Interactive 2D Cartesian, Polar & Parametric Graphing Studio

Models underdamped mechanical springs and RLC circuits where exponential envelope e^(−ax) bounds rapid cosine oscillations.

Normalized probability density function with total area equal to 1, peak at x = μ, and inflection points at x = μ ± σ.

Bounded S-shaped activation and population carrying-capacity curve with inflection symmetry at y = L/2.

Ideal low-pass Nyquist reconstruction kernel in DSP; its square sinc²(x) governs single-slit optical diffraction fringes.

Rational bell curve studied by Maria Gaetana Agnesi (1748), identical in form to spectral Lorentzian line shapes and Cauchy distributions.

Exact equilibrium shape of a uniform flexible cable hanging under gravity, compared side-by-side against its osculating parabola.

Demonstrates exact pole branch splitting at x = ±1, roots at x = ±2, y-intercept at (0, 4), and horizontal asymptote y = 1.

Visualizes how local maximum at x = −√a and minimum at x = +√a align directly with the roots of f′(x) = 3x² − 3a.

Superposition of two close frequencies produces rapid carrier waves modulated by slow beat envelope 2·cos(Δω·x/2).

Minimax polynomial on [−1, 1] exhibiting six alternating ±1 extrema that suppress Runge’s phenomenon in polynomial interpolation.

Balances Pauli short-range r⁻¹² repulsion against London dispersion r⁻⁶ attraction with equilibrium minimum at r = 2^(1/6)σ.

Compares smooth non-monotonic neural network activations that eliminate ReLU dead-neuron gradients.