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math-visualizer

math-visualizer

github.com/rohitg00创意与媒体30955 次安装39 周前更新
代码仓库

关于 math-visualizer

用于制作 Manim 动画的技能，通过方程、图表、证明和几何形状讲解数学概念。面向数学可视化内容创作者，提供节奏、符号和配色方面的指导。

主要功能

  1. 01涵盖七类数学领域
  2. 02提供方程呈现节奏指导
  3. 03为数学元素设定统一配色
  4. 04提供图表与证明动画建议
  5. 05提供方程和几何 Manim 模板

适用场景

  1. 01制作方程推导动画
  2. 02用图表动画讲解函数
  3. 03演示几何证明
  4. 04可视化三维数学曲面

安装

复制下面的命令，在终端中运行。

$npx skills add https://github.com/rohitg00/manim-video-generator --skill math-visualizer

安装后在 Claude Code 中输入/math-visualizer确认已加载。

包含的文件

除 SKILL.md 外，安装时一起下载的参考资料和脚本。

examples/
derivative-visualization.py
pythagorean-theorem.py
rules/
best-practices.md
color-coding-math.md
community-edition-patterns.md
concept-decomposition.md
equation-presentation.md
graphing-best-practices.md
opengl-renderer-patterns.md
proof-visualization.md
templates/
concept-flow-scene.py
equation-transform.py
graph-function.py

详细介绍

数学可视化技能

数学可视化工具通过精准优美的动画，让数学概念鲜活呈现，揭示数学内部的结构与关系。

数学领域

支持的领域
  • 代数：方程、不等式、多项式
  • 微积分：导数、积分、极限、级数
  • 几何：图形、变换、证明
  • 三角学：函数、恒等式、单位圆
  • 线性代数：向量、矩阵、变换
  • 复分析：复数、变换
  • 数论：素数、数列、规律

规则

rules/equation-presentation.md

如何通过恰当的节奏和强调来呈现方程。

rules/color-coding-math.md

数学元素的一致配色方案。

rules/graphing-best-practices.md

绘制清晰且信息丰富的函数图像。

rules/proof-visualization.md

循序渐进的证明动画，帮助加深理解。

配色标准

元素颜色Hex
变量（x、y）蓝色#58C4DD
常量黄色#FFFF00
运算符白色#FFFFFF
关键术语绿色#83C167
等号/结果金色#FFD700
负数/减法红色#FC6255

模板

方程推导
from manim import *

class EquationDerivation(Scene):
    def construct(self):
        # Initial equation
        eq1 = MathTex(r"x^2 + 2x + 1 = 0")
        self.play(Write(eq1))
        self.wait()

        # Transform step by step
        eq2 = MathTex(r"(x + 1)^2 = 0")
        eq3 = MathTex(r"x + 1 = 0")
        eq4 = MathTex(r"x = -1")

        # Show each transformation
        for new_eq in [eq2, eq3, eq4]:
            self.play(TransformMatchingTex(eq1, new_eq))
            self.wait()
            eq1 = new_eq

        # Highlight final answer
        box = SurroundingRectangle(eq4, color=GREEN, buff=0.2)
        self.play(Create(box))
彩色编码方程
from manim import *

class ColorCodedEquation(Scene):
    def construct(self):
        # Equation with color-coded parts
        equation = MathTex(
            r"f(", r"x", r") = ", r"a", r"x^2", r" + ", r"b", r"x", r" + ", r"c"
        )

        # Color code
        equation[1].set_color(BLUE)   # x
        equation[3].set_color(YELLOW) # a
        equation[4].set_color(BLUE)   # x^2
        equation[6].set_color(YELLOW) # b
        equation[7].set_color(BLUE)   # x
        equation[9].set_color(YELLOW) # c

        self.play(Write(equation))

        # Explain each part
        labels = [
            (equation[3], "coefficient"),
            (equation[1], "variable"),
            (equation[9], "constant")
        ]

        for part, label_text in labels:
            self.play(Indicate(part))
            label = Text(label_text, font_size=24).next_to(part, DOWN)
            self.play(Write(label))
            self.wait()
            self.play(FadeOut(label))
带动画的函数图像
from manim import *

class FunctionGraph(Scene):
    def construct(self):
        # Create axes
        axes = Axes(
            x_range=[-4, 4, 1],
            y_range=[-2, 8, 1],
            x_length=8,
            y_length=5,
            axis_config={"include_tip": True}
        )
        labels = axes.get_axis_labels(x_label="x", y_label="y")

        self.play(Create(axes), Write(labels))

        # Function
        func = axes.plot(lambda x: x**2, color=BLUE)
        func_label = MathTex(r"f(x) = x^2", color=BLUE).to_corner(UR)

        self.play(Create(func), Write(func_label))

        # Show derivative
        deriv = axes.plot(lambda x: 2*x, color=GREEN)
        deriv_label = MathTex(r"f'(x) = 2x", color=GREEN).next_to(func_label, DOWN)

        self.play(Create(deriv), Write(deriv_label))

        # Tangent line demonstration
        x_tracker = ValueTracker(-2)

        tangent = always_redraw(lambda: axes.get_secant_slope_group(
            x=x_tracker.get_value(),
            graph=func,
            dx=0.01,
            secant_line_color=YELLOW,
            secant_line_length=4
        ))

        dot = always_redraw(lambda: Dot(
            axes.c2p(x_tracker.get_value(), x_tracker.get_value()**2),
            color=RED
        ))

        self.play(Create(tangent), Create(dot))
        self.play(x_tracker.animate.set_value(2), run_time=4)
三维数学曲面
from manim import *

class Surface3D(ThreeDScene):
    def construct(self):
        # Set up camera
        self.set_camera_orientation(phi=75 * DEGREES, theta=-45 * DEGREES)

        # Create axes
        axes = ThreeDAxes(
            x_range=[-3, 3, 1],
            y_range=[-3, 3, 1],
            z_range=[-2, 2, 1]
        )

        # Create surface
        surface = Surface(
            lambda u, v: axes.c2p(u, v, np.sin(u) * np.cos(v)),
            u_range=[-PI, PI],
            v_range=[-PI, PI],
            resolution=(30, 30),
            fill_opacity=0.7
        )
        surface.set_fill_by_value(
            axes=axes,
            colorscale=[(RED, -1), (YELLOW, 0), (GREEN, 1)]
        )

        # Animate
        self.play(Create(axes))
        self.play(Create(surface), run_time=3)
        self.begin_ambient_camera_rotation(rate=0.2)
        self.wait(5)
几何证明
from manim import *

class PythagoreanProof(Scene):
    def construct(self):
        # Create right triangle
        triangle = Polygon(
            ORIGIN, RIGHT * 3, RIGHT * 3 + UP * 4,
            color=WHITE, fill_opacity=0.3
        )

        # Labels
        a_label = MathTex("a").next_to(triangle, DOWN)
        b_label = MathTex("b").next_to(triangle, RIGHT)
        c_label = MathTex("c").move_to(
            (ORIGIN + RIGHT * 3 + UP * 4) / 2 + LEFT * 0.5 + UP * 0.3
        )

        self.play(Create(triangle))
        self.play(Write(a_label), Write(b_label), Write(c_label))

        # Show squares on each side
        sq_a = Square(side_length=3, color=BLUE, fill_opacity=0.5)
        sq_a.next_to(triangle, DOWN, buff=0)

        sq_b = Square(side_length=4, color=GREEN, fill_opacity=0.5)
        sq_b.next_to(triangle, RIGHT, buff=0)

        self.play(Create(sq_a), Create(sq_b))

        # Area labels
        area_a = MathTex(r"a^2", color=BLUE).move_to(sq_a)
        area_b = MathTex(r"b^2", color=GREEN).move_to(sq_b)

        self.play(Write(area_a), Write(area_b))

        # Conclusion
        theorem = MathTex(r"a^2 + b^2 = c^2").to_edge(UP)
        box = SurroundingRectangle(theorem, color=GOLD)

        self.play(Write(theorem), Create(box))

LaTeX 快速参考

常见表达式
% Fractions
\frac{a}{b}

% Square root
\sqrt{x}  \sqrt[n]{x}

% Summation
\sum_{i=1}^{n} x_i

% Integral
\int_{a}^{b} f(x) \, dx

% Limit
\lim_{x \to \infty} f(x)

% Matrix
\begin{pmatrix} a & b \\ c & d \end{pmatrix}

% Partial derivative
\frac{\partial f}{\partial x}
希腊字母
\alpha \beta \gamma \delta \epsilon
\theta \lambda \mu \pi \sigma \omega
\Gamma \Delta \Theta \Lambda \Sigma \Omega

最佳实践

  1. 逐步呈现方程 - 将复杂方程拆分成多个步骤逐步呈现
  2. 使用一致的符号 - 同一符号在全文中表示相同含义
  3. 添加有意义的注释 - 标签应阐明内容，而非造成混乱
  4. 重在展示，而非陈述 - 为数学关系添加动画
  5. 联系直觉 - 搭建抽象数学与视觉理解之间的桥梁

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