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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
WolframAlphaMath`AreaMethod`
PythagoreanDifference
​
PythagoreanDifference
[a,b,c]
denotes the Pythagorean difference

abc
of the points
a
,
b
, and
c
.
​
​
PythagoreanDifference
[a,b,c,d]
denotes the Pythagorean difference

abc
of the points
a
,
b
,
c
, and
d
.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
Prove the British Flag Theorem:
In[1]:=
VerifyConjecture
​​
PythagoreanDifference
[a,p,a]+
PythagoreanDifference
[d,p,d]
PythagoreanDifference
[b,p,b]+
PythagoreanDifference
[c,p,c],​​
OnParallel
[d,c,a,b,1]@
OnPerpendicular
[c,a,b]@
FreePoint
[a,b,p]​​
Out[1]=
True
SeeAlso
SignedArea
 
▪
SignedDistance
 
▪
VerifyConjecture
RelatedGuides
▪
Area Method Proofs
RelatedLinks
▪
The Area Method in the Wolfram Language
- ArXiv article
""

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