different perceptions of invariants and generality of proof in dynamic geometry
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8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 1/18
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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 2/18
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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 3/18
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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 4/18
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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 5/18
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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 6/18
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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 7/18
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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 8/18
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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 9/18
@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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 10/18
Zyvpvnzngb Fidasnhv
8/6/2019 Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 11/18
]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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 12/18
… 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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 13/18
]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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 14/18
… }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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 15/18
]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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 16/18
… }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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 17/18
]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
http://slidepdf.com/reader/full/different-perceptions-of-invariants-and-generality-of-proof-in-dynamic-geometry 18/18
… }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