Interactive Math Lab

Math Graphic Lab

Explore mathematics through interactive graphics.

Choose an experiment

Select a module to begin exploring.

01 · Radial Line Explorer

Explore how radial lines create geometric patterns.

02 · Taiji Spiral Explorer

Explore how mathematical parameters shape spirals.

03 · Linear Function Explorer

Explore how slope and y-intercept change a straight line.

04 · Quadratic Function Explorer

Explore how the coefficients change a parabola.

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.

3. Linear Function Explorer

Cartesian coordinates · Slope and y-intercept

Function: y = kx + b
Slope (k): determines the direction and steepness of the line.
Y-intercept (b): determines where the line crosses the y-axis.

4. Quadratic Function Explorer

Cartesian coordinates · Parabolas and their properties

Function: y = ax² + bx + c
Condition: a ≠ 0
Vertex Form: y = a(x + b 2a )² + c − b² 4a
Axis of Symmetry: x = − b 2a
Coefficient (a): determines the opening direction and width.
Coefficient (b): helps determine the vertex and axis of symmetry.
Coefficient (c): determines the y-intercept.