March 19, 2026
Mean Wars: Geometry Gets Spicy
The Shape of Inequalities
Pretty circles, mean drama: is it wrong and where’s the pause button
TLDR: A math post used slick animations to explain how different averages line up, and the audience split between “wow” and “wait.” Commenters debated a possible mistake in the first animation, begged for a pause button, and pointed to a broader theory—all underscoring that clarity matters as much as beauty.
Math blog drops mesmerizing animations of four “means” (types of averages) showing how the Harmonic, Geometric, Arithmetic, and Quadratic means line up—and the comments instantly turned into Mean Wars. Fans swooned over the visuals and the idea of “seeing” inequalities, but the crowd split fast.
On Team Pedant, one commenter marched in with a correction flag: “the first animation seems wrong… vary b, not the circle.” Cue frantic rewinds and “wait, what am I looking at?” Meanwhile, the usability squad staged a mini-revolt: those looping gifs might be pretty, but where is the pause button? “I love it, I just need it to stop moving so I can actually think,” summed up the vibe. Then the theory purists arrived, coolly noting this four-mean chain is just a slice of the bigger power mean inequality. Translation: “Nice art, kid—here’s the encyclopedia.”
Amid the nitpicks, one playful voice hyped a game where you repeatedly average two means until they meet—a surprisingly wholesome subplot in this otherwise spicy thread. Verdict: gorgeous math visuals met the classic internet trifecta—“Actually…” corrections, UX complaints, and a Wikipedia drive-by. And yes, everyone learned something, even if they wanted a pause button to do it.
Key Points
- •The article explores geometric representations of classical inequalities, inspired by a 1985 image from Memorial University of Newfoundland.
- •It states the HM ≤ GM ≤ AM ≤ QM inequality chain for positive numbers, in both three-variable and two-variable forms.
- •HM is illustrated as the correct average speed over two legs with different speeds.
- •GM is illustrated as the correct average for multiplicative returns, showing +100% and −50% leading to 0% average growth.
- •QM (RMS) is noted as the measure used for AC voltage (e.g., 230V in Europe), contrasting with simple averaging.