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#mathanimation — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #mathanimation, aggregated by home.social.

  1. USM is a single, systematic framework that unifies trigonometric, hyperbolic, and complex-exponential substitutions into one coherent method. No more hunting through a dozen separate “recipes” for different radicals or inverse-trig integrals—you rewrite x + b as e^(±i α) (or e^θ), track sign/branch choices algorithmically, and reduce everything to a rational (“polynomish”) integral in a new variable.

    Why USM shines for ∫ e^(arccos(x)) dx:
    • Transforms e^(arccos(x)) into simple powers of t = e^(–i arccos(x))
    • Eliminates the usual integration-by-parts slog
    • Integrates term-by-term in one shot, then back-substitutes for a crisp final form

    📄 Dive deeper! Check out my draft article “A Unified Substitution Method for Integration” for full proofs, more examples, and the USM’s broader scope (link in bio).

    #UnifiedSubstitutionMethod #USM #Calculus #Integration #MathAnimation #Manim #MathHack #STEM #Education #InstaMath #LearnWithAnimation #MathLife #GarciaUSM #ReadTheDraft

  2. USM is a single, systematic framework that unifies trigonometric, hyperbolic, and complex-exponential substitutions into one coherent method. No more hunting through a dozen separate “recipes” for different radicals or inverse-trig integrals—you rewrite x + b as e^(±i α) (or e^θ), track sign/branch choices algorithmically, and reduce everything to a rational (“polynomish”) integral in a new variable.

    Why USM shines for ∫ e^(arccos(x)) dx:
    • Transforms e^(arccos(x)) into simple powers of t = e^(–i arccos(x))
    • Eliminates the usual integration-by-parts slog
    • Integrates term-by-term in one shot, then back-substitutes for a crisp final form

    📄 Dive deeper! Check out my draft article “A Unified Substitution Method for Integration” for full proofs, more examples, and the USM’s broader scope (link in bio).

    #UnifiedSubstitutionMethod #USM #Calculus #Integration #MathAnimation #Manim #MathHack #STEM #Education #InstaMath #LearnWithAnimation #MathLife #GarciaUSM #ReadTheDraft

  3. USM is a single, systematic framework that unifies trigonometric, hyperbolic, and complex-exponential substitutions into one coherent method. No more hunting through a dozen separate “recipes” for different radicals or inverse-trig integrals—you rewrite x + b as e^(±i α) (or e^θ), track sign/branch choices algorithmically, and reduce everything to a rational (“polynomish”) integral in a new variable.

    Why USM shines for ∫ e^(arccos(x)) dx:
    • Transforms e^(arccos(x)) into simple powers of t = e^(–i arccos(x))
    • Eliminates the usual integration-by-parts slog
    • Integrates term-by-term in one shot, then back-substitutes for a crisp final form

    📄 Dive deeper! Check out my draft article “A Unified Substitution Method for Integration” for full proofs, more examples, and the USM’s broader scope (link in bio).

    #UnifiedSubstitutionMethod #USM #Calculus #Integration #MathAnimation #Manim #MathHack #STEM #Education #InstaMath #LearnWithAnimation #MathLife #GarciaUSM #ReadTheDraft

  4. I don't do a lot of animations, but couldn't resist with this one. This traces the path of 25 iterations of the system

    x ↦ x - 0.4 sin(y + sin(0.4y))
    y ↦ y - 0.4 sin(x + sin(-2x))

    with initial (x, y) the set of points on a circle of radius 12, as the center moves from (-5, -0.4) to (+5, -0.4).

    #mathart #mathanimation #fractalanimation #trippy #iteratedfunctionsystem #generativeart #ffmpeg

  5. I don't do a lot of animations, but couldn't resist with this one. This traces the path of 25 iterations of the system

    x ↦ x - 0.4 sin(y + sin(0.4y))
    y ↦ y - 0.4 sin(x + sin(-2x))

    with initial (x, y) the set of points on a circle of radius 12, as the center moves from (-5, -0.4) to (+5, -0.4).

    #mathart #mathanimation #fractalanimation #trippy #iteratedfunctionsystem #generativeart #ffmpeg

  6. I don't do a lot of animations, but couldn't resist with this one. This traces the path of 25 iterations of the system

    x ↦ x - 0.4 sin(y + sin(0.4y))
    y ↦ y - 0.4 sin(x + sin(-2x))

    with initial (x, y) the set of points on a circle of radius 12, as the center moves from (-5, -0.4) to (+5, -0.4).

    #mathart #mathanimation #fractalanimation #trippy #iteratedfunctionsystem #generativeart #ffmpeg