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{"embedding_dim": 1024, "data": [{"__id__": "ent-043d3380caf00eb2310dd3faa6a84004", "__created_at__": 1752209912, "entity_name": "Triangle ABC", "content": "Triangle ABC\nTriangle ABC is the geometric figure used to demonstrate the triangle inequality theorem.", "source_id": "chunk-a5e3dacee89618f913c4948b6ffe64ec", "file_path": "unknown_source"}, {"__id__": "ent-8f4c99eefe09648d35e0adb3a70e4e46", "__created_at__": 1752209912, "entity_name": "Triangle Inequality", "content": "Triangle Inequality\nThe triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.", "source_id": "chunk-a5e3dacee89618f913c4948b6ffe64ec", "file_path": "unknown_source"}, {"__id__": "ent-db5203dcd8d28444cb765e0a69fabc39", "__created_at__": 1752209912, "entity_name": "Euclid's Fifth Postulate", "content": "Euclid's Fifth Postulate\nEuclid's Fifth Postulate is a fundamental principle in geometry, used here to compare angles and sides in the proof.", "source_id": "chunk-a5e3dacee89618f913c4948b6ffe64ec", "file_path": "unknown_source"}, {"__id__": "ent-847c21da8ab5c456b960f60c394aa01c", "__created_at__": 1752209912, "entity_name": "Proposition 19", "content": "Proposition 19\nProposition 19 from Euclid's Elements states that in any triangle, the greater angle is subtended by the greater side.", "source_id": "chunk-a5e3dacee89618f913c4948b6ffe64ec", "file_path": "unknown_source"}, {"__id__": "ent-8ba3a27004f706af0260e986bc6a092f", "__created_at__": 1752209912, "entity_name": "三角形ABC", "content": "三角形ABC\n三角形ABC is the specific triangle used to demonstrate the geometric proof of the triangle inequality theorem.", "source_id": "chunk-a5e3dacee89618f913c4948b6ffe64ec", "file_path": "unknown_source"}, {"__id__": "ent-8a5ebf15695060ebf00d53ab04833554", "__created_at__": 1752209912, "entity_name": "三角不等式", "content": "三角不等式\n三角不等式(Triangle Inequality) is a fundamental theorem in geometry stating that the sum of any two sides of a triangle must be greater than the third side.", "source_id": "chunk-a5e3dacee89618f913c4948b6ffe64ec", "file_path": "unknown_source"}, {"__id__": "ent-c28aba2ebce9095cd8d78f1df53c3cbe", "__created_at__": 1752209912, "entity_name": "欧几里得第五公理", "content": "欧几里得第五公理\n欧几里得第五公理(Euclid's Fifth Postulate) is a classical geometric principle used in this proof to compare angles.", "source_id": "chunk-a5e3dacee89618f913c4948b6ffe64ec", "file_path": "unknown_source"}, {"__id__": "ent-33baeb08781cf03b07b33ac6f4b4165b", "__created_at__": 1752209912, "entity_name": "几何原本", "content": "几何原本\n几何原本(Elements of Geometry) is Euclid's foundational mathematical work containing Proposition 19, referenced in this proof.", "source_id": "chunk-a5e3dacee89618f913c4948b6ffe64ec", "file_path": "unknown_source"}, {"__id__": "ent-9ac5593950faa90a93f1b5feec7e9295", "__created_at__": 1752209912, "entity_name": "命题19", "content": "命题19\n命题19 (Proposition 19) states that in any triangle, the greater angle is subtended by the greater side, used in this proof.", "source_id": "chunk-a5e3dacee89618f913c4948b6ffe64ec", "file_path": "unknown_source"}, {"__id__": "ent-1c05bc513bda1ef4c9e16fbdd1e1776a", "__created_at__": 1752209912, "entity_name": "点D", "content": "点D\n点D (Point D) is an auxiliary point constructed in the proof by extending side AB to create an isosceles triangle.", "source_id": "chunk-a5e3dacee89618f913c4948b6ffe64ec", "file_path": "unknown_source"}, {"__id__": "ent-6864816e2804264ec4a684abb1343e5b", "__created_at__": 1752209912, "entity_name": "等腰三角形BCD", "content": "等腰三角形BCD\n等腰三角形BCD (Isosceles Triangle BCD) is formed in the proof construction, showing equal angles at its base.", "source_id": "chunk-a5e3dacee89618f913c4948b6ffe64ec", "file_path": "unknown_source"}], "matrix": "yVbxuifFmjyJJ4K9gOy2vCFgtzu7ioW88f1WPKM95DxT/B68QumlPJVk8rxOND+8vVJEPGgtbrxpkIs7moLpPLKzWT1dVB29XziNu1kalrzKKza9EmqSPNTKILxC
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