재귀 최적화(Tail Call Optimization)를 통한 성능 향상, 그리고 행렬 곱셈을 이용한 고성능 피보나치 수 계산법까지 다양한 접근법을 소개한다. 각 방법의 장단점과 구현 예제를 통해 루비에서 피보나치 수를 효율적으로 계산하는 여러 기법을 비교 분석한다.

https://www.rorvswild.com/blog/2025/fibonacci-ruby-algorithms

#ruby #fibonacci #algorithm #tailcalloptimization #bigdecimal

When prompting a locally run Llama 3.2 1B Instruct to explain the difference between #Fibonacci tree and a Fibonacci sequence for a 11-year-old in German (as requested by K2), the response started off with "Ze Fibonacci-Treier und ze Fibonacci-Sequenz ..." 😂

#ZeGerman in front of the screen coudn't help but subvocalize (in an approximation of the accent of #Snorri, a character from the great #Maniac series) and LOL a bit.

(The rest of the response was quite unintelligible, but not in a funny way. Definitely worked to discourage K2 from using LLMs much for school-related stuff.)

what? … Miles to Kilometre conversion can be approximated by the #Fibonacci sequence?*

<https://youtube.com/shorts/K_QgsJV6wI0> * 1xMi ~ 1.6 km ~ Fib ratio of 1.609

Oxford mathematician explains how to convert miles to km in your head 🤯

https://youtube.com/shorts/K_QgsJV6wI0?si=nrCDS7eJ8uF1rrin

> Dr Josh Bull has a quick way to convert miles to kilometres as you run, using the #Fibonacci sequence.

The Infinite Flow.

Most see a flower; my eye locks onto the system. In this 2013 dahlia, the Fibonacci spiral doesn’t stop at the edges of the frame, it wraps around the rectangle and continues out into the world.

My "Intuitive Artistry" just catches the center of the storm. I click the shutter when the universal geometry aligns, capturing a window into a pattern that never truly ends.

#Fibonacci #GoldenRatio #VisualIntelligence #IntuitiveArtistry #PatternRecognition #Nature #FloralGeometry

@jasoncoon I was tracking down an unrelated (?) mathematical oddity, and I fell into this page. It has some clever interactive Fibonacci spiral graphs; have you seen it?

I especially like the part at the very bottom where you can replace φ with other constants.

#Fibonacci

https://observablehq.com/@meetamit/fibonacci-lattices

An interesting math video: https://www.youtube.com/watch?v=fVVspcjQr5M
The most interesting part for me: the sum of (n'th Fibonacci number times x^n), for all nonnegative integers n, equals x / (1 - x - x^2). For example:
- if x = 0.1: 0.1 / 0.89 = 10/89 = 0.11235...
- if x = 0.01: 0.01 / 0.9899 = 100 / 9899 = 0.01010203050813...

#math #fibonacci