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Descubre animaciones Manim creadas por la comunidad AnimG.
Evaluating the Gaussian Integral with Polar Coordinates
The animation walks through the classic proof that the integral of e to the minus x squared from negative infinity to infinity equals the square root of pi. It starts by drawing the Gaussian curve, shades the area, highlights symmetry, then squares the integral to form a two‑dimensional region. A polar‑coordinate transformation is shown, the radial integral is evaluated, and the angular sweep completes the calculation, culminating in the final result displayed on a dark background.
Gradient Steepest Ascent in 3D Scalar Field
This animation visualizes a 3D scalar field defined by V(x,y) equals 0.6 times x squared plus 0.3 times y squared. It shows the surface plot, equipotential curves projected onto a plane, and highlights the gradient vector at a specific point, demonstrating how it points in the direction of greatest increase. Smooth camera movements and text overlays enhance the educational explanation.
Merging Two Sorted Linked Lists with Dummy Node
This animation visualizes the algorithm for merging two sorted singly-linked lists into one sorted list. Using a dummy node technique, it demonstrates step-by-step comparisons of node values, pointer manipulation, and splicing of nodes. The process ensures the merged list remains in non-decreasing order, illustrated with color-coded nodes and arrows for clarity.
Mathematical Odyssey: Geometry to Chaos
An animated journey begins with a gold‑purple title, then shows a 3‑4‑5 right triangle with colored squares and the Pythagorean formula. A quadratic equation is factored step by step to reveal its solution. A sine wave transforms into a cosine wave while the derivative label appears. A purple normal distribution curve highlights the area between –1 and 1. A 2×2 matrix determinant is computed with a concrete example. Euler’s famous identity glows with gradient colors, followed by a slowly drawn strange attractor, and ends with a particle‑filled closing statement.
RC Circuit Modeling with Differential Equations
This educational animation demonstrates how to model an RC circuit using first-order differential equations. It introduces key concepts including the time constant tau equals RC, displays the governing differential equation, and visualizes the capacitor charging curve as an exponential function. The animation highlights the significance of tau, where the voltage reaches approximately 63% of its final value, and presents the analytical solution for capacitor voltage over time.
RC Circuit Charging: Differential Equations Visualized
This animation introduces the RC circuit charging process through differential equations. It displays the governing equation, visualizes the exponential charging curve on a coordinate system, and highlights the time constant tau where the capacitor voltage reaches approximately 63 percent of the maximum voltage E. The neon-styled visualization on a dark background concludes with the analytical solution, making the mathematical relationship between voltage, time, and the RC time constant clear and intuitive.
Athena: Living Mathematics Goddess Animation
An elegant 35‑second Manim scene introduces Athena, a goddess‑warrior built from mathematical perfection. The camera pans from a battlefield grid to reveal her golden‑ratio silhouette, symmetric torso triangle, and precise motion vectors. Floating symbols such as pi and summation drift around her. Close‑ups show a perfectly symmetric face, sinusoidal hair, fractal helmet, hexagonal armor, a spear tracing a parabolic path, and a polygonal owl. The finale transforms the ground into a tactical grid with probability lines, highlighting her ultimate mathematical aura.
Interference of Two Sinusoidal Waves
The scene draws two traveling sine waves of equal amplitude and frequency, then adds their superposition as a bold white curve. A phase offset smoothly changes from zero to half a cycle and back, turning constructive interference green and destructive interference red, while a yellow arrow indicates the instantaneous phase difference. The animation highlights how the combined amplitude varies with phase.
Interference of Two Sinusoidal Waves
The scene draws two traveling sine waves of equal amplitude and frequency, then adds their superposition as a bold white curve. A phase offset smoothly changes from zero to half a cycle and back, turning constructive interference green and destructive interference red, while a yellow arrow indicates the instantaneous phase difference. The animation highlights how the combined amplitude varies with phase.