EXA-18 · RECURSION

A Function That Calls Itself

Understand Fibonacci as a mathematical function first. Then watch the recursive calls before writing Python.

BASE CASE

Where recursion stops

F(1) = 1

F(2) = 1

These values are already known, so the function does not call itself again.

RECURSIVE RULE

Build a new value from two earlier calls

F(n) = F(n−1) + F(n−2)

For n > 2, solving one function means asking the same function to solve two smaller problems.

EXPAND THE MATH

F(3)=F(2)+F(1)
=1+1=2

F(4)=F(3)+F(2)
=2+1=3

F(5)=F(4)+F(3)
=3+2=5

F(6)=F(5)+F(4)
=5+3=8

INTERACTIVE CALL TREE

Watch F(5) call itself

F(5)

↙ ↘

F(4)

F(3)

recursive calls continue until F(1) / F(2)

F(3)

F(2)=1

F(1)=1

F(2)=1

F(1)=1

CURRENT STEP

Ready

Press Play or Step.

CALL / RETURN TRACE

I understand the recursive flow.
A call expands into smaller calls until it reaches a base case; then values return upward and are added together.

💻 Recursive Fibonacci Lab

Translate the math function into Python.

PYTHON CONSOLE

Ready.