论文标题
地球上的几何量的符号比较
Symbolic Comparison of Geometric Quantities in GeoGebra
论文作者
论文摘要
几何量的比较通常意味着获得给定几何图的不同代数表达式的总体真实相等性。当今的技术可能性已经通过利用某些动态几何系统的计算机代数功能来支持猜想定理的符号证明。我们介绍了Geogebra的新功能The Compare Command，该功能可以帮助用户进行平面几何学的实验。我们专注于同时自动获得猜想及其证明，包括不仅仅是平等，而且不平等。我们的贡献已经可以成功地用于支持二级教学几何课程，通过在现代个人计算机上获得几秒钟内的一些知名和一些以前未发表的结果。
Comparison of geometric quantities usually means obtaining generally true equalities of different algebraic expressions of a given geometric figure. Today's technical possibilities already support symbolic proofs of a conjectured theorem, by exploiting computer algebra capabilities of some dynamic geometry systems as well. We introduce GeoGebra's new feature, the Compare command, that helps the users in experiments in planar geometry. We focus on automatically obtaining conjectures and their proofs at the same time, including not just equalities but inequalities too. Our contribution can already be successfully used to support teaching geometry classes at secondary level, by getting several well-known and some previously unpublished result within seconds on a modern personal computer.
