Wheel of Names & Random Decision Spinner

Rotational Dynamics & Easing

The motion of the wheel is modeled on physical rotational inertia and Coulomb friction. The deceleration matches:
\(\omega(t) = \omega_0 \cdot e^{-kt}\)Where \(\omega_0\) represents the starting angular velocity and \(k\) is the friction factor. To maximize anticipation, our system utilizes a cubic Bezier curve easing:
\(B(t) = 3(1-t)^2 t P_1 + 3(1-t) t^2 P_2 + t^3\)This generates a smooth slowdown mimicking a real physical roulette spinner. Read the scientific overview on the Rotational Kinematics Wikipedia Page.

Color Spacing via the Golden Angle

To guarantee that consecutive segments never have identical or clashing colors, we distribute sector hues dynamically using the Golden Angle derived from the Golden Ratio fraction:
\(\theta_{idx} = (idx \times 137.508^\circ) \pmod{360^\circ}\)This provides optimal color spacing and distinct adjacent sectors, regardless of the option count. Learn more about the biology and mathematics of this on the Golden Angle Wikipedia Page.

Uniform Probability Theory

Every sector on a uniform wheel has an identical probability of selection, modeled by the uniform probability distribution:
\(P(X = x_i) = \frac{1}{N}\)Where \(N\) is the count of wedges. For weighted distributions, the probability is proportional to individual slice weights. Reference the official Wolfram MathWorld Probability Distribution Guide.