The Beauty of Bézier Curves
Why Hacker News recommends it
HN repeatedly calls it one of the best math and graphics explainers on YouTube, praised for bridging game dev and math.
What it is
Freya Holmer explains how Bezier curves work, from the helper-line construction to their uses in animation, text rendering and shapes. It uses visuals from her Unity Shapes plugin and was a SoME1 contest winner.
Recommended by 16 HN commenters across 13 different months, 2021 to 2026.
What Hacker News said
Strong rec progbits · 2021-11 · on “SoME1 results”
Probably "The Beauty of Bézier Curves" [1], one of the choices by 3B1B, comes closest. It is already a relatively large channel although usually focused on game dev tutorials rather than math explanations. This video bridges those two areas and is absolutely beautiful. [1] [this video]
Strong rec eveningtree · 2022-01 · on “A Primer on Bézier Curves”
Another beautifully explained piece on bézier curves is: The beauty of bézier curves by Fréya Holmer [this video] Found this via a contest by Grant Sanderson, and it absolutely blew me away(and most people I forwarded it to)
Strong rec armchairhacker · 2022-07 · on “Ask HN: Higher order derivatives in everyday life?”
Bezier curves. Cubic bezier curves (generally the most common type) are represented by cubic polynomials x(t) and y(t) (or just one polynomial P(t) where the coefficients are vectors). The first derivative gives you the tangent and normal. The second derivative gives you the direction the normal will gradually become as t increases. The third derivative gives you the change in this change (the fourth derivative is zero). Curvature is also computed from the first and second derivatives: K = det(P', P'')/||P'||^3 Other kinds of bezier curves are similar. In quadratic ones the first and second derivatives are normal and normal change but the third derivative is zero. In higher-polynomial bezier
Strong rec viggity · 2025-02 · on “Jacksonpollock.org (2003)”
If splines/beziers are of any interest to you, I could not recommend these videos from Freya Holmer enough. [LINK] [this video]
Strong rec viggity · 2025-08 · on “Bezier-rs – algorithms for Bézier segments and shapes”
Anytime béziers are mentioned on HN, I feel compelled to share these absolutely incredible videos from Freya Holmér [LINK] (73 minutes) [this video] (24 minutes)
Strong rec amtunlimited · 2025-08 · on “An interactive guide to SVG paths”
I'm really glad the article links to Freya's "Beauty of Bezier Curves" videos, it's genuinely one of the best math/graphics/explainer videos ever made [this video]
Strong rec jedimastert · 2026-04 · on “A Primer on Bézier Curves – So What Makes a Bézier Curve?”
Related, I think Freya Holmér's "The Beauty of Bézier Curves" is in the running for one of the best educational videos on YouTube. [this video]
Recommends nrjames · 2021-08 · on “Manim: An animation engine for explanatory math videos”
While not Manim generated, I came across this video explaining Bezier curves yesterday and thought it was pretty awesome. [this video]