Automated Geometry Reasoning and Methods for Diagram Generation

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ABSTRACT0201253Shang-Ching CouWichita State UAutomated geometry reasoning has been a very successful area in the past twenty years. Highlysuccessful methods for automated geometry theorem proving and discovering have been introducedsince the late 70s. With these methods, one can not only prove most of the geometry theoremswithin seconds, but also discover many new theorems. One may also prove and discover theoremsin differential geometries and mechanics. In the early 90s, methods were developed to generatehuman-readable proofs, multiple proofs, and the shortest proofs in geometry.Methods for automated geometry diagram generation (AGDG) have been developed recently.The purpose of AGDG is to draw a declaratively described diagram automatically. Compared toautomated theorem proving, AGDG has a wider range of applications, including intelligent CAD,robotics, linkage design, computer vision, nanotechnology and chemical molecular modeling,interactive constraint-based graphic systems, numerically controlled machines, and computer aidedinstruction.