February 6, 2026
Shots fired, derivatives required
Dark Alley Mathematics
Solve-it-or-else math tale sparks jokes, panic, and 'why so hard' energy
TLDR: A tongue‑in‑cheek alleyway math challenge uses heavy calculus to tackle a simple-sounding geometry question. Commenters split between wanting a slick shortcut and roasting the grind, with one fan admitting a bungled “method acting” fix—proof that the real action is in the peanut gallery.
A math blog drops a noir short: you’re in a dark alley; a hooded figure demands you solve a geometry riddle—what are the odds that the circle through three random points stays inside the big circle? Instead of a neat shortcut, the author goes full calculus, wrestling a huge “Jacobian” (a change-of-variables matrix) and a monster determinant. The comments? Equal parts panic and punchlines. derelicta wonders who could actually survive this pop quiz; fancyswimtime dreams of a world with more whimsy and danger; layman51 admits they expected Street-Fighting Mathematics vibes (quick heuristics), not a textbook grind.
The real drama: team Clever Geometry versus team Do It The Hard Way. mehulashah speaks for the skeptics—why all this pain? Meanwhile dooglius confesses a faceplant, editing to say their own attempt “is actually wrong” after forgetting rotations, then shrugging, “that’s what I get for method acting.” Readers christen it “Jacobians at gunpoint” and trade memes about solving for pi under pressure. Love the theatrical setup or hate the algebra slog, the crowd agrees: it’s hilarious, a little terrifying, and weirdly relatable. Nothing unites the internet like a life‑or‑death word problem—and the comment section brought the popcorn.
Key Points
- •Problem: probability that the circumcircle of three random points inside a unit circle is entirely contained within the unit circle.
- •Approach: transform six Cartesian coordinates into circumcircle center (x0, y0), radius R, and three angles θ1, θ2, θ3.
- •A 6×6 Jacobian matrix is computed for the variable change, requiring determinant evaluation.
- •Determinant simplification uses factoring (R^3 from three columns), row operations, and block-triangular reduction to an identity in the top-left 2×2 block.
- •The calculation reduces to finding the determinant of a 4×4 submatrix after clearing columns and applying row operations; the final probability is not stated.