Patterns in Sequences

Discrete Math · Axiom Academy

INTRO Fibonacci's Rabbit Population Discover one of mathematics' most famous sequences by solving a medieval puzzle about breeding rabbits! The Original Problem (Year 1202) Let's run the simulation for several months and record the total number of rabbit pairs. Pay attention to how the numbers grow! You've seen the sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55... How does each number relate to previous numbers? Click on what you think is the correct pattern! Let's break down the logic behind the pattern to understand why each term depends on the previous two. Spiral patterns in nature (shells, flowers, galaxies) Branching patterns in trees and plants Algorithm analysis and computational complexity Financial markets and the golden ratio Optimization problems in computer science Sequence: An ordered list of numbers Term: Each individual number in the sequence Recurrence Relation: A rule defining terms using previous terms Initial Conditions: The starting values (F(0) and F(1))

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