Use one equal-unit orthonormal Euclidean Cartesian frame. The circle radius is r=0≥0. Find its diameter length.
G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. The circle radius is r=0≥0. Find its diameter length.
Definition and scope
Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
C={P:distance(P,O)=r} is a boundary,not a filled disk
Conditions: none
The circle is the boundary at distance exactly r from the center,not the filled disk.For r=0 use the degenerate singleton{O},with no inside points and diameter length0.
Step identifiers and dependencies
Rule: circle_boundary_convention · Uses: G001
S002 · calculation
Before
diameter length := sum(0, 0)
After
diameter length = 0
Conditions: none
Add two opposite radial lengths to obtain2r;this is a length,not circumference or area.
The center location does not affect this length;for r=0 the result is0 without division by r.
Step identifiers and dependencies
Rule: diameter_twice_radius · Uses: G001, S002
Reverse checks
S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S002 · premise_and_result_audit — Recompute diameter length with exact rational arithmetic, not rounded decimals.
S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
Result
0
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.