{"schema_version":"ocme-site-results-v1","locale":"en","page_type":"derivations","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"q":"mko-distance-formula"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-distance-formula-01","title":{"zh-Hant":"歐氏距離公式：計算距離、拒絕負根並以平方比較","en":"Euclidean distance formula: computing, rejecting the negative root and comparing by squares"},"summary":{"zh-Hant":"在同一個等單位正交座標系中，設 P=(1,2)、Q=(4,6)、R=(6,−1)。求 d(P,Q)，並說明候選值 −5 為何不是距離；求 d(P,R) 的精確形式並判定它不是整數；以平方比較 d(P,Q) 與 d(P,R)；最後核對重合點的距離為零，以及距離與兩點的書寫順序無關。","en":"In one equal-unit orthonormal Cartesian frame let P=(1,2), Q=(4,6) and R=(6,−1). Find d(P,Q) and explain why the candidate −5 is not a distance; find the exact form of d(P,R) and decide that it is not an integer; compare d(P,Q) with d(P,R) through their squares; finally check that coincident points have distance zero and that the distance does not depend on the order in which the two points are written."},"mko_ids":["mko-distance-formula"]}],"title":"Concept derivation guides"}