Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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Mnccivig} _ivjip}nhgz hc 

Ngsavnag}z agm Bigivakn}~ hc 

_vhhc ng M~ga`nj Bih`i}v~

Agga Fajjabkngn-Cvage Ygnsivzn}ï mn Zniga $N}ak~. #Ygnsivzn}~ hc Gir Da`pzdnvi $YZA.

@avna Akizzagmva @avnh}}n Ygnsivzn}ï mn Zniga $N}ak~.

Za`yiki Ag}hgngn Ygnsivzn}ï mn _asna $N}ak~.

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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Ngsavnag}z ng M~ga`nj

Bih`i}v~

Ng }di kn}iva}yvi $i'b' ^ivyzdak`~

i} ak'+ 1>>:5 Bhkmigfivb

i} ak'+ 1>>45 Damaz i} ak'+

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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6???.+ ‛ngsavnag}z+‐ ‛bih`i}vnjak

ngsavnag}z+‐ ‛ngsavnag} pvhpiv}niz‐

hc a cnbyvi dasi fiig yzim }h

viciv }h jiv}ang pvhpiv}niz }da}

avi `ang}angim rdig zh`i

}vagzchv`a}nhgz hg }di cnbyvi avipivchv`im'

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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Ngsavnag}z ng M~ga`nj

Bih`i}v~

‛A bih`i}vnj pvhpiv}~ nz ag

ngsavnag} za}nzcnim f~ a savnafki

hflij} az zhhg az }dnz hflij}

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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savniz ng a zi} hc hflij}z

za}nzc~ngb zh`i jh``hg

jhgmn}nhgz'‐ $Kafhvmi+ 6??9+ p'

66.'

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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Ngsavnag}z ng M~ga`nj

Bih`i}v~

Ng MB a ‛m~ga`nj cnbyvi‐ jag

fi ziig az a zi} hc hflij}z

za}nzc~ngb zh`i jh``hg

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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jhgmn}nhgz pvhsnmim myvngb }di

jhgz}vyj}nhg hc }di cnbyvi n}zikc'

]dyz ag ngsavnag} pvhpiv}~ nz a

pvhpiv}~ }da} rnkk fi `ang}angim

f~ }di m~ga`nj cnbyvi myvngb

mvabbngb'

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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Z}ymig}z„ _ivjip}nhg hc 

Ngsavnag}z

Hgi $hc `ag~. z}vigb}d$z. hc 

MBIz nz }dinv phriv hc visiakngb

ngsavnag}z }h z}ymig}z'

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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@a}di`a}njak Ngsavnag}z

$vipvizig}im ng a Jafvn-cnbyvi.

8

_ivjinsim Ngsavnag}z $myvngb a

m~ga`nj itpkhva}nhg.

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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Zyvpvnzngb Fidasnhv 

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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]di Bhak hc }dnz

_vizig}a}nhg

Ri ng}vhmyji a mnz}ngj}nhg hc 

}rh }~piz hc ngsavnag}z hc Jafvn-

cnbyviz<

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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… phng}-ngsavnag}z+

… jhgz}vyj}nhg-ngsavnag}z' ]dizi}dihvi}njak gh}nhgz jag fi a

yzicyk }hhk hc agak~znz chv zh`i

z}ymig}z„ fidasnhvz hfzivsim

myvngb hc m~ga`nj itpkhva}nhgz'

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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]di Bvia}iv _vhlij}]hma~„z }hpnj nz hgi hc }di

}di`iz hc a bvia}iv z}ym~

misikhpim rn}dng }di Jafvnigsnvhg`ig}+ chjyzim hg<

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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… }di misikhp`ig} hc jhglij}yviz ng

}di jhg}it} hc hpig pvhfki`z ng MB5

 ‚ ng pav}njykav `a}di`a}njak ng}ivpvi}a}nhg hc 

a m~ga`nj

itpkhva}nhg5

… }di yzi hc jiv}ang $}aybd}. mvabbngb

zjdi`iz5 ‚ jhbgn}nsi pvhjizziz $ng pav}njykav 

afmyj}nsi. jhggij}im }h

}di yzi hc jiv}ang mvabbngb zjdi`iz5

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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]di Bvia}iv _vhlij}]hma~„z }hpnj nz hgi hc }di

}di`iz hc a bvia}iv z}ym~

misikhpim rn}dng }di Jafvnigsnvhg`ig}+ chjyzim hg<

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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… }di misikhp`ig} hc jhglij}yviz ng

}di jhg}it} hc hpig pvhfki`z ng MB5

 ‚ ng pav}njykav `a}di`a}njak ng}ivpvi}a}nhg hc 

a m~ga`nj

itpkhva}nhg5

… }di yzi hc jiv}ang $}aybd}. mvabbngb

zjdi`iz5 ‚ jhbgn}nsi pvhjizziz $ng pav}njykav 

afmyj}nsi. jhggij}im }h

}di yzi hc jiv}ang mvabbngb zjdi`iz5

}di nmig}ncnja}nhg hc ngsavnag}zagm }dinv ng}ivpvi}a}nhg rn}dng }di

}dihv~ hc Iyjknmiag Bih`i}v~

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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]di Bvia}iv _vhlij}]hma~„z }hpnj nz hgi hc }di

}di`iz hc a bvia}iv z}ym~

misikhpim rn}dng }di Jafvnigsnvhg`ig}+ chjyzim hg<

8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry

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… }di misikhp`ig} hc jhglij}yviz ng

}di jhg}it} hc hpig pvhfki`z ng MB5

 ‚ ng pav}njykav `a}di`a}njak ng}ivpvi}a}nhg hc 

a m~ga`nj

itpkhva}nhg5

… }di yzi hc jiv}ang $}aybd}. mvabbngb

zjdi`iz5 ‚ jhbgn}nsi pvhjizziz $ng pav}njykav 

afmyj}nsi. jhggij}im }h

}di yzi hc jiv}ang mvabbngb zjdi`iz5

}di nmig}ncnja}nhg hc ngsavnag}zagm }dinv ng}ivpvi}a}nhg rn}dng }di

}dihv~ hc Iyjknmiag Bih`i}v~

Mnccivig} _ivjip}nhgz hc Ngsavnag}z