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7 days ago
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{"embedding_dim": 1024, "data": [{"__id__": "ent-8ba3a27004f706af0260e986bc6a092f", "__created_at__": 1752656859, "entity_name": "三角形ABC", "content": "三角形ABC\nA geometric figure used to demonstrate the triangle inequality theorem and other geometric properties.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "ent-8a5ebf15695060ebf00d53ab04833554", "__created_at__": 1752656859, "entity_name": "三角不等式", "content": "三角不等式\nA mathematical inequality stating 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-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "ent-c28aba2ebce9095cd8d78f1df53c3cbe", "__created_at__": 1752656859, "entity_name": "欧几里得第五公理", "content": "欧几里得第五公理\nA foundational axiom in Euclidean geometry, also known as the parallel postulate, used in geometric proofs.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "ent-33baeb08781cf03b07b33ac6f4b4165b", "__created_at__": 1752656859, "entity_name": "几何原本", "content": "几何原本\nA classical mathematical text by Euclid, containing foundational principles of geometry, including propositions like 'the larger angle subtends the larger side.'", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "ent-1c05bc513bda1ef4c9e16fbdd1e1776a", "__created_at__": 1752656859, "entity_name": "点D", "content": "点D\nA constructed point in the geometric proof used to demonstrate the triangle inequality by forming an isosceles triangle.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "ent-53f81d92778b193b6fdd66710857e1d7", "__created_at__": 1752656859, "entity_name": "点P", "content": "点P\nAn arbitrary interior point of triangle ABC used to prove that ∠BPC > ∠A through geometric relationships.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "ent-79ed6b780adbd4b5c54eaee839998163", "__created_at__": 1752656859, "entity_name": "直线AB", "content": "直线AB\nA line segment in triangle ABC extended to point D in the proof of the triangle inequality.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "ent-6864816e2804264ec4a684abb1343e5b", "__created_at__": 1752656859, "entity_name": "等腰三角形BCD", "content": "等腰三角形BCD\nAn isosceles triangle formed in the proof, where |BD|=|BC| and ∠BDC=∠BCD.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "ent-9ac5593950faa90a93f1b5feec7e9295", "__created_at__": 1752656859, "entity_name": "命题19", "content": "命题19\nA proposition from Euclid's Elements stating that the larger angle subtends the larger side, used in the proof.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "ent-96d4cdff8ed57e93e3b3d843cffe3af7", "__created_at__": 1752656859, "entity_name": "BP", "content": "BP\nBP is a line segment in the geometric figure, intersecting AC at point D.", "source_id": "chunk-618195be0ad6c05ea189e352a4c2e7bb", "file_path": "unknown_source"}, {"__id__": "ent-4144e097d2fa7a491cec2a7a4322f2bc", "__created_at__": 1752656859, "entity_name": "AC", "content": "AC\nAC is a line segment in the geometric figure, intersected by BP at point D.", "source_id": "chunk-618195be0ad6c05ea189e352a4c2e7bb", "file_path": "unknown_source"}, {"__id__": "ent-f623e75af30e62bbd73d6df5b50bb7b5", "__created_at__": 1752656859, "entity_name": "D", "content": "D\nD is the point of intersection between BP and AC in the geometric figure.", "source_id": "chunk-618195be0ad6c05ea189e352a4c2e7bb", "file_path": "unknown_source"}, {"__id__": "ent-878558a0c2eb6eb671bbfd2afe6fffbe", "__created_at__": 1752656859, "entity_name": "∠BPC", "content": "∠BPC\n∠BPC is an angle in
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