寻找图形中相等的角[未完成]

hbghlyj · 发表于 2020-1-19 01:10

本帖最后由 hbghlyj 于 2021-7-3 02:58 编辑 把所有线段连起来,计算倾斜角,然后用这帖的算法.不知有没有更好的算法

郝酒 · 发表于 2021-7-1 20:20

哈哈，看样子你想写个平几辅助证明程序。
我想的是用定理和结构来推导而非计算。

TSC999 · 发表于 2022-4-13 11:00

楼主的问题有人已经全面解决。软件叫【几何神算】。给定一个几何图形，这软件能搜索出哪些线段相等，哪些角度相等，哪些三角形全等，哪些三角形相似，........

hbghlyj · 发表于 2022-4-13 11:43

回复 3# TSC999
它实际上是依赖于Mathematica的FindGeometricConjectures,但是Mathematica是闭源的,本帖希望讨论具体算法...

hbghlyj · 发表于 2022-4-13 11:50

本帖最后由 hbghlyj 于 2023-7-5 01:30 编辑 Mathematica v12增加了GeometricScene及相关的内置函数,见
wolfram.com/language/12/plane-geometry/
以及Stephen Wolfram的博客
writings.stephenwolfram.com/2019/04/version-12-launches-today-bi ... etry-made-computable

mathematica stackexchange:
mathematica.stackexchange.com/questions/214527/how-to-calculate- ... this-geometric-scene
notebook 示例:
杨圣汇 "GeometricScene in Olympiad Geometry" from the Notebook Archive (2020), notebookarchive.org/2020-10-4nd733c
“无情天魔精致”的文章:
jingyan.baidu.com/article/425e69e62a4354be15fc16dc.html

hbghlyj · 发表于 2022-4-13 12:08

mathematica stackexchange的synthetic-geometry标签下有14个问题
mathematica.stackexchange.com/questions/tagged/synthetic-geometry

Automated Drawings, Conjectures, and Proofs in Planar Geometry Using the Wolfram Language
Describe Scene
Developing "scene description language" within the Wolfram Language framework to allow users to symbolically describe coordinate-free scenes in plane geometry.
Draw Scene
FindGeometricSceneInstance
Turn scene descriptions into randomized drawings of those scenes.
Give visual representations of scenes.
Find coordinates for points that satisfy the scene.
Make Conjectures About Scene
FindGeometricConjectures
Using coordinates returned by scene drawer, make conjectures about original abstract scene.
Prove Theorems About Scene
FindProof
Give human-readable synthetic proofs of theorems that hold given the hypotheses of the original abstract scene.

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