Home▸Mathematics▸Riemann Zeta Critical Strip Explorer

∑ Riemann Zeta Critical Strip Explorer

Interactive 3D complex plane where sweeping through the critical strip shows how the Riemann zeta function's zeros align on the critical line and relate to prime distribution.

Mathematics3DModerate60 FPS

A 3D trace of ζ(σ+it) winding around the "zero axis" as t climbs, showing how the curve grazes zero repeatedly on the critical line σ=0.5 but never does at σ=1 — the fact behind the Prime Number Theorem.

🔬 What It Demonstrates

Height represents the imaginary part t; horizontal position is the complex value ζ(σ+it) itself. Touching the vertical axis means ζ(σ+it)=0 at that height — this only recurs at σ=0.5.

🎮 How to Use

Drag σ away from 0.5 and watch the curve pull off the axis; snap back to see it graze the marked zero heights. Toggle the σ=1 comparison curve and the zero-counting stats to connect zeros with prime distribution.

💡 Did You Know?

Over ten trillion nontrivial zeros have been computed and all sit precisely on the critical line — the Riemann Hypothesis remains unproven, one of the seven Clay Millennium Prize Problems.

⚙ Under the hood

Interactive 3D complex plane where sweeping through the critical strip shows how the Riemann zeta function's zeros align on the critical line and relate to prime distribution.

riemann-zeta-functioncritical-stripprime-numberscomplex-analysisnumber-theorymathematics

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install