按主題瀏覽精選的Math動畫範例。打開任何主題頁，即可找到可重用的 Manim 場景、視覺化證明，以及可直接教學使用的點子。
34 個動畫 · 11 個主題
13 個動畫
This animation visualizes the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ... by repeatedly halving a unit square. Each term is shown as a filled rectangle that fits beside the previous ones like puzzle pieces, and the partial sums are displayed numerically, all converging toward the limit of 2.
This animation introduces linear functions of the form y = mx + b by visually demonstrating how the slope (m) and y-intercept (b) affect the graph. A line rotates as the slope changes from -2 to 2, then shifts vertically as the intercept changes from -3 to 3. A rise/run right-triangle indicator reinforces the geometric meaning of slope.
This animation establishes the relationship between exponential and logarithmic functions. It plots y = 2^x and y = log₂(x) side-by-side reflected across y = x, demonstrating inverse symmetry. A concrete numeric example (2³ = 8 → log₂(8) = 3) is shown with perpendicular guide lines, making the inverse relationship tangible.
This animation walks through the algebraic derivation of the quadratic formula by completing the square step-by-step. Each line of algebra appears via a MathTex Write or TransformMatchingTex animation, building from ax² + bx + c = 0 all the way to x = (-b ± √(b²-4ac)) / 2a. The discriminant is highlighted in a distinct color to emphasize its role.
9 個動畫
This animation shows the unit circle definition of sine and cosine. A point traces the circle as angle θ sweeps from 0 to 2π. Vertical (sin) and horizontal (cos) projections are drawn in real time. Simultaneously, sin and cos waves trace out on a graph panel to the right, creating an intuitive visual connection between circular motion and wave graphs.
Derives the area formulas for a triangle and a circle using visual proofs. Students see that a triangle is half a rectangle (A = ½bh), and that a circle can be rearranged into a near-rectangle whose dimensions involve π and r (A = πr²).
Introduces the Cartesian coordinate system by drawing labeled x and y axes with gridlines, then plotting four points across all four quadrants. For each point, dashed guide lines reveal how to read x and y coordinates.
Presents the visual square-area proof of the Pythagorean Theorem using a 3-4-5 right triangle. Students see squares growing on each side and observe that the two smaller areas add up to the largest area, giving intuition for a² + b² = c².
7 個動畫
This animation introduces linear functions of the form y = mx + b by visually demonstrating how the slope (m) and y-intercept (b) affect the graph. A line rotates as the slope changes from -2 to 2, then shifts vertically as the intercept changes from -3 to 3. A rise/run right-triangle indicator reinforces the geometric meaning of slope.
This animation establishes the relationship between exponential and logarithmic functions. It plots y = 2^x and y = log₂(x) side-by-side reflected across y = x, demonstrating inverse symmetry. A concrete numeric example (2³ = 8 → log₂(8) = 3) is shown with perpendicular guide lines, making the inverse relationship tangible.
This animation explores the standard form of a quadratic y = ax² + bx + c by animating each coefficient. Students see how 'a' controls width and direction, 'c' shifts the parabola vertically, and the vertex traces a path as parameters change. The formula updates in real time alongside the graph.
Visualizes the chain rule through three stacked number lines representing the input x, the intermediate value g(x), and the output f(g(x)). Animated small changes Δx propagate through the composition, making the multiplicative structure of the chain rule visually intuitive.
6 個動畫
Introduces negative numbers by showing a number line from -10 to +10 and demonstrating that numbers extend to the left of zero. Students see that negative and positive numbers are mirror images, then practice addition and subtraction using animated hops.
Animates factor trees for 60 and 84, showing how any composite number can be broken down into a unique product of prime numbers. Prime numbers are highlighted in distinct colors and the final exponential form is displayed with MathTex.
Show a number line from 0 to 20 with a colorful arrow hopping right for addition and left for subtraction. Two worked examples are shown: 5+3=8 (three hops right) and 8-3=5 (three hops left). Each hop is animated individually with equation labels updating live.
A visual introduction to counting for primary school students (ages 6–11), using animated dot groups on a number line to build number sense and subitizing skills. The animation shows dots appearing in groups, connecting visual quantity to numerals 1–10.
5 個動畫
This animation visualizes the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ... by repeatedly halving a unit square. Each term is shown as a filled rectangle that fits beside the previous ones like puzzle pieces, and the partial sums are displayed numerically, all converging toward the limit of 2.
Visualizes the chain rule through three stacked number lines representing the input x, the intermediate value g(x), and the output f(g(x)). Animated small changes Δx propagate through the composition, making the multiplicative structure of the chain rule visually intuitive.
Builds intuition for the derivative by animating the limit definition. A secant line between two points on f(x) = x² is drawn and animated as h approaches 0, visually converging to the tangent line. The difference quotient formula transforms into the derivative formula.
Visualizes how Riemann sums approximate the definite integral by increasing the number of rectangles under f(x) = x² from 0 to 3. As n grows from 4 to 32, the approximation converges to the exact area of 9, illustrating the limit definition of the integral.
3 個動畫
This animation introduces 2D vectors through visual demonstrations on a number plane. It shows a vector as an arrow, demonstrates scalar multiplication (stretching/shrinking), and vector addition using the tip-to-tail method. Component form and magnitude formula are displayed with MathTex.
Demonstrates the geometric meaning of eigenvalues and eigenvectors by applying a 2D linear transformation to the plane and contrasting how most vectors rotate and stretch while eigenvectors only stretch along their own span. The equation Av = λv is derived visually.
Visualizes how 2x2 matrices transform the plane by animating a NumberPlane grid through four key transformations: identity, 90-degree rotation, shear, and stretch. The basis vectors i-hat and j-hat are highlighted to show how the matrix columns determine the transformation outcome.
3 個動畫
This animation contrasts permutations (order matters) with combinations (order doesn't matter) using a concrete example of choosing 2 items from {A, B, C}. A tree diagram visually enumerates all 6 permutations, then groups are collapsed to show only 3 combinations, making the divide-by-r! factor intuitive.
Demonstrates the Central Limit Theorem by starting with a non-normal (uniform) population, then repeatedly drawing samples of size n=30 and computing their means. As more sample means are collected, the histogram of means converges to a bell curve regardless of the original distribution's shape.
Introduces three fundamental probability distributions — Normal, Binomial, and Poisson — with visual representations and key formulas. For the Normal distribution, the 68-95-99.7 empirical rule is animated by progressively shading regions under the bell curve.
3 個動畫
Builds understanding of percentages by shading a 10×10 grid and connecting it to fractions and decimals. A real-world discount example (20% off $50) anchors the concept in everyday math.
Demonstrates the Central Limit Theorem by starting with a non-normal (uniform) population, then repeatedly drawing samples of size n=30 and computing their means. As more sample means are collected, the histogram of means converges to a bell curve regardless of the original distribution's shape.
Introduces three fundamental probability distributions — Normal, Binomial, and Poisson — with visual representations and key formulas. For the Normal distribution, the 68-95-99.7 empirical rule is animated by progressively shading regions under the bell curve.
3 個動畫
This animation shows the unit circle definition of sine and cosine. A point traces the circle as angle θ sweeps from 0 to 2π. Vertical (sin) and horizontal (cos) projections are drawn in real time. Simultaneously, sin and cos waves trace out on a graph panel to the right, creating an intuitive visual connection between circular motion and wave graphs.
Shows the complex plane as a geometric framework where multiplication by i corresponds to a 90-degree rotation. Builds up to Euler's formula e^(iθ) as a general rotation, culminating in the famous identity e^(iπ) = -1.
Demonstrates how a square wave can be decomposed into and reconstructed from sine waves. Individual harmonic components animate in one by one, and the running partial sum curve updates to show convergence toward the square wave.
2 個動畫
This animation introduces 2D vectors through visual demonstrations on a number plane. It shows a vector as an arrow, demonstrates scalar multiplication (stretching/shrinking), and vector addition using the tip-to-tail method. Component form and magnitude formula are displayed with MathTex.
Demonstrates the geometric meaning of eigenvalues and eigenvectors by applying a 2D linear transformation to the plane and contrasting how most vectors rotate and stretch while eigenvectors only stretch along their own span. The equation Av = λv is derived visually.
1 個動畫
