benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / From the point (x,y), a legal move is a move to ((x)/(3)+u,(y)/(3)+v), where u and v are real numbers such that u²+v²≤1. What is the area of the set of points that can be reached f…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

From the point (x,y)(x, y), a legal move is a move to (x3+u,y3+v)\left(\frac{x}{3}+u, \frac{y}{3}+v\right), where uu and vv are real numbers such that u2+v2≤1u^{2}+v^{2} \leq 1. What is the area of the set of points that can be reached from (0,0)(0,0) in a finite number of legal moves?
Plain-text mathematical notation (without MathML)
From the point (x,y), a legal move is a move to ((x)/(3)+u,(y)/(3)+v), where u and v are real numbers such that u²+v²≤1. What is the area of the set of points that can be reached from (0,0) in a finite number of legal moves?
Original LaTeX notation
From the point $(x, y)$, a legal move is a move to $\left(\frac{x}{3}+u, \frac{y}{3}+v\right)$, where $u$ and $v$ are real numbers such that $u^{2}+v^{2} \leq 1$. What is the area of the set of points that can be reached from $(0,0)$ in a finite number of legal moves?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
0eeacef8-551b-5b3c-b75c-4532b5d58213
task_key
test--0eeacef8-551b-5b3c-b75c-4532b5d58213
task_revision_id
1
config / split
/ test

Official source

initial import