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Mathematical Universe

DIMEN
SIONS

Where equations breathe and geometry comes alive.

Explore the Universe ↓
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01 — Unit Circle

The Circle That
Defines All Waves

Every oscillation in nature traces back to this. Watch sine and cosine breathe in real time, born from a single rotating point.

Speed 3
sin²θ + cos²θ = 1 e^(iθ) = cosθ + i·sinθ
Trigonometry
02 — 4D Hypercube

The Tesseract —
4th Dimension

16 vertices, 32 edges — a 4D cube projected onto your screen. Toggle rotation planes to see it fold through dimensions.

Speed 6
vertices = 2ⁿ = 16 edges = n·2^(n-1) = 32
Tesseract
03 — Parametric Curves

Lissajous Figures —
Mathematics as Art

x = sin(aθ+δ), y = sin(bθ) — varying the ratio a:b creates hypnotic, symmetric patterns beloved by mathematicians and artists alike.

04 — Wave Physics

Interference Field

Move your mouse to add a wave source

05 — Fourier Series

Circles Building
Any Shape

Epicycles — circles on circles — can trace ANY periodic shape. This is the mathematical heart of signal processing, music, and quantum mechanics.

Harmonics 5
f(x) = Σ (4/πn)·sin(nωx) Square Wave
Epicycles
Resulting Wave
Mathematical Constants

The Numbers Behind Reality

π
3.14159265...
Circle ratio
φ
1.61803398...
Golden ratio
e
2.71828182...
Euler's number
i
√(−1)
Imaginary unit