Realization of a geometry-theorem proving machine
Computers & thought
A New Way for Visual Reasoning in Geometry Education
ITS '96 Proceedings of the Third International Conference on Intelligent Tutoring Systems
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
Reasoning visually about spatial interactions
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
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A new model of problem solver for geometric theorems with construction of auxiliary lines is discussed. The problem solver infers based on schematic knowledge with diagrammatic information (diagrammatic schema, DS for short). The inference algorithm invokes forward and backward chaining. The diagrammatic schema as well as the inference algorithm was designed through a series of observations of human problem solving. This paper also describes that DS is beneficial for instructions, especially for teaching students how to draw auxiliary lines.