Home▸Mathematics▸New Year Spiral: The Golden Ratio in Time

New Year Spiral: The Golden Ratio in Time

A real logarithmic (golden) spiral r = a·e^(bθ) rising through time as a 3D helix, with a live Fibonacci-ratio convergence chart showing F(n+1)/F(n) approaching φ term by term.

Mathematics3DModerate60 FPS📱 Mobile-adapted⇄ 2D version

Details

CategoryMathematics

RenderingThree.js · WebGL

DifficultyModerate

Target FPS60

ControlsToggle to snap to the true golden spiral (k=phi per quarter turn); sliders for growth rate k, turn count, and years-per-turn (time rise); slider for number of Fibonacci terms shown plus a step button and autoplay; click on the spiral to probe its angle/radius/year offset at that point; orbit-drag to rotate the 3D view.

golden-ratiofibonaccilogarithmic-spiralmathematicsnew-year

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A logarithmic spiral r = a·e^(bθ) rendered as a rising 3D helix, one turn per "year", alongside a genuinely computed Fibonacci sequence whose consecutive-term ratio F(n+1)/F(n) converges to the golden ratio φ live as more terms are added. Adjustable growth rate, turn count and time-rise, with a one-click snap to the mathematically exact golden spiral (k = φ per quarter turn).

⚙ Under the hood

A real logarithmic spiral r = a·e^(bθ) rendered as a rising 3D helix (one turn per year) next to a live Fibonacci-ratio convergence chart approaching φ, with a one-click snap to the exact golden-spiral growth rate.

golden-ratiofibonaccilogarithmic-spiralmathematicsnew-year

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