瀏覽動畫
探索由 AnimG 社群創作的 Manim 動畫。
Optimizing Travel Time Using Derivatives
An animated calculus explainer shows how to minimize total travel time from a point on the beach to an offshore station by combining a run and a boat ride. The scene builds the geometric model, derives the distance and time formulas, differentiates the total‑time function, solves for the optimal running distance, and confirms the minimum with a graph, ending with the optimal distance result.
Entropy as Surprise with Coins
The animation compares a fair and a biased coin to illustrate entropy as a measure of surprise. It shows coin flips, updates bar charts for probability distributions, displays the entropy formula for two outcomes, and links it to cross‑entropy loss in a simple classifier diagram. The video ends with a caption about entropy being the mathematics of not knowing.
Pythagorean Theorem Visual Proof by Geometric Dissection
An elegant geometric proof of the Pythagorean theorem. A right triangle is constructed edge by edge, then squares are grown from each side with soft colored fills representing their areas. The square on one leg is dissected into pieces that, together with the other leg's square, smoothly rearrange to perfectly fill the hypotenuse square. The animation concludes with the classic formula, where each term flashes in the color of its corresponding square, reinforcing the visual connection between geometry and algebra.
Similar Triangles and Thales Configuration
The animation draws a large triangle ABC with side lengths six, seven and eleven centimeters and angles twenty‑nine and thirty‑five degrees. A smaller triangle DEF with the same two angles appears. Equal angles are highlighted, the third angles are computed, and the similarity property is stated. The small triangle slides into the large one, creating parallel corresponding sides. Proportional relationships are shown, a known side of two centimeters is used, and the missing sides are calculated.
Incircle Construction of a 9‑8‑7 Triangle
A top-down notebook-style animation builds a triangle with sides 9, 8, and 7 centimeters, then constructs its incircle using classic compass-and-straightedge methods. The steps show drawing the base, creating arcs to locate the third vertex, drawing the triangle, constructing angle bisectors at two vertices, finding the incenter, dropping a perpendicular to the base, and finally drawing the red incircle.
Parabola Exploration: Focus, Vertex Form, and Transformations
The animation introduces a parabola on a coordinate plane, shows the focus and directrix definition, and demonstrates how moving a point on the curve keeps equal distances to both. It then presents the vertex form equation, using sliders for the parameters a, h, and k to smoothly reshape the curve while updating the displayed formula. The expanded standard form appears next, linking its coefficients to the vertex parameters. An optional brief example of a projectile path illustrates a real‑world use, ending with a concise summary.
Visual Proof of the Pythagorean Theorem
The animation draws a right triangle, builds squares on each side, fills each square with tiny unit squares to show their areas, then slides and rotates the unit squares from the two smaller squares to perfectly fill the large square, illustrating that the sum of the areas of the two smaller squares equals the area of the largest square. The final equation a squared plus b squared equals c squared appears at the end.
Classroom vs Test Math Meme
The scene splits into two panels. The top panel brightens to a chalkboard where the caption 'What we learned in class' appears and a hand‑drawn 'one plus one equals two' is written in chalk. The bottom panel slides up, showing a dark chalkboard with the caption 'What appeared on the test' followed by a rapid cascade of complex formulas such as the cosine series, integrals, matrix symbols, all glowing, and a stressed student silhouette. The screen holds briefly then fades out.
Trading Slippage Illustrated with Candlestick Chart
A minimalist animation shows a downward-trending candlestick chart where an order is placed at a certain price, the market moves lower, and the order executes at a worse price. Dotted lines mark the intended and actual prices, and a double-arrow highlights the price gap labeled as slippage.