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AreaMethod

Guides

  • Area Method Proofs

Symbols

  • Collinear
  • Concyclic
  • CongruentAngles
  • ECS1
  • ECS2
  • ECS3
  • ECS4
  • ECS5
  • EqualPoints
  • Equidistant
  • FreePoint
  • IsCentroid
  • IsCircumcenter
  • IsIntersection
  • IsMidpoint
  • IsOrthocenter
  • OnLine
  • OnParallel
  • OnPerpendicular
  • ParallelLines
  • PerpendicularFoot
  • PerpendicularLines
  • PythagoreanDifference
  • SignedArea
  • SignedDistance
  • VerifyConjecture
Area Method Proofs
The area method is a decision procedure for geometry developed by Chou et al. in the 1990's. The method aims to reduce a specified hypothesis to an algebraically verifiable form by applying elimination lemmas. The order in which the lemmas are applied is determined by the stated conjecture and the underlying geometric construction.
VerifyConjecture
— formally verify a geometric theorem
Elementary Construction Steps
ECS1
 ▪
ECS2
 ▪
ECS3
 ▪
ECS4
 ▪
ECS5
Composite Construction Steps
FreePoint
 ▪
IsCentroid
 ▪
IsCircumcenter
 ▪
IsIntersection
 ▪
IsOrthocenter
 ▪
IsMidpoint
 ▪
OnLine
 ▪
OnParallel
 ▪
OnPerpendicular
Primitive and Derived Functions
SignedArea
 ▪
SignedDistance
 ▪
PythagoreanDifference
Conjecture Stating Predicates
Collinear
 ▪
Concyclic
 ▪
CongruentAngles
 ▪
EqualPoints
 ▪
Equidistant
 ▪
ParallelLines
 ▪
PerpendicularLines
 ▪
PerpendicularFoot
RelatedLinks
▪
The Area Method in the Wolfram Language
- ArXiv article
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