← Back to the little math lab EXPLORER 02 / PATTERNS IN NUMBERS

Simple rules.
Unexpected beauty.

Add the last two numbers. Cross out the multiples.
Small steps reveal something extraordinary.

01 / GROWTH FROM ADDITION

The Fibonacci sequence.

Every term remembers the two before it.

A SPIRAL, ONE SQUARE AT A TIME 10 SQUARES

TWO SEEDS. INFINITE POSSIBILITY.

Begin with 0 and 1. Add the previous two terms to find the next.

F₁₀55↗

21 + 34 = 55

Sequence index n10 / 24

F₀ = 0 · F₁ = 1 · F₂ = 1

THE RATIO, GETTING CLOSER

1.617647059→ φ

55 ÷ 34 · φ ≈ 1.618033989

THE SEQUENCE SO FAR

The square spiral joins quarter-circles with Fibonacci radii. It resembles a golden spiral as the terms grow; the two curves are not identical.

02 / THE BUILDING BLOCKS

A very old idea. A beautiful way to see.

THE SIEVE OF ERATOSTHENESUp to

PrimeCandidateCrossed out

Select any number to take a closer look.

LET THE COMPOSITES FALL AWAY

Start at 2. Keep it, then cross out its multiples from 2² onward. Repeat with the next remaining number, stopping at √100.

Current prime—

Candidates99

Ready to begin. The number 1 is neither prime nor composite.

CONFIRMED PRIMES

The primes will appear here.

A prime has exactly two positive divisors: 1 and itself. Every composite has a prime factor at most its square root, so the sieve can stop there.