Bringing More Intelligence to Dynamic Geometry by Using Symbolic Computation

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Bringing More Intelligence to Dynamic Geometry by
Using Symbolic Computation

• Francisco BotanaUniv. Vigo (Spain)
  http//webs.uvigo.es/fbotana

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Outline

• DG problems continuity, loci, proof
• GDI (Intelligent Dynamic Geometry)
• (partial) Solutions to DG problems
• webDiscovery breaking up the Algebra and
  Geometry parts
• Intercommunication

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Discontinuity ...
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... or non determinism
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Geometric loci(sampling approach pitfalls)
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Geometric loci(a posteriori conditions)
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Proof
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GDIGeometría Dinámica Inteligente
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GDI(textfile)
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GDI(geometric properties)
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GDI(CoCoA)
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GDI(discovering and/or proving)
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GDI(discovering)
The triangle ABX 1.- Is impossible 2.- Is
isosceles 3.- Is equilateral 4.- Is a right
triangle 5.- None of the above
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GDI(discovering)
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GDI(discovering)
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webDiscovery
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webDiscovery(An Eulers formula)
Midpoint(X1,A,B) Midpoint(X2,A,C) Aligned(X3,A,B)
Aligned(X4,A,C) Aligned(X5,B,C)
Perp(A,B,X1,Ci) Perp(A,C,X2,Ci) Perp(A,B,I,X3) Per
p(A,C,I,X4) Perp(B,C,I,X5) d(I,X3)d(I,X4) d(I,X3)
d(I,X5)
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webDiscovery(An Eulers formula)
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webDiscovery(An Eulers formula)
Use RQhu5..10drc Elim(h..u10,Ideal(h
u6-1, d2-((u9-u7)2(u10-u8)2), r-u8
, c2-(u92u102), 2u9 -
1, ... )) Ideal(1/2d4 - d2c2 - 2r2c2
1/2c4) -------------------------------
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Intercommunication
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Intercommunication
1 Point(-31,227)hidden 2
Point(590,227)hidden 3 Point(206,107) 4
Point(296,107) 5 Line(2,1)black 6
Segment(4,3)black 7 Point on
object(5,0.32528180)label('A') 8 Point on
object(5,0.58454108)label('B') 9 Circle by
radius(7,6)black 10 Circle by
radius(8,6)black 11 Intersect2(10,9)traced,l
abel('P')
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Intercommunication
nash.sip.ucm.es/CabriOM
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References
http//webs.uvigo.es/fbotana
Thank you.