#Plane Vector Math

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#Plane Vector Math Reel by @mathematisa - Curlicue curves are fascinating geometric paths created by repeatedly adding tiny complex-number steps, one after another. In this animation, the curv
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@mathematisa
Curlicue curves are fascinating geometric paths created by repeatedly adding tiny complex-number steps, one after another. In this animation, the curve is generated by an iterative rule of the form z(n+1) = z(n) + step(n, t), where each new point depends on the previous one. The step itself is a rotating complex number whose direction is controlled by an exponential with an imaginary argument, and whose size slowly changes with n. The angle of each step is not random. It is driven by trigonometric functions involving both the iteration index n and a continuous time parameter t. As t changes, the direction of the steps oscillates, producing smooth curls, loops, and dense spiral structures. This is why the curve looks organic and fractal-like, even though it is fully deterministic. Because the curve is built from thousands of small additions, local patterns repeat at different scales, a key idea behind fractals. At the same time, the gradual decay in step size keeps the curve bounded and visually coherent. Curlicue curves like this connect complex numbers, iteration, trigonometry, and geometry in a single visual process, showing how rich structure can emerge from a simple mathematical rule.
#Plane Vector Math Reel by @not_abdo_benf - visualizing calculus. finding the roots of z^3 - 1 = 0 on the complex plane, zooming straight into the origin where the math completely breaks down.#c
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@not_abdo_benf
visualizing calculus. finding the roots of z^3 - 1 = 0 on the complex plane, zooming straight into the origin where the math completely breaks down.#calculus #fractals #complexmath #mathart #programming
#Plane Vector Math Reel by @aman.kumar.3348 - Polar coordinates (r,θ) are essential for modeling systems with circular symmetry, rotation, or direction-based data. E.g. navigation 🧭, robotics, da
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AM
@aman.kumar.3348
Polar coordinates (r,θ) are essential for modeling systems with circular symmetry, rotation, or direction-based data. E.g. navigation 🧭, robotics, data analysis and modelling, nature & biology. #geometry #naturelovers #math #graphics #desmos
#Plane Vector Math Reel by @eeanimation - Elliptical hypocycloids: trajectories of points on an ellipse that rolls inside a circle without skidding 

#math #geometry #trigonometry #satisfying
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@eeanimation
Elliptical hypocycloids: trajectories of points on an ellipse that rolls inside a circle without skidding #math #geometry #trigonometry #satisfying
#Plane Vector Math Reel by @eeanimation - Corrected elliptical cycloids

#math #geometry #ellipse
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@eeanimation
Corrected elliptical cycloids #math #geometry #ellipse
#Plane Vector Math Reel by @jieli.wip - Parametric Inspiration - 2026-02-20

Concept Behind It: Superformula
r(theta) = (|cos(m * theta / 4) / a|^n2 + |sin(m * theta / 4) / b|^n3)^(-1 / n1)
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JI
@jieli.wip
Parametric Inspiration — 2026-02-20 Concept Behind It: Superformula r(theta) = (|cos(m * theta / 4) / a|^n2 + |sin(m * theta / 4) / b|^n3)^(-1 / n1) x(theta) = r(theta) * cos(theta) y(theta) = r(theta) * sin(theta) The superformula blends trig waves with power-law exponents. Small changes in n1, n2, n3 create dramatically different silhouettes, while m sets rotational symmetry. Parameters: m=7, a=1.0, b=1.0, n1=0.3, n2=0.5, n3=0.3 #parametric_design
#Plane Vector Math Reel by @pi.mathematica - "So close 🤏🏼 , yet so far ♾️" 

Ideally the simulation could run for days, months, years, decades , for eternity , Yet the lines would never connect
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PI
@pi.mathematica
"So close 🤏🏼 , yet so far ♾️" Ideally the simulation could run for days, months, years, decades , for eternity , Yet the lines would never connect. Credits: @fascinating.fractals | Full video on his YT channel. Copyright belongs to original creator. #math #programming #satisfying #coding #fibonacci goldenratio geometry sacredgeometry
#Plane Vector Math Reel by @s13_7 - Geometric Motion Waves ⚡
#DopplerEffect #GeometricDesign #VisualPhysics
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@s13_7
Geometric Motion Waves ⚡ #DopplerEffect #GeometricDesign #VisualPhysics
#Plane Vector Math Reel by @the_science.room - Intuitive visualization of the gradient in multivariable calculus.

The curves show equal values of the function.
Moving along them does not change he
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@the_science.room
Intuitive visualization of the gradient in multivariable calculus. The curves show equal values of the function. Moving along them does not change height. The gradient points across those curves in the fastest way. That means: it gives the maximum increase. Any other direction grows slower. A simple idea shown visually. #calculus #gradient #multivariable #vectors #math
#Plane Vector Math Reel by @rarest.fact - This video is about transforming abstract mathematical concepts into mesmerizing visual animations that reveal the hidden beauty and rhythm within tri
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@rarest.fact
This video is about transforming abstract mathematical concepts into mesmerizing visual animations that reveal the hidden beauty and rhythm within trigonometry. This 86-second compilation features TikTok-style visualizations that turn sine waves, cosine functions, and geometric proofs like the Pythagorean theorem into concrete, moving shapes formed by rolling circles and dynamic patterns. What makes these animations so effective—and why this reel gained 1.2 million views within hours—is that they take mathematical functions most people only encounter as formulas on paper and show them as living, breathing geometric relationships. You can actually see how a circle rolling along a line creates a sine wave, or how geometric shapes prove mathematical identities through motion rather than equations. It’s similar to how Fourier transforms reveal that complex waveforms in music are actually built from simple sine waves. The educational value here is backed by research: studies in math-art education show that geometric visualizations like these significantly improve understanding and long-term retention of STEM concepts. When you can see the relationship instead of just memorizing the formula, the knowledge sticks. Posted by a musicology PhD who bridges art and mathematics, the content highlights how these disciplines aren’t separate but deeply interconnected through pattern and rhythm. 📐 Disclaimer: All visualizations belong to their respective creators. This content is for educational appreciation—proper attribution should be given to original sources. 🧠 Follow us @Rarest.Fact to learn something new every day!

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