Norms Memes

That awkward moment when your "unit circle" looks like it had one too many energy drinks! What we're seeing here isn't a circle at all—it's a scattered plot of points in Q 2 norm space that's basically saying "Euclidean geometry? I don't know her." The L 1 norm (Manhattan distance) combined with the Q 2 space creates this diamond-like pattern instead of the perfect circle we're used to. It's mathematics flexing on us mere mortals who think circles are, you know, actually round. The top text is right—we weren't ready for this mathematical plot twist!

For those who slept through linear algebra, this is peak math humor. The Japanese flag normally features a red circle on white background, but in the L0 norm, we don't care about magnitude—only whether something is non-zero. So that perfect circle becomes a cross because the L0 norm essentially counts the number of non-zero elements. It's basically what happens when mathematicians try to be efficient: "Why use many pixels when few pixels do trick?" Next time someone asks why math matters, just show them how it can transform international symbols with a single notation change.

The Japanese flag normally features a red circle on white background, representing the rising sun. But in L ∞ norm (infinity norm), distances are measured by the maximum coordinate difference rather than Euclidean distance. So instead of a circle, you get a square. The kind of joke that makes mathematicians snort coffee through their noses while everyone else at the conference table wonders what's wrong with them.

Welcome to the mathematical twilight zone where circles have identity crises! What you're witnessing is the mathematical equivalent of ordering a "round" pizza and getting a diamond, a rounded square, or a literal square. In different metric spaces (L₁, Lₖ, L∞), the definition of "distance" changes, so the shape of a "circle" (points equidistant from center) changes too! The Euclidean metric (L₂) gives us the familiar round circles we know and love, but these other metrics are like "hold my beer, I've got a different idea of what 'same distance' means." Next time you tell someone to "draw a circle," make sure to specify which universe's definition of distance you're using, or you might end up with some very angular "circles" that would make Euclid roll in his perfectly round grave.

The mathematical glow-up we never knew SpongeBob needed. The infinity norm (left) keeps SpongeBob's dimensions normal, while the L2 norm (right) stretches him into that unsettling oval shape. It's literally a visual representation of how different norms distort vector spaces. That professor didn't just understand math—they understood meme culture on a fundamental level. The kind of educator who probably says "I don't always use memes to teach linear algebra, but when I do, I make my students question their life choices."