• Non ci sono risultati.

High school students analyzing the phenomenology of superconductivity and constructing model of the Meissner effect

N/A
N/A
Protected

Academic year: 2021

Condividi "High school students analyzing the phenomenology of superconductivity and constructing model of the Meissner effect"

Copied!
14
0
0

Testo completo

(1)

High School Students Analyzing the Phenomenology of

Superconductivity and Constructing Models of the

Meissner Effect

Marisa Michelini, !"!#$%&'()*+'*)',&-"*%"'./0%#12)3'()*4!$"*+-'25'(/*)!3'6+#7- Alberto Stefanel, !"!#$%&'()*+'*)',&-"*%"'./0%#12)3'()*4!$"*+-'25'(/*)!3'6+#7- !"#$%!&'($)*& !"#$%&#' 809!$%2)/0%14*+-' 2:!$"' ;#)-' 2992$+0)*1!"' +2' !<972$!' #' $!7!4#)+' 9&!)2;!)272=-' *)+!$!"1)=' 52$' "+0/!)+"'>!%#0"!'9!$%!*4!/'#"'#'%&#77!)=!'"1;07#1)='+&!'%2)"+$0%12)'25';2/!7"3'#%14#1)='#'%$*1%#7' $!?#)#7-"*"'25';#=)!1%'#)/'!7!%+$*%#7'9$29!$1!"'25';#+!$*#7"3'>$*/=*)='"%*!)%!'#)/'+!%&)272=-@'6)'+&!' .0$29!#)'9$2A!%+"'BC8.BD?E3'#)'!/0%#12)#7'9#+&'F#"'/!4!729!/'2)'"09!$%2)/0%14*+-'52$'&*=&'"%&227' >#"!/'2)'!<972$#14!'!<9!$*;!)+"'#)/'2)?7*)!';!#"0$!;!)+"'%2)%!$)*)='+&!'B!*"")!$'#)/'+&!'9*))*)=' !:!%+"@'G!#"*>*7*+-' +!"+"'F!$!'9!$52$;!/'*)' "!4!$#7'6+#7*#)' &*=&' "%&227"' F*+&';2$!'+&#)' HII'"+0/!)+"@' J' $!"!#$%&' !<9!$*;!)+#12)' %#$$*!/' 20+' F*+&' KI' "!7!%+!/' "+0/!)+"3' #=!/' DL?DM3' F#"' 52%0"!/' 2)' +&!' ;2/!7"' +&!-' /!4!729' #)#7-N*)=' +&!' B!*"")!$' !:!%+' 0"*)=' +&!' O!7/' 7*)!"' $!9$!"!)+#12)@' P#+#' F!$!' %277!%+!/'>-'+&!'F2$Q"&!!+"'0"!/'>-'"+0/!)+"'#)/'>-'+&!'#0/*2?+#9!'/*#72=0!"'*)'+&!'=$209'#%14*1!"@'J' R0#7*+#14!'#)#7-"*"'25'+&!'"+0/!)+"S'#)"F!$"3'"!)+!)%!"3'!<97*%*+'$!#"2)*)='#)/'/$#F*)="'F#"'9!$52$;!/@' T&!'"+0/!)+"'7!#$)*)='9#+&"'"&2F'#'9$2=$!""*4!'%2)"+$0%12)'25';2/!7"'>#"!/'2)'+&!'*/!#7'/*#;#=)!1%' 9$29!$1!"'25'"09!$%2)/0%+2$"3'*)'F&*%&'+&!'%2)%!9+'25'O!7/'&#"'#)'*;92$+#)+'$27!@' ()#$*+,&#-*) 8!4!$#7'$!"!#$%&!"'"+$!""'+&!')!!/'+2'$!)!F'&*=&'"%&227'9&-"*%"'%0$$*%07#'*)%70/*)='%2)+!)+"'25'%2)+!;92$#$-' 9&-"*%"'UJ0>$!%&+3'DMVMW'X*7'Y'827>!"3'DMMZW'[#Q!'EIII3'C"+!$;#))3'B2$!*$#'EIIK\@'J7+&20=&3'+&!';#*)' #]!)12)'*"'2$*!)+!/'+2'*)+$2/0%!'50)/#;!)+#7'+29*%"'#"'R0#)+0;';!%&#)*%"'#)/'$!7#14*+-'UC"+!$;#))3' B2$!*$#' EIII#\3' #)' *)%$!#"*)=' )0;>!$' 25' 9#9!$"' !4*/!)%!"' +&!' *;92$+#)%!' +2' %2)"*/!$' 2+&!$' #"9!%+"' #"'"09!$%2)/0%14*+-@'P!;2)"+$#14!'!<9!$*;!)+"'25'7!4*+#12)'*)'/*/#%1%'7#>2$#+2$*!"'F!$!'9$292"!/'*)' /*:!$!)+'"!^)='U8%&)!*/!$'!+'#73'DMMDW'J>/?8&0Q2$3'_!!'DMMV3'`$2F)'EIIIW'X2)Na7!N?b2$=!3'P2;#$%2'EIIKW' cF*]7*)=!$3'EIIdW'8%&2$)'!+'#7@'EIIVW'8+$!&72F3'8077*4#)'EIIM\@'./0%#12)#7'9#+&"'2)'"09!$%2)/0%14*+-'#)/' 9#9!$"' 52$' +!#%&!$"3' 9$!"!)1)=' +&!' 9$2=$!""' *)' +!%&)*%#7' #997*%#12)"' 25' "09!$%2)/0%+2$"' UC"+!$;#))3' !+'#7@'DMMV#3'X20=&'DMMV3'JJee'EIIL\3'%#)'#%14#+!'+&!'%2)"+$0%12)'25';2/!7"3'#'%$*1%#7'$!?#)#7-"*"'25' +&!'Q)2F7!/=!'#>20+';#=)!1%'#)/'!7!%+$*%#7'9$29!$1!"'25';#+!$*#7"3'"1;07#1)='7*)Q"'>!+F!!)'"%*!)%!' #)/'+!%&)272=-3'>$*/=*)='%7#""*%#7'#)/'R0#)+0;'9&-"*%"'UC"+!$;#))3'B2$!*$#'EIIK\3'29!)*)='#'$!f!%12)' 2)'gC8'UT#"#$'EIIM\@'./0%#12)#7'9#+&"'*;97!;!)+!/'*)'&*=&'"%&227'F*+&'"+0/!)+"'#)/'F*+&'+!#%&!$"'*)' 52$;#12)' %2)"1+0+!' O$"+' 92"*14!' 5!#"*>*7*+-' +!"+"' UC"+!$;#))' EIII3' C"+!$;#))3' B2$!*$#' EIII>3' EIIKW' 8%&2$)'EIIVW'T#"#$'EIIM\@

T2' 24!$%2;!' +&!' /!"%$*914!?R0#7*+#14!' #99$2#%&' 0"0#77-' 52772F!/' *)' +&!' R02+!/' F2$Q"3' *)' +&!' %2)+!<+' 25'+&!'.0$29!#)'9$2A!%+"'BC8.BD?E'UJJee'EIDI3'EIDDW'h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i2$)*'!+'#7@'EIIMW'B*%&!7*)*3'e*27#'EIDDW'e*27#'EIDI\@

(2)

B!+&2/272=*!"'25'+&!'R0#7*+#14!'$!"!#$%&'U`7*""'!+'#7@'DMVZW'.$*%Q"2)'DMMVW'8#4!)-!3' 2>*)"2)'EIDD\3'+&!' +#<2)2;-'25'%#0"#7';2/!7'25',!$Q*)"'Y'X$2+N!$'UEIII\'#)/'+&!'T-9!"'25'B2/!7"'25'k*)/"%&*+73'T&2;9"2)' UEIIK\3' #$!' #+' +&!' >#"!' 25' +&!' +&!2$!1%#7' 5$#;!F2$Q' 25' +&!' 9$!"!)+' "+0/-3' 52%#7*N*)=' 2)' +&!' 52772F*)=' $!"!#$%&'R0!"12)"j'

lD\'k&#+';2/!7"'#$!'#%14#+!/'*)'"+0/!)+"'5$2;'+&!'#)#7-"*"'25'/*:!$!)+'#"9!%+"'25'+&!'9&!)2;!)272=-' #)/'&2F'+&!"!';2/!7"'!4274!m

lE\'k&*%&'#"9!%+"'25'+&!'7!4*+#12)'"+0/!)+"'"0==!"+'+2'!<972$!'+2'0)/!$"+#)/'+&!'B!*"")!$'!:!%+'#)/' F&#+'"2$+'25'&-92+&!"*"'+&!-'F#)+'+2'4!$*5-n5#7"*5-m'k&#+';2/!7"'#$!'!;>2/*!/'*)'"0%&'%#"!"m

lZ#\' k&#+' ;2/!7"' #$!' #%14#+!/' *)' +&!*$' #)#7-"*"' 25' +&!' B!*"")!$' !:!%+' #)/' lZ>\' k&#+' #$!' +&!' %2)%!9+0#7'$!5!$!)%!"'+&#+'"+0/!)+"'0"!m

lK\'k&*%&'#$!'+&!';2"+'9$2>7!;#1%'Q)2+"m ./0'&*)#01#'*2'#/0'$0"0%$&/'0130$-40)#%#-*)

T&!' $!"!#$%&' !<9!$*;!)+#12)' &!$!' 9$!"!)+!/' F#"' 9!$52$;!/' *)' d' &20$"' F*+&' KI' "+0/!)+"3' "0>/*4*/!/' *)' +F2' =$209"j' X D' %2)"*"+"' 25' gD' o' EK' "+0/!)+"' 25' =$#/!' DE' U#=!/' DLnDV\' F*+&20+' 9$!4*20"' "%&27#"1%' 52$;#12)' 2)' !7!%+$2;#=)!1";W' X E' %2)"*"+"' 25' Dd' "+0/!)+"' 25' =$#/!' DZ' U#=!/' DVnDM\3' F*+&' #' D?-!#$' "%&27#"1%'52$;#12)'2)'!7!%+$2;#=)!1";@'T&!'"+0/!)+"3'"!7!%+!/'5$2;'"%&227"'5$2;'#77'6+#7-'#)/'#]!)/*)=' +&!'80;;!$'8%&227'&!7/'#+'()*4!$"*+-'25'(/*)!'*)'b07-'EIDD3'F!$!'*)4274!/'0"*)='+0+2$*#7"'*)'9!$"2)#7'#)/' 5$!!'!<972$#12)"'25'+&!'>$!#Q/2F)'25'$!"*"14*+-'UE&\'#)/'25'+&!'B!*"")!$'!:!%+'UK&\3'#"'*+'F*77'>!'/*"%0""' *)'+&!')!<+'9#$#=$#9&@'`!52$!'+&!'#%14*+-'%2)%!$)*)='"09!$%2)/0%14*+-3'+&!'"+0/!)+"'F!$!'*)4274!/'*)'#' ;2/07!'25'd'&20$"'2)';#=)!1%'9&!)2;!)#'#)/'!7!%+$2;#=)!1%'*)/0%12)3'%2)"+$0%1)='29!$#14!7-'+&!' O!7/'7*)!'$!9$!"!)+#12)'#)/'+&!'%2)%!9+'25'f0<@ ./0'"#03'0135*$0+'!6'"#,+0)#",'#/0'4*)-#*$-)7'#**5". T&!'!/0%#12)#7'9#+&3'#+'+&!'>#"!'25'+&!'!<9!$*;!)+#12)"'&!$!'/2%0;!)+!/3'*;97!;!)+'#)'6`_'#99$2#%&' UB*%&!7*)*3'e*27#'EIDD\'0"*)='#'"!+'25'&#)/"?2)n;*)/"?2)'#99#$#+0"!"'/!"*=)!/'F*+&'"*;97!';#+!$*#7"'#)/' &*=&'+!%&)272=-'Q*+"'UJJeeEIDI3'EIDD3'h!/N*!$"Q#'.@'!+'#7@'EIDI\3'p`iC'"#;97!"3'(8`'9$2>!'+2'!<972$!' $!"*"14*+-'4!$"0"'+!;9!$#+0$!'25'"27*/"'UX!$4#"*23'B*%&!7*)*'EIDI\@'6)'+&!'!<9!$*;!)+#12)'&!$!'/*"%0""!/' +&!'"+0/!)+"'F!$!'*)4274!/'*)'+&!'52772F*)='!<972$#14!'"+!9"j 8I\'B!#"0$!;!)+'25'+&!'`$!#Q/2F)'25'$!"*"14*+-'25'#)'p`iC'/*"%W 8D\' .<972$#12)' 25' +&!' ;#=)!1%' 9$29!$1!"' 25' /*:!$!)+' 2>A!%+"j' *)+!$#%12)' 25' #' ;#=)!+' #)/' /*:!$!)+' 2>A!%+"' 90+' 2)' +&!' +#>7!3' +2' $!%2=)*N!' +&!' 5!$$2;#=)!1%' 2)!"W' *)+!$#%12)' >!+F!!)' +F2' 5$!!' #)/' %2)"+$#*)!/' ;#=)!+"3' *)+!$#%12)' 25' #' "+$2)=' )!2/*;*0;' ;#=)!+' #)/' 9#$#;#=)!1%' #)/' /*#;#=)!1%' "-"+!;"'"0"9!)/!/'2)'#'F*$!'2$'2)'#'-2Q!'*)'2$/!$'+2';#Q!'!4*/!)+'!4!)'4!$-'";#77'$!907"*4!n#]$#%14!' 52$%!"W

(3)

8DD\'8+0/!)+"'"-)+&!1N!'+&!';#*)'%&#$#%+!$*"1%'25'+&!'B!*"")!$'!:!%+ T&!"!'"+!9"'F&!$!'"-"+!;#1%#77-';2)*+2$!/3'0"*)='O4!'+0+2$*#7'F2$Q"&!!+"'Uk8I3'k8D?K\3'#0/*2'$!%2$/*)=' 25'+&!'"+0/!)+'/*#72=0!"3')2+!"'$!=*"+!$!/'>-'+&!'$!"!#$%&!$"'%2)/0%1)='+&!'*)+!$#%12)'F*+&'"+0/!)+"@' T&!'"+$#+!=-'#/29+!/'*)%70/!"'+&!'52772F*)='9&#"!"j'9$!"!)+#12)'25'#'"*+0#12)?9$2>7!;3'!<9!$*;!)+#7' !<972$#12)'25'*+3'"+0/!)+'*)/*4*/0#7'#)"F!$'+2'+&!'R0!"12)"'25'+&!'$!7#+!/'F2$Q"&!!+3'/*"%0""*2)'*)'7*]7!' =$209'2)'"*)=7!'R0!"12)"3'/*"%0""*2)'*)'7#$=!'=$209'#+'+&!'!)/'25'!#%&'F2$Q"&!!+@'

P#+#' F#"' %277!%+!/' 9$!4#7!)+7-' >-' +&!' +F2' F2$Q"&!!+"' 0"!/' /0$*)=' +&!' *)*1#7' #)/' O)#7' 9&#"!"' 25' +&!' #)#7-"*"' 25' +&!' B!*"")!$' !:!%+' 7!4*+#12)j' F2$Q"&!!+?I' UO=' D\' #)/' F2$Q"&!!+?K' UO=' E\@' l0#7*+#14!' /#+#' F&!$!'"0992$+!/'>-'+&!'#0/*2'+#9!/'/*#72=0!"'25'+&!'"+0/!)+"'/0$*)='+&!'#%14*+-@

T&!'92*)+'J'25'+&!'F2$Q"&!!+?I'"0==!"+"'#'9$!7*;*)#$-'#)#7-"*"'25'520$'"*+0#12)"'U8E?8H'#)/'O=@'D\3'#"Q*)=' s20+%2;!'25'+&!'*)+!$#%12)'#)/'$!7#14!'%2)%70"*2)t@

,2*)+'`'2)'+&!'F2$Q"&!!+?I'$!R0*$!"'"+0/!)+"'+2'sP!"*=)'"*+0#12)"'#)/'+$*#7"'+2'>!'%2)/0%+!/'+2'!<972$!' +&!' 9&!)2;!)2)' 25' 7!4*+#12)3' $!92$+' +&!;' 2)' +&!' +#>7!' F*+&' +&!' &-92+&!"*"' 0)/!$7-*)=' !#%&' Uk&#+' &-92+&!"*"'/2'-20'F#)+'4!$*5-m\t'U8d\@

(4)

Figure 2.' ,2*)+"' J3' i3' G3' X' 25' +&!' F2$Q"&!!+?K3' *)' F&*%&' "+0/!)+"' #$!' $!R0!"+' +2' 0"!' +&!' O!7/' 7*)!"' +2' /!"%$*>!'+&!'7!4*+#12)'B!*"")!$'!:!%+'#)/'+&!)'"0;;#$*N!'+&!'#"9!%+"'+&#+'%&#$#%+!$*N!'*+@' 6)'+&!'92*)+"'J'#)/'i'"+0/!)+"'#$!'$!R0*$!/'+2'/$#F'+&!'O!7/'7*)!"'*)'+&!'%2)O=0$#12)'"&2F)'$!"9!%14!7-' #+'Tq'#)/'TNL'U8V\@'T&!'7#"+'+F2'92*)+"'#*;"'#+'%277!%1)='&2F'"+0/!)+"'%&#$#%+!$*N!'+&!'B!*"")!$'!:!%+'*)' #'"9!%*O%'9&!)2;!)272=-'U92*)+'G'?8M\'#)/'*)'+&!'O)#7'"0;;#$-'U92*)+'X'?8DD\@ 8%#%'%)%56"-"'40#/*+*5*76 J'R0#7*+#14!'#)#7-"*"'U.$*%Q"2)'DMMV\'25'+&!'"+0/!)+S"'#)"F!$"3'"!)+!)%!"'#)/'/$#F*)="'F#"'9!$52$;!/3' 52$'F&#+'%2)%!$)'+&!'52772F*)='92*)+"j A. k2$Q"&!!+?I?O$"+'9#$+'u'/!"%$*914!';2/!7"'2$';2/!7"'F*+&'*)+!$9$!+#14!'!7!;!)+"3'72%#7'#)/' 9#$1#7' ;2/!7"3' #)/' =72>#7' +-9!' ;2/!7"3' >$*)=*)=' +2=!+&!$' %2)%!9+"' #)/' 9$2%!""!"3' 9$24*/*)=' %#0"#7'%2))!%12)"'Ug!$"!""*#)'DMVL\W B. k2$Q"&!!+?I?"!%2)/' 9#$+' ?' ' ;2/!7"' /!4!729!/' F*+&' /!"%$*914!' 2$' *)+!$9$!+#14!' !7!;!)+"' 25' #' 72%#7' #)/' 9#$1#73' 2$' =72>#7' #)/3' >$*)=*)=' +2=!+&!$' %2)%!9+"' #)/' 9$2%!""!"3' 9$24*/!' %#0"#7' %2))!%12)"W C. #"9!%+"'25'+&!'9&!)2;!)272=-'+&#+'"+0/!)+"'%2)"*/!$'$!7!4#)+'+2'0)/!$"+#)/'+&!'9&!)2;!)2)' 25'7!4*+#12)3'52%0"'25'!<972$#12)'9$292"#7"'#)/'F&!+&!$'+&!-'#$!'2)7-'9$2%!/0$#7'2$'"!!Q'+2' 4!$*5-n5#7"*5-'&-92+&!"!"W

P@' k2$Q"&!!+?K?,2*)+"' Jni@' !9$!"!)+#12)' 25' +&!' ;#=)!1%' O!7/' 20+"*/!' #)/' *)"*/!' +&!' "09!$%2)/0%+2$3'#+'ToTq'#)/'#+'ToTNL'#)/'+-9!'25'$!9$!"!)+#12)'25'+&!'`oI'%2)/*12)

(5)

J%%2$/*)=' +2' +&!' +#<2)2;-' 25' %#0"#7' ;2/!7' 25' ,!$Q*)"' Y' X$2+N!$' UEIII\' #)/' +&!' T-9!"' 25' B2/!7"' 25'' T&2;9"2)3' k*)/"%&*+7' B' UEIIK\3' +&!' %2)%!9+0#7' %2)"+$0%+"' 25' "+0/!)+' F!$!' %7#""*O!/' *)' +&!' 52772F*)=' %#+!=2$*!"j' Developmental models $!9$!"!)+' +&!' %&#)=!"' 24!$' 1;!3' 2$' !427012)' 25' #)' 2>A!%+' 2$' 25' 9&!)2;!)#W' !"##$%&"'()* +(,-!#* /!9*%+' $!7#12)"&*9"' #;2)=' /*:!$!)+' +-9!"' 25' 2>A!%+"W Underlying Causality models !42Q!' %#0"#7' %2))!%12)"' F*+&20+' "9!%*5-*)=' +&!;W' .-!"'()"!* "/#"!* +(,-!#' 9$24*/!' "*)=7!'%2))!%12)"'25'%#0"!?!:!%+3'9#$1#7'#)/'72%#7; Emergent Causality models *)%70/!'%&#*)"'25'%#0"#7' $!7#12)"'+$*==!$!/'>-'=72>#7'4*"*2)"'25'9&!)2;!)#@'

T&!'5$!R0!)%*!"'25'+&!'%#+!=2$*!"'!;!$=!/'F!$!'!4#70#+!/3'9!$52$;*)='#'vE'+!"+'+2'!4*/!)%!'/*:!$!)%!"' F*+&'#=!"'*)'+&!'/*"+$*>012)"@

8%#%'%)%56"-"'%)+'2-)+-)7"

./0'0130$-40)#%5'%)%56"-"'*2'#/0'!$0%9+*:)'*2'#/0'$0"-"#-;-#6

6)' +&!' *)*1#7' !<9!$*;!)+#7' #)#7-"*"' 25' +&!' >$!#Q/2F)' 25' +&!' $!"*"14*+-' 25' #' /*"%' 25' p`iC3' +&!' "+0/!)+"' !4*/!)%!'*)'+&!*$'=$#9&"'UG*=@'Z\3'2)7-'+&!'"+#$+n!)/'+!;9!$#+0$!'25'+&!'9$2%!""'UDZnKI\3''>2+&'25'+&!"!' UELnKI\3'#7"2'+&!'*)*1#7'4#70!'25'+&!'p`iC'$!"*"+#)%!'UEInEL\@ i#912)"3'%2;97!1)='DMnKI'=$#9&*%"3'!;9&#"*N!'+&!'s$#9*/*+-t'25'+&!'>$!#Q/2F)'2$'+&!'"&2$+'$#)=!'25' +!;9!$#+0$!"'*)'F&*%&'*+'2%%0$"@'C)7-'*)'+&$!!'%#"!"'+&!-'9$24*/!'#)'*)+!$9$!+#12)3'/2%0;!)1)='9$!4*20"' $!#/*)="'2)'+&!'"0>A!%+'Us#+'72F'+!;9!$#+0$!"'+2'!<97#*)'+&!'9&!)2;!)2)'#+';*%$2"%29*%'7!4!7'+&!$!'*"'#' +&!2$-'%#77!/'`i83'#%%2$/*)='+2'F&*%&'+&!'!7!%+$2)"'#$$#)=!'+&!;"!74!"'+2'52$;'9#*$"3'%#77!/'i229!$'9#*$"3' +&#+'/2')2+'!<%&#)=!'!)!$=-'F*+&'+&!'7#^%!t\

T&!'#)#7-"*"'25'+&!'=$#9&' ?T'#%R0*$!/'*)'$!#7'1;!'&#"'#%14#+!/'*)'#77'"+0/!)+"'UKInKI\'/!4!729;!)+#7' ;2/!7"'>#"!/'2)'+&!'%$0%*#7'$27!'25'+&!'+!;9!$#+0$!'25'p`iC'"#;97!@'6)'+&!';#A2$*+-'25'%#"!"'UELnKI\3' *+' #%14#+!/' #7"2' +&!' $!%2=)*12)' +&#+' +&!' 9&!)2;!)2)' #)#7-N!/' %2)"*"+"' *)' #' "0//!)' %&#)=!' 25' p`iC' 9$29!$1!"'UELnKI\@'T&!')!!/'52$'#)'*)+!$9$!+#12)'25'+&!'9$2%!""'$!;#*)"'#+'#)'*;97*%*+'7!4!7'#+'+&*"'"+#=!3' #'9#$+'52$'+&!'5!F'"+0/!)+"'&#4*)='9$*2$'Q)2F7!/=!@

./0'-)-#-%5'0135*$%#-*)'*2'#/0'<0-"")0$'0220&#

(6)

k2$Q"&!!+?Ij'8*+0#12)'JE\'u'k*+&'$!=#$/'+2'+&!'"*+0#12)'*)'F&*%&'#';#=)!+'7*r*)='+&!'"#)/F*%&';#=)!+n p`iCn$*)='#+'T'o'T'q3'+&!';2/!7"'%#+!=2$*!"'!;!$=!/'#$!'"0;;#$*N!/'*)'G*=@'K@'

Figure 4.'B2/!7'%#+!=2$*!"3'&*=&7*=&+!/'*)'+&!'!<97#)#12)"'25'+&!'92*)+'8Z

6)'+&!'%#+!=2$*!"'BJE@D?Z3'*)%70/*)='"7*=&+7-';2$!'+&#)'&#75'25'+&!'"#;97!'UEDnKI\3'+&!'.;!$=!)+'i#0"#7*+-' ;2/!7"'&#4!'+F2'50)/#;!)+#7'#"9!%+"'+2'#%%20)+'52$'+&!'9&!)2;!)2)j'#)'!)1+-'%$2""*)='+&!'p`iC3'+&!' ;#=)!1%' O!7/' U%#+!=2$*!"' BJE@D' ?BJE@E\3' +&!' *)+!$#%12)' U%#+!=2$-' BJE@Z\W' +&!' #]$#%14!' *)+!$#%12)' >!+F!!)';#=)!+?$*)=@ T&!' !7#12)#7'i#0"#7*+-';2/!7'25'i#+!=2$-'`'*)%70/!"'2)7-'+&!'O$"+'#"9!%+3'>!*)='*;97*%*+'+&!'*)+!$#%12)@' T&!'O)/*)='+&#+'#)'!)1+-';0"+'%$2""'+&!'p`iC'*)'2$/!$'+2'2>"!$4!'#)'!:!%14!';#=)!+?$*)='*)+!$#%12)3' %2;;2)'+2'+&!'EZnKI'$!"92)"!'25'+&!'%#+!=2$*!"'BJE'#)/'B`E3'F#"'#%14#+!/'>-'+&!'!<972$#12)'25'+&!' *)+!$#%12)'>!+F!!)'#';#=)!+'#)/'#'5!$$2;#=)!1%'2>A!%+'+&$20=&'#'9#9!$'2$'#'F22/!)'"0$5#%!'25'#'+#>7!' U8D\3'#"'!;!$=!/'*)'+&!';214#12)"'!<9$!""!/'>-'+&!'"+0/!)+"'/*#72=0!"@

(7)

TF2'"+0/!)+"3'O)#77-3'"*;97-')2+!/'+&#+'s;#=)!+'*"'*)%7*)!/' )2+'!)/2$"!/'2)'+&!'p`iCt'#)/'+&#+'sT&!' ;#=)!+'7!4*+#+!"'2)'p`iC'#+'Tg_'52$'+&!'B!*"")!$'!:!%+@t

(8)

k2$Q"&!!+?I?',2*)+'`'?'.<9!$*;!)+#7'/!"*=)

k&!)'#"Q!/'+2'/!"*=)'!<9!$*;!)+"'+2'0)/!$"+#)/'+&!'9&!)2;!)2)'25'7!4*+#12)3'+&!'"+0/!)+"'9$292"!/' 2)'#4!$#=!'E@IxD@D'U;#<'H\'/*:!$!)+'%2)+!<+"3'#)/'E@Z'x''D@D'U;#<'H\'#%+0#77-'/*:!$!)+'!<9!$*;!)+"@ g!<+' +2' "!4!$#7' 9$292"#7"' 52$' >!&#4*2$' !<972$#12)' UEnZ' s+$-' +2' "!!' F&#+' &#99!)"' *5' @@@t\3' #' "*=)*O%#)+' 9#$+' U2)!' +&*$/\' 25' +&!' !<9!$*;!)+"' *"' #*;!/' #+' 4!$*5-*)=n5#7"*5-*)=' *)+!$9$!+#14!' &-92+&!"!"' %24!$*)=' +&!' 52772F*)=' 5077' $#)=!' 25' %2)+!<+"' U%#+!=2$*!"' )2+' !<%70"*4!\3' #77' "*=)*O%#)+' 52$' +&!' %&#$#%+!$*N#12)' 25' +&!' 9&!)2;!)2)j' $27!' 25' T' UDVnKI\W' 9$29!$1!"' p`iC' UDdnKI\W' %&#$#%+!$*"1%"' 25' +&!' *)+!$#%12)' p`iC? B#=)!+'#)/'*)'9#$1%07#$'*+"';#=)!1%')#+0$!'UELnKI\'W';!#"0$!;!)+'25'+&!'9#$#;!+!$"'F&*%&'/!+!$;*)!' +&!'*)+!$#%12)'UEdnKI\W'*)+!$#%12)'25'#'p`iC'F*+&'2>A!%+"'25';#+!$*#7"'F*+&'/*:!$!)+';#=)!1%'9$29!$1!"' UDMnKI\W'>!&#4*2$'n'!7!%+$*%#7'9$29!$1!"'p`iC'UMnKI\ [#75'25'+&!'"#;97!'#/29+"'#'4!$*5-'#99$2#%&3'9$292"*)='+2'%&#)=!'+&!'=!2;!+$-'2$'+&!'9$29!$1!"'25'+&!' "-"+!;"'*)4274!/@'T&!'$!;#*)*)='&#75'#*;"'#+'5#7"*5-*)='&-92+&!"*"3'9$292"*)='+2'!<972$!'*5'+&!'7!4*+#12)' 2%%0$"'2$')2+'>-'%&#)=*)='#'"9!%*O%'%2)/*12)'U!@=@'sT&!';#=)!1%'O!7/'25'+&!'8i'*"'"*;*7#$'+2'+&#+'25'#' ;#=)!+@'C>"!$4#12)@'65'+&!$!'*"'#';#=)!1%'O!7/3'+&!';#=)!+'F207/'+0$)'#)/'F207/';#)*5!"+'#]$#%12)' s\@'T&!$!'*"')2'/!9!)/!)%-'>!+F!!)'#=!'#)/'#99$2#%&!"'U9'wI@D\@'80%&'#)'#^+0/!3')2+'%2;;2)'#;2)=' "+0/!)+"'U,#$Q'!+'#7'EIID\3'*"'9#$1%07#$7-'*;92$+#)+'&!$!'#"'*+'&#"'7!/'+2'/!"*=)'"*+0#12)"'+&#+'&*=&7*=&+'+&!' /-)#;*%')#+0$!'25'+&!'9$2%!""!"'0)/!$7-*)='+&!'9&!)2;!)2)@ ./0'%)%56"-"'*2'#/0'0220&#'<0-"")0$'%#'#/0'0)+'*2'#/0'3%#/

Worksheet-4 –Point A@'J77'+&!'$!9$!"!)+#12)"'25'+&!';#=)!1%'O!7/'#+'T'o'T'q'*)%70/!'7*)!"'F&*%&'$#/*#+!' 5$2;'+&!'927!"'25'+&!';#=)!+3'+&$20=&'+&!'"09!$%2)/0%+2$3'#$!'29!)'%72"!'+2'+&!';#=)!1%'#<!@'T&!-'/*:!$' *)'+&!'+&$!!'+-9!"'"&2F)'*)'G*=@'H3'*)'F&*%&'!;!$=!'+&!';#*)'/*:!$!)%!'>!+F!!)'+&!'=$209"'X D'#)/'X E3' $!=#$/*)='&2F'+&!-'/$#F)'+&!';#=)!1%'O!7/'7*)!"j'#7"2'/!9*%+!/'*)"*/!'+&!';#=)!+3'F&*%&'9$2+$0/!'2)7-' 5$2;'+&!'>#"!"'25'+&!';#=)!+3'5$!R0!)+'/$#F*)=3'#7"2'9$!"!)+'*)'+&!'+!<+>22Q"'UT*97!$'DMMD3'[#>!$?8%#*;' (3'!+'#7@'DMMH\'UKnKI'#77'25'X E\W'$!9$!"!)+!/'2)7-'2)'+&!'20+"*/!'25'+&!';#=)!+3'F&*%&'9$2+$0/!'5$2;'+&!' >#"!'#$!#"'UEVnKI3'DH'25'X D'#)/'X E'DZ\W'!<+!$)#7'+2'+&!'"09!$%2)/0%+2$'#)/'9$2+$0/!'5$2;'>2+&'>#"!"' 5$2;'>2+&'"*/!'"0$5#%!"'25'+&!';#=)!+'UVnKI3'#77'25'X D\3'#"'$!%2=)*N!/'*)'+&!'!<972$#12)'25'+&!'%#;9'F*+&' %2;9#""!"

'''''''''''''''''''' D\'''KnKI'''''''''''''''''''''''''''''''''''''''''''' E\''EVnKI''''''''''''''''''''''''''''''''''''''' Z\''VnKI

(9)
(10)
(11)

>*)&5,"-*)"

6)'+&!'9!$"9!%14!'25'*)%70/*)=';2/!$)'9&-"*%"'*)'"%&227'%0$$*%07#3'"09!$%2)/0%14*+-'*"'#'9$*4*7!=!/'#$!#' >2+&'52$'*+"'$!7!4#)+'+!%&)272=*%#7'#997*%#12)"'#)/'52$'+&!'/*:!$!)+'7!4!7"'25'*+"'*)+!$9$!+#12)@'6)'+&!'%2)+!<+' 25' .0$29!#)' 9$2A!%+"' BC8.BD?E3' #' +!#%&*)=' 9$292"#7' F#"' /!4!729!/' 2)' "09!$%2)/0%14*+-' *)+!=$#+!/' *)+2'+&!'&*=&'"%&227'%0$$*%07#'25'!7!%+$2;#=)!1";3'52%0"!/'2)'+&!'!<972$#12)'25'+&!'9&!)2;!)272=*%#7' ;#=)!1%'#)/'!7!%+$*%'9$29!$1!"'25'"09!$%2)/0%+2$"@'

!"!#$%&'!<9!$*;!)+#12)"'&#4!'>!!)'%#$$*!/'20+'*)'"!4!$#7'6+#7*#)'"%&227"'#)/'52$;!/'+&!'>#"*"'52$'+&!' $!"!#$%&'/2%0;!)+!/'&!$!3'%#$$*!/'20+'F*+&'KI'"+0/!)+"'25'+F2'/*:!$!)+'#=!'=$209"'UDL?DV'#)/'DV?DM' -!#$"'27/\'"!7!%+!/'5$2;'"%&227"'5$2;'#77'6+#7-@

(12)

O!7/'+&#+'"0$$20)/"'+&!'p`iCW'+&!'09F#$/'/!52$;#12)'25'+&!'O!7/'7*)!"'9$2/0%!/'>-'+&!';#=)!+W'+&!' +$#)"7#12)'25'+&!'O!7/'$*=*/7-'+2'+&#+'25'+&!';#=)!+'U lZ\@'6)'+&!'O$"+'+F2'+-9!"3'F&*%&'&#4!'>!!)'%7#""*O!/' #"'.;!$=!)+'i#0"#7*+-';2/!7"3'+&!'7!4*+#12)'*"'+&!'$!"07+'25'+&!'%2)O=0$#12)'25'+&!';#=)!1%'O!7/'%$!#+!/' >-' +&!' p`iC' 9$!"!)%!@' T&!' #)#72=' ;2/!7"' 0)/!$7-*)=' +&!"!' $!9$!"!)+#12)"' &#4!' #' =72>#7' %2)%!912)' >!%#0"!'+&!-'*)%70/!'#'%&#*)'25'%#0"#7'%2))!%12)"3'+&!'"-)+&!"*"'25'/*:!$!)+'!<972$!/'"*+0#12)"3'!#%&'25' F&*%&'#72)!'/2!"')2+'!<97#*)'+&!'/*:!$!)+'#"9!%+"'25'7!4*+#12)j'+&!'O!7/'%2)O=0$#12)'25'+F2';#=)!+"' ;#*)+#*)!/' F*+&' 927!"' %20)+!$9#$+"' 5#%*)=W' +&!' $!907"*2)' >!+F!!)' ;#=)!+"' #)/' /*#;#=)!1%' ;#+!$*#7"' #""2%*#+!/'F*+&'#'";#77'$!/0%12)'25'+&!';#=)!1%'f0<'*)'+&!';#+!$*#7W'+&!'"+$2)='/!52$;#12)'25'+&!'O!7/' 7*)!"' *)' 9$!"!)%!' 25' #' 5!$$2;#=)!1%' 2>A!%+' U lZ>\@' 6)' +&!"!' ;2/!7"' $!;#*)' 29!)' F&#+' #$!' +&!' 52$%!"' /!4!729!/'#)/'+&!'%2)/*12)"'0)/!$'F&*%&'+&!-'2$*=*)#+!/'U lK\3'&*=&7*=&1)='/*z%071!"'*)'+&!'*)+!=$#12)' 25';!%&#)*%#7'%2)%!9+"'*)'!7!%+$2;#=)!1";'UX#7*7*'DMMV\@

T&!' !7#12)#7'i#0"#7';2/!73'2)'F&*%&'+&!'+&*$/'+-9!'25'"+0/!)+"S'$!9$!"!)+#12)'*"'>#"!/3'#/29+!/'#7"2' *)'#'5!F'$!9$!"!)+#12)"'*)'F&*%&'+&!'O!7/'9!)!+$#+!"'+&!'p`iC3'"0>+!)/"'+F2'#"9!%+"j'+&!'%2)%!912)' +&#+' +&!' ;#=)!1%' O!7/' 9$2/0%!/' >-' +&!' ;#=)!+' *"' 9$!"!)+' *)' #' 7*;*+!/' $!=*2)' 25' "9#%!3' *"' "+#1%' #)/' $*=*/7-'#""2%*#+!/'+2'*+'U`2$=!"3'X*7>!$+'DMMV\W'+&!'*/!#'+&#+'+&!'p`iC'#%+"'/*$!%+7-'2)'+&!';#=)!+3')2+'>-' ;2/*5-*)='+&!'%2)O=0$#12)'25'+&!';#=)!1%'O!7/'U l>Z\@'6)'+&*"'%#"!3'+&!'$!%2=)*12)3'+&#+'+&!'*)+!$#%12)' ;#=)!+?p`iC'*"'/*:!$!)+'5$2;'+&!'*)+!$#%12)'>!+F!!)'+F2';#=)!+"3'*"')2+'52772F!/'>-'+&!'"+$0%+0$*)='25' #)'#7+!$)#14!'*)+!$9$!+#14!';2/!7'U lK\@ J'520$+&'!;!$=!/'$!7#12)#7'%#0"#7*+-';2/!7'52$!"!!"'+&#+'+&!'p`iC'9$2/0%!"'#';#=)!1%'*;#=!'O!7/'25' +&#+'25'+&!';#=)!+@'T&*"';2/!7'*"'"92)+#)!20"7-'#%14#+!/'>-'+&!'2>"!$4#12)'25'+&!';#=)!1%'7!4*+#12)' 9&!)2;!)2)'U lD#\'#)/'*+'$!%#77"'+&!';2/!7'25'*;#=!'O!7/'0"!/'*)'7*+!$#+0$!'+2'/*"%0""'+&!'"+#>*7*+-'25' 7!4*+#12)'UJ$Q#/*!4'DMKL\@'6+'&#"'$!;#*)!/'#'"+$2)='%2)%!9+0#7'$!5!$!)%!3'52$'+&2"!'52%0"!/'2)'+&!'"+#>*7*+-' 25'7!4*+#12)3'#)/'*+'!;!$=!/'*)'+&!'#)"F!$"'25'#7;2"+'&#75'25'+&!'"#;97!'*)'+&!'/*:!$!)+'"+!9"'25'+&!'9#+&3' >!*)='!<9$!""!/'*)'#'/*$!%+'F#-'7*Q!'s+&!'"*+0#12)'25'$!907"*2)'>!+F!!)'+F2';#=)!+"'*"'$!#7*N!/t3'*)'+!$;"' 25'>!&#4*2$'s#%1)='7*Q!'+F2';#=)!+"'+&#+'$!907"!'!#%&'2+&!$t3'#"'#'&-92+&!"*"'+2'!<972$!'s4!$*5-'F&!+&!$' T_g'p`iC'*"'#';#=)!+t'U lZ\@'T&*"';2/!7'*;9!/!"'+&!'0)/!$"+#)/*)='25'+&!'/-)#;*%')#+0$!'25'+&!'s*;#=!' O!7/t'9$2/0%!/'>-'+&!'50)/#;!)+#7'!7!%+$2;#=)!1%'*)/0%12)3'*)'2$/!$'+2'0)/!$"+#)/'+&!')#+0$!'25'+&!' B!*"")!$'!:!%+'U`#/{#?B#A2"'EIId\@'T&!'"-)+&!"*"';2/!7"'/*"%0""!/'#>24!'%2)+#*)'!7!;!)+"'+2'24!$%2;!' "0%&'#'7*;*+'U lK\@

T&!' "*=)*O%#)%!' 25' +&!' $!%2=)*12)' +&#+' `' o' I' *"' "0992$+!/' *)' +&!' 9$!"!)+' F2$Q' #7"2' >-' +&!' 5#%+' +&#+' #' 7#$=!' 9#$+' 25' +&!' "#;97!' U24!$' EnZ\' >#"!/' UD\' +&!' #)#7-"*"' 25' +&!' *)+!$#%12)' >!+F!!)' #' ;#=)!+' #)/' #' 5!$$2;#=)!1%'$*)='F*+&'+&!'*)+!$92"!/'/*"%'25'p`iC3'#)/'UE\'+&!'%&#$#%+!$*N#12)'25'+&!'B!*"")!$'!:!%+'#+' +&!'!)/'25'+&!'9#+&3'2)'+&!'%#)%!77#12)'25'+&!'O!7/'*)"*/!'+&!'"09!$%2)/0%+2$'2$'2)'*+"')#+0$!'25'9!$5!%+' /*#;#=)!+'U lZ\@ T&!'%#)%!77#12)'25'+&!'p`iC'$!"*"+#)%!'#+'T'o'Tg_'F#"'*)/*%#+!/'#"'#'$!7!4#)+'#"9!%+'>-'#'+&*$/'25'+&!' "#;97!' U lZ\@' T&!' !<97*%*+' %2))!%12)' 25' +&!' !7!%+$*%#7' #)/' ;#=)!1%' 9$29!$1!"' 25' #' "09!$%2)/0%+2$3' !;!$=!/'2)7-'*)'+&!'DI|'25'"+0/!)+"3'$!;#*)!/'#)'29!)'Q)2+'52$'+&!';#A2$*+-'U lK\@ T&!'!<972$#12)'%#$$*!/'20+'!)#>7!/'+&!'$!%2=)*12)'25'+&!'%!)+$#7'$27!'25'+!;9!$#+0$!'*)'+&!'#%14#12)' 25'+&!'"09!$%2)/0%1)='"+#+!'U lZ\3'#"9!%+'!;!$=!/'#7"2'*)'+&!'O)#7'"0;;#$-'25';2$!'+&#)'&#75'25'+&!' "#;97!3' !<97#*)*)=' +&!' %&#)=!' +2' #' "09!$%2)/0%14!' "+#+!' #"' #' 9&#"!' +$#)"*12)' UEZnKI\@' T&*"' #"9!%+' F#"' #%14#+!/3' #"' F!77' #"' )2+' 5077-' $!%2=)*N!/3' !4!)' *)' +&2"!' F&2' /*/' )2+' &#4!' #' %7!#$' 4*"*2)' 25' +&!' 2$/*)#$-' 9&#"!' +$#)"*12)"' "0%&' #"' ;!71)=' #)/' >2*7*)=' U lK\@' T&!' /!!9!)*)=' 25' +&!' !<972$#12)' 25' +&!' "09!$%2)/0%1)='9&#"!'+$#)"*12)'%#)'>!'*;92$+#)+')2+'2)7-'52$'0)/!$"+#)/*)='+&!'B!*"")!$'!:!%+3'>0+' #7"2'52$'#'9&!)2;!)272=*%#7'#99$2#%&'+2'+&!'%2)%!9+'25'9&#"!'+$#)"*12)@

(13)

k!' "+$!""' *)' %2)%70"*2)' +&!' *;92$+#)%!' *)' +&!' !<9!$*;!)+#12)"' 25' +&!' #%14!' #)/' %277#>2$#14!' 7!#$)*)=' !)4*$2);!)+'"1;07#+!/'>-'+&!'+0+2$*#7"' #)/' +&!'"+$2)=';214#12)' %$!#+!/'>-'+&!'%&#77!)=*)=' 9&!)2;!)272=-3'%2)O$;*)='+&!'5!#"*>*7*+-'25'+&!'*)+$2/0%12)'25'"09!$%2)/0%14*+-'*)'&*=&'"%&227'Ue*27#' EIDIW' C"+!$;#))3' B2$!*$#' EIDI\@' T&!' $!"07+"' 2)' +&!' %&#$#%+!$*N#12)' 25' +&!' B!*"")!$' !:!%+' *)/*%#+!' &2F'+2';2/*5-'+&!'9#+&'+2'#:!%+'+&!'Q)2+"'*)'+&!'$!%2=)*12)'25'+&!'9&#"!'+$#)"*12)3'*)'+&!'$27!'25'+&!' !7!%+$2;#=)!1%' 7!4*+#12)3' *)' +&!' *)+!=$#12)' *)+2' #' %2;;2)' 5$#;!F2$Q' 25' !7!%+$*%#7' #)/' ;#=)!1%' 9$29!$1!"@ ?-!5-*7$%3/6 JJee'UEIIL\'809!$%2;!+'E'+!#%&!$'=0*/!3'8*;97*%#+0"'J83'g2$F#- JJee'UEIDI\'BC8.B'+!#%&!$'=0*/!3'8*;97*%#+0"'J83'g2$F#- JJee'UEIDD\'BC8.BE'+!#%&!$'=0*/!3'8*;97*%#+0"'J83'g2$F#-J>/?8&0Q2$3' @3'_!!3'h@'[@'UDMMV\j'[*=&'+!;9!$#+0$!'"09!$%2)/0%+2$'7!4*+#12)';2+2$@',&-"*%"'./0%#12)3' ZZ3'KL?HI@ J$Q#/*!4'e@'UDMKL\@'J'f2#1)=';#=)!+3''g#+0$!3'DdI3''ZZI@ J0>$!%&+3'X@'UDMVM\@' !/!"*=)*)='%20$"!"'#)/'+!<+>22Q"'52$'+&!'+F!)+-?O$"+'%!)+0$-@'Jb,3'HL3'ZHE?ZHM@ `#/{#?B#A}"'J'UEIId\'()/!$"+#)/*)='"+#>7!'7!4*+#12)'25'"09!$%2)/0%+2$"3'Jb,'LK'UDE\3'DDZd?DDKE@ `2$=!"3'J@'T@3'X*7>!$+@'b@'h@'UDMMV\@'B2/!7"'25'B#=)!1";3'6b8.3'EI'UZ\3'ZdD?ZLV@ `$2F)3' @'UEIII\@'P!;2)"+$#1)='+&!'B!*"")!$'.:!%+'#)/',!$"*"+!)+'i0$$!)+3'T&!',&-"*%"'+!#%&!$3'ZV'UZ\' 8@'DdV@''' i2$)*'G3'B*%&!7*)*'B3'8#)1'_3'8+!5#)!7'J3'e*27#' 'UEIIM\'i0$$*%07#$',#+&"'*)'+&!'809!$%2;!+E'.<9!$*;!)? +#12)'*)'6+#7-3'*)',&-"*%"'i0$$*%070;'P!"*=)3'i2)"+#)1)20'i,3',#9#/20$*"'g'!/"3'&]9jnn7"=@0%-@#%@%-n =*$!9EIIVn*)+$2@&+; .$*%Q"2)3'G@'UDMMV\@'l0#7*+#14!'$!"!#$%&';!+&2/"'52$'8%*!)%!'./0%#12)@'6)'`@'b@'G$#"!$3'T2>*)3'h@'X@'U./@\3' 6)+!$)#12)#7'&#)/>22Q'25'8%*!)%!'./0%#12)3',#$+'E3'P2$/$!%&+j'h70F!$3'DDHH?DDLK@ X#7*7*3'6@'UDMMH\@'B!%&#)*%"'>#%Q=$20/'*)f0!)%!"'"+0/!)+"S%2)%!912)"'*)'!7!%+$2;#=)!1";3'6b8.3'DL'UZ\3' ZLD?ZVL@ X!$4#"*23'B@3'B*%&!7*)*3'B@'UEIDI\@'J'(8`'9$2>!'52$'$!"*"14*+-'4!$"0"'+!;9!$#+0$!3'&]9jnnFFF@O"*%#@0)*? 0/@*+n( PGn;9+7DKn%2)+!)+"@&+; X*73'P@',@3'827>!"@3'b@'UDMMZ\@'T&!'*)+$2/0%12)'25';2/!$)'9&-"*%"@'6b8.3'DH3'EHH?EdI@ X2)Na7!N?b2$=!'[@3'P2;#$%2'X@'UEIIK\@'809!$%2)/0%1)='%-7*)/!$"'#*/'*)'#)'0)/!$"+#)/*)='25'%0$$!)+'*)? /0%12)3',&-"@'./0%@'ZM3'EZK X20=&3'i@'UDMMV\@'[*=&'+!;9!$#+0$!'"09!$%2)/0%+2$"'+#Q!'2:@',&-"@'./0%@3'ZZ3'ZV?Kd@ X$!%N-723'T@3'`20R0!+3'G@3'6$!"2)3'X@3'B*%&!7*)*3'B@3'.)="+$2;3'e@'UEIDI\@'[*=&?T!%&'h*+3'67'g0242'i*;!)+2'i3' UZZ\'Z3'EED?EEM@

X0#$)!$3' .@3' 8a)%&!N3' J@B@' UDMME\@' T&!' "09!$%2)/0%1)=' >*$/j' #' /*/#%1%#7' +2-@' T&!' ,&-"*%"' T!#%&!$3' ZI3' DLd?DLM@

[#>!$?8%#*;'(3'!+'#7@'UDMMH\3'G*"*%#'#'%0$#'/!7',88i'E3'c#)*%&!77*'`272=)#3'*+@'!/@'9@'ZIZ T*97!$','J'UDMMD\@'6)4*+2'#77#'O"*%#'Z3'c#)*%&!77*'`272=)#3'*+@'!/@3'9@'ddD

(14)

B*%&!7*)*'B3'e*27#' 'UEIDD\@' !"!#$%&?2$*!)+!/'+$#*)*)='52$'6+#7*#)'+!#%&!$"'*)4274!/'*)'.0$29!#)'BC8.B' ,$2A!%+3'67'g0242'i*;!)+23'ZK'UH\3'99@'EHH?ELH C"+!$;#))3'G@'UEIII\@'i2)+!;92$#$-'9&-"*%"'+29*%"'*)'&*=&'"%&227"'#)/'*)'+&!'+!#%&!$'9$!9#$#12)@'()90>? 7*"&!/',&P'T&!"*"@ C"+!$;#))3'G@3'G!$$!*$#3'_@B@3'i#4#7%#)13'i@b@[@'UDMMV\@'T}9*%2"'/!'~"*%#'%2)+!;92$)!#')2'!)"*)2';€/*2j' 0;'+!<+2'9#$#'9$25!""2$!"'"2>$!'"09!$%2)/014*/#/!@' !4*"+#'`$#"*7!*$#'/!'.)"*)2'/!'G{"*%#3'EI3'ELI? EVV@ C"+!$;#))3'G@3'B2$!*$#3'B@J'UEIII#\@'(;#'$!4*"2'>*>7*2=$aO%#'"2>$!'#'a$!#'/!'9!"R0*"#'sG{"*%#'B2/!$)#' !'i2)+!;92$)!#')2'!)"*)2';€/*2t@'6)4!"1=#‚ƒ!"'!;'.)"*)2'/!'i*„)%*#"3'H3'D?EV@ C"+!$;#))3'G@W'B2$!*$#3'B@J@'UEIII>\@'G{"*%#'i2)+!;92$)!#'!;'7#'!"%0!7#'"!%0)/#$*#j'0)#'!<9!$*„)%*#' !)'!7'#07#'*)4270%$#)/2'52$;#%*})'/!'9$25!"2$!"@' !4*"+#'/!'.)"!…#)N#'/!'7#"'i*!)%*#"3'Z'UE\3'DV3'ZMD? KIK@ C"+!$;#))3'G@3'B2$!*$#3'B@J@'UEIIK\@'(9/#1)='+&!'9&-"*%"'%0$$*%070;'*)'&*=&'"%&227"3' !4*"+#'/!'.)"!…#)? N#'/!'7#"'i*!)%*#"3'Z'UE\3'DMI?EID@ g!$"!""*#)'g@'b@'UDMVM\'i2)%!9+0#7'%&#)=!'*)'"%*!)%!'#)/'*)'"%*!)%!'!/0%#12)3'8-)+&!"!'VI'UD\3'DdZ?DVZ@ ,#$Q3'b@3'h*;3'6@3'h*;3'B@3'_!!3'B@'UEIID\@'J)#7-"*"'25'"+0/!)+"S'9$2%!""'25'%2)O$;#12)'#)/'5#7"*O%#12)3'6)+@' b@'8%*@'./0%@3'EZ'UDE\3'DEDM?DEZd@ ,!$Q*)"3'P@g@3'Y'X$2+N!$3'T@J@'UEIII\@'B2/!7"'#)/';24!"j'G2%0"*)='2)'/*;!)"*2)"'25'%#0"#7'%2;97!<*+-'+2' #%&*!4!'/!!9!$'"%*!)1O%'0)/!$"+#)/*)=@'J. J'i2)5!$!)%!3'g!F'C$7!#)"3'_J@ 8%&)!*/!$3'k@3'!+'#7@''UDMMD\@'k!*+!$!'()+!$*%&+"4!$"0%&!'N0$'[2%&+!;9!$#+0$?809$#7!*+0)=@'P*/#Q1Q'/!$' ,&-"*Q?e2$+$†=!3'dEE'u'dEL@ 8%&2$)3'`@3'!+'#7@'UEIIV\@'8(,. iCB.T'E3''.@'4#)'/!)'`!$=3'!+'#7@3'J;"+!$/#;j'()*4!$"*+-'25'J;"+!$/#;3' MDH?MDM@ 8+$!&72F3'i@',@3'8077*4#)3'B@'i@'UEIIM\@'J'i7#""$22;'P!;2)"+$#12)'25'_!4*+#12)3'Jb,'LL3'VKL?VHD@ T#‡#$3'B@G@'UEIIM\@'6)'T&!'6)+!$)#12)#7'[*"+2$-3',&*72"29&-3'820+&'`!)/3'6g@ e*27#' j' UEIDI\' 6))24#N*2)!' /*/#^%#' )!77#' 8%027#' 8!%2)/#$*#j' 0)#' 9$292"+#' %0$$*%27#$!' "077#' "09!$%2)/0^4*+ˆ3'0)90>7*"&!/',&P'T&!"*"3'()*4!$"*+-'25'(/*)!3'99@DLD?DLZ@'

k*)/"%&*+73' B@J@' Y' T&2;9"2)3' b@b@' UEIIK\@' ("*)=' "%*!)1O%' ;2/!7"' +2' 5$#;!'*)R0*$-@' ,#9!$'9$!"!)+!/'#+' J. J3'8#)'P*!=23'iJ@

Riferimenti

Documenti correlati

Words: Inquiries into Non-Linguistic Normativities,” we sought to present a specific branch of the phenomenology of normativity in which rules emerge from phenomena and then also

As part of a project aimed at identifying methodological tools to enhance a comprehensive understanding of iteration, in this paper we have analyzed the answers of a sample of 164

contains the Rasch model’s property of measurement invariance: the measurement of parameters does not depend on the characteristics of the test adopted; for instance, the

Se si considerano gli inizi della tradizione scritta delle lingue germaniche continentali (Bibbia di Vulfila, Abrogans, Heliand) non si può non osservare come questi si collochino

Module Factor Expert weight Wastewater module Rate of Application Pollution 10 Time Past from the Last Shedding Vulnerability 6 Floating Impurities Pollution 2 pH Pollution 2

Organization of the system, a comprehensive work on the formation of energy-saving competence of the future teachers of vocational school promotes environmental awareness

The following procedure is used to determine the manganese content of various types of steel, provided that the chromium content is low:.. Approximately 1 g of the steel sample

Questa scarsa attenzione dedicata alla trattatistica riguardante l’organizzazione delle attività manuali, tipica dalla visione ascetica e provvidenziale del lavoro