{"id":"W4210627851","doi":"10.2307/27642919","title":"Euler's Ratio-Sum Theorem and Generalizations","year":2006,"lang":"en","type":"article","venue":"Mathematics Magazine","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Euler's formula; Pure mathematics; Calculus (dental); Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001391107,0.0008019625,0.0008690941,0.002704341,0.001552338,0.003463208,0.001078299,0.001402095,0.009645014],"category_scores_gemma":[0.004029821,0.0004485063,0.0007490851,0.002321198,0.005576791,0.01056092,0.001743462,0.004811983,0.002058719],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002030518,"about_ca_system_score_gemma":0.0005227702,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008166454,"about_ca_topic_score_gemma":0.0007422348,"domain_scores_codex":[0.9994276,0.0001620902,0.00003525331,0.00014201,0.0001905223,0.00004256187],"domain_scores_gemma":[0.9989532,0.0005702485,0.00007905805,0.0001568147,0.0001845054,0.00005613284],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000003822518,0.000003183883,0.00003034235,0.00001881154,0.000001898266,0.00001008737,0.00004038926,0.00007512198,0.00004756582,0.9934154,0.003164058,0.003189409],"study_design_scores_gemma":[0.000002977523,0.000002031883,0.00005077649,0.000006882693,0.000002152602,0.00004691,0.00001444109,0.0001745361,0.00004973193,0.9823326,0.01731393,0.000003065531],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.03103879,0.07558163,0.0730071,0.03041647,0.006402172,0.00002882591,0.0003617833,0.0002802657,0.782883],"genre_scores_gemma":[0.6758124,0.05293222,0.04744418,0.00859505,0.02418094,0.0001360292,0.0003734493,0.0003880534,0.1901378],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009645014,"threshold_uncertainty_score":0.03226578,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02458382290958025,"score_gpt":0.2588330767393202,"score_spread":0.23424925382974,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}