Interactive Math Lab

Explore how mathematical rules create different geometric patterns.

1. Radial Line Explorer

Cartesian coordinates · Non-negative radial lengths

Length: L = |Atⁿ + B|
Endpoint: x = L cos(t),   y = L sin(t)
The absolute value keeps every line length non-negative.
Red lines: radial segments. Green dots: endpoints. Equal x/y scale preserves the true geometry.

2. Taiji Spiral Explorer

Polar coordinates · Signed radius · Endpoint trajectory

Radius: r = Atⁿ + B
Cartesian conversion: x = r cos(t),   y = r sin(t)
The radius may be negative. The angle t is measured in radians.
Blue curve: endpoint trajectory. Concentric circles indicate radial distance; rays indicate angle.