math-typography

# Math Typography Mathematical typography patterns for Manim animations. ## MathTex vs Tex ### MathTex - Mathematical Expressions ```python # Single equation (entire string is math mode) eq = MathTex(r"E = mc^2") # Multiple parts for animation control eq = MathTex(r"E", r"=", r"m", r"c^2") # eq[0] = "E", eq[1] = "=", eq[2] = "m", eq[3] = "c^2" ``` ### Tex - Mixed Text and Math ```python # Text with inline math label = Tex(r"The equation $E = mc^2$ is famous") # Multiple parts label = Tex(r"The value is ", r"$x = 5$") label[1].set_color(BLUE) # Color the math part ``` ## Semantic Coloring ### tex_to_color_map ```python # Automatic coloring of matched substrings. Manim splits the string at each # key and compiles the pieces as separate LaTeX, so every key must sit at the # TOP LEVEL -- never inside a braced group such as \frac{...}{...} (that # orphans the braces and fails to compile). Color top-level tokens only: formula = MathTex( r"P(A \mid B) = P(B \mid A)\, P(A) / P(B)", tex_to_color_map={ r"A": BLUE, r"B": ORANGE, r"P": GREEN, }, ) ``` > ⚠️ **Coloring inside fractions:** a `tex_to_color_map` key that lands inside > `\frac{...}{...}` (or any `{...}`) breaks LaTeX compilation. To color variables > in a fraction, use the multi-argument form and color submobjects directly > (see **Manual Coloring** below), e.g. > `MathTex(r"P(A|B)", r"=", r"\frac{P(B|A)P(A)}{P(B)}").set_color_by_tex("frac", GREEN)`. ### Manual Coloring ```python # Color specific parts eq = MathTex(r"y", r"=", r"m", r"x", r"+", r"b") eq[0].set_color(BLUE) # y eq[2].set_color(RED) # m eq[3].set_color(GREEN) # x eq[5].set_color(PURPLE) # b ``` ### Color by Index ```python # Access characters within a part eq = MathTex(r"f(x) = x^2") eq[0][0].set_color(BLUE) # 'f' eq[0][2].set_color(GREEN) # 'x' in f(x) ``` ## Split Strategies for Animation ### Simple Split ```python # Each term separate eq = MathTex(r"a", r"+", r"b", r"=", r"c") # Animate part by part self.play(Write(eq[0])) # a self.play(Write(eq[1:3])) # + b self.play(Write(eq[3:])) # = c ``` ### Grouped Split ```python # Logical groupings eq = MathTex(r"y = ", r"mx", r" + ", r"b") self.play(Write(eq[0])) # y = self.play(Write(eq[1])) # mx self.play(Write(eq[2:])) # + b ``` ### Complex Formula Split ```python # Fraction with separate parts frac = MathTex( r"\frac{", # 0: opening r"a + b", # 1: numerator r"}{", # 2: middle r"c", # 3: denominator r"}" # 4: closing ) ``` ## Common LaTeX Patterns ### Fractions ```python MathTex(r"\frac{numerator}{denominator}") MathTex(r"\frac{1}{2}") MathTex(r"\frac{x^2 + 1}{x - 1}") ``` ### Greek Letters ```python MathTex(r"\alpha, \beta, \gamma") MathTex(r"\mu, \sigma, \theta") MathTex(r"\Delta, \Omega, \Pi") ``` ### Subscripts and Superscripts ```python MathTex(r"x_1, x_2, x_n") MathTex(r"x^2, x^{10}, x^{n+1}") MathTex(r"x_i^{(k)}") # Both ``` ### Sums and Products ```python MathTex(r"\sum_{i=1}^{n} x_i") MathTex(r"\prod_{i=1}^{n} x_i") MathTex(r"\sum_{x \in S} f(x)") ``` ### Integrals ```python MathTex(r"\int_{a}^{b} f(x) \, dx") MathTex(r"\int\int_D f(x,y) \, dA") MathTex(r"\oint_C \vec{F} \cdot d\vec{r}") ``` ### Matrices ```python MathTex(r"\begin{bmatrix} a & b \\ c & d \end{bmatrix}") MathTex(r"\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}") MathTex(r"\begin{vmatrix} a & b \\ c & d \end{vmatrix}") ``` ### Aligned Equations ```python MathTex(r""" \begin{aligned} f(x) &= x^2 + 2x + 1 \\ &= (x + 1)^2 \end{aligned} """) ``` ### Cases ```python MathTex(r""" f(x) = \begin{cases} x^2 & x \geq 0 \\ -x^2 & x < 0 \end{cases} """) ``` ## Custom MathTex Classes ### Pattern: Structured Formula ```python class QuadraticFormula(MathTex): """Quadratic formula with accessible parts""" def __init__(self, **kwargs): super().__init__( r"x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}", **kwargs ) # Store references to parts self.x = self[0][0] # x self.equals = self[0][1] # = self.negative_b = self[0][2:4] # -b self.discriminant = self[0][6:13] # b^2 - 4ac self.denominator = self[0][14:16] # 2a ``` ### Pattern: Parameterized Formula ```python class BinomialCoeff(MathTex): """Binomial coefficient with custom n and k""" def __init__(self, n, k, **kwargs): super().__init__( r"\binom{" + str(n) + r"}{" + str(k) + r"}", **kwargs ) self.n_value = n self.k_value = k ``` ### Pattern: Color-Coded Variables ```python class RegressionEquation(MathTex): """Regression with color-coded coefficients""" def __init__(self, **kwargs): super().__init__( r"y", r"=", r"\beta_0", r"+", r"\beta_1", r"x", r"+", r"\epsilon", **kwargs ) self.y = self[0].set_color(BLUE) self.intercept = self[2].set_color(RED) self.slope = self[4].set_color(GREEN) self.x = self[5].set_color(ORANGE) self.error = self[7].set_color(GRAY) ``` ## Formula Animation Patterns ### Write with Timing ```python # Simple write self.play(Write(formula), run_time=2) self.wait(2) ``` ### Part by Part ```python formula = MathTex(r"E", r"=", r"m", r"c^2") for i, part in enumerate(formula): self.play(Write(part), run_time=0.5) self.wait(0.3) ``` ### Transform Between Formulas ```python eq1 = MathTex(r"a", r"+", r"b", r"=", r"c") eq2 = MathTex(r"a", r"=", r"c", r"-", r"b") self.play(Write(eq1)) self.wait(1) self.play(TransformMatchingTex(eq1, eq2)) ``` ### Substitution ```python # Original eq = MathTex(r"y = ", r"x", r"^2") # With value substituted eq_sub = MathTex(r"y = ", r"3", r"^2") eq_sub[1].set_color(BLUE) self.play(Write(eq)) self.wait(1) self.play(TransformMatchingTex(eq, eq_sub)) ``` ### Highlight Term ```python formula = MathTex(r"E = mc^2") # Temporary highlight self.play(formula.animate.set_color(YELLOW)) self.wait(0.5) self.play(formula.animate.set_color(WHITE)) ``` ## Layout and Alignment ### Centering ```python # Default: centered on screen formula = MathTex(r"x^2 + y^2 = r^2") ``` ### Positioning ```python formula.to_edge(UP, buff=0.5) formula.to_corner(UL) formula.move_to([2, 1, 0]) formula.next_to(other_object, DOWN) ``` ### Multiple Equations ```python equations = VGroup( MathTex(r"f(x) = x^2"), MathTex(r"f'(x) = 2x"), MathTex(r"f''(x) = 2"), ).arrange(DOWN, aligned_edge=LEFT) ``` ### With Labels ```python equation = MathTex(r"E = mc^2") label = Tex(r"Einstein's equation") label.next_to(equation, DOWN) group = VGroup(equation, label) ``` ## Common Statistical Formulas ```python # Normal PDF MathTex(r"f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}") # Bayes' theorem MathTex(r"P(A|B) = \frac{P(B|A) P(A)}{P(B)}") # Linear regression MathTex(r"y_i = \beta_0 + \beta_1 x_i + \epsilon_i") # Maximum likelihood MathTex(r"\mathcal{L}(\theta) = \prod_{i=1}^n f(x_i | \theta)") # Expected value MathTex(r"\mathbb{E}[X] = \sum_x x \cdot P(X = x)") # Variance