Results for “euclidean”

Perform a ruler-and-compass construction with step-by-step justification for each operation, producing a constructible geometric figure from given elements. Covers classical Euclidean constructions including perpendicular bisectors, angle bisectors, parallel lines, regular polygons, and tangent lines. Use when given geometric elements (points, segments, angles) and asked to produce a Euclidean construction, verify constructibility, or generate ordered construction steps for educational or documentation purposes.

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Prove geometric theorems using Euclidean axiomatic methods, coordinate geometry, or vector methods with rigorous step-by-step logical structure. Covers direct proof, proof by contradiction, coordinate proofs, vector proofs, and handling of special cases and degenerate configurations. Use when given a geometric statement to prove, verifying a conjecture, establishing a lemma, converting geometric intuition into a rigorous proof, or comparing the effectiveness of different proof methods.

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Solve Diophantine equations (integer-only solutions) including linear, quadratic, and Pell equations. Covers the extended Euclidean algorithm, descent methods, and existence proofs. Use when finding all integer solutions to ax + by = c, solving Pell's equation, generating Pythagorean triples, proving no integer solutions exist via modular constraints, or finding the fundamental solution from which all others are generated.

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Use ONLY when the user asks to check, validate, review or audit analysis code for scientific correctness, or when you are the reviewer agent running its checks. Never run it unprompted as part of ordinary analysis work. Covers physics, earth/geo, biology, chemistry, social science and bioprocess/fermentation. Runs a deterministic domain-correctness gate that catches code which runs but is scientifically wrong (unit/dimension mismatch, Euclidean distance on lat/lon without a CRS, 0-based/1-based coordinate and strand errors, impossible SMILES valence, uncorrected multiple comparisons, averaging a categorical code, unconstrained kinetic-parameter fits, kLa computed from raw DO instead of the driving force, arithmetic mean of raw CFU counts, ANOVA/Tukey with no assumption check, a curvature DOE design fit with a first-order model, an ML model fit across process scales with no correction). Surfaces structured findings; never claims the code is correct.

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Use this skill when computing 3D step-response performance metrics for point-to-point drone flight — rise time, settling time, percent overshoot, and steady-state error based on Euclidean distance to the final target. Use instead of 1D stepinfo for any flight where all three position axes move simultaneously.

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Cosmic, eldritch, and Lovecraftian horror art direction for Blender with non-Euclidean cues, impossible scale, and incomprehensible forms.

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Create and manage Neo4j vector indexes, run vector similarity search (ANN/kNN), store embeddings on nodes or relationships, use SEARCH clause (Neo4j 2026.01+, preferred) or db.index.vector.queryNodes() procedure (deprecated 2026.04, still works on 2025.x), configure HNSW and quantization options, pick similarity function and embedding provider dimensions, and batch-update embeddings. Use when tasks involve CREATE VECTOR INDEX, vector.dimensions, cosine/euclidean search, embedding ingestion pipelines, semantic or structural nearest-neighbor lookup, or hybrid search (vector + fulltext, multiple vector sources, or graph-derived scores). Does NOT handle GraphRAG retrieval_query graph traversal — use neo4j-graphrag-skill. Does NOT handle fulltext-only/keyword-only search — use neo4j-cypher-skill. Does NOT compute GDS graph embeddings (FastRP, Node2Vec) — use neo4j-gds-skill.

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Spatial reasoning, coordinate geometry, transformations, and trigonometry for geometric problem solving. Covers Euclidean geometry (points, lines, angles, congruence, similarity), triangle geometry (Pythagorean theorem, laws of sines and cosines), circle geometry (tangent lines, inscribed angles, power of a point), coordinate geometry (distance, midpoint, slope, conic sections), transformations as functions (rotation, reflection, translation, dilation), trigonometry (unit circle, identities, inverse functions), and geometric proof techniques. Use when reasoning about shapes, angles, spatial relationships, coordinate problems, or trigonometric computations.

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