❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐st❛ ✏❏ú❧✐♦ ❞❡ ▼❡sq✉✐t❛ ❋✐❧❤♦✑ ■♥st✐t✉t♦ ❞❡ ●❡♦❝✐ê♥❝✐❛s ❡ ❈✐ê♥❝✐❛s ❊①❛t❛s
❈â♠♣✉s ❞❡ ❘✐♦ ❈❧❛r♦
❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✿ ❆♣❧✐❝❛çõ❡s ❡♠
❖❜❥❡t♦s ❞❡ ❆♣r❡♥❞✐③❛❣❡♠
❱❛❧❝✐ ❘♦❞r✐❣✉❡s ❇❛❧❜✐♥♦ ❏ú♥✐♦r
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲ ●r❛❞✉❛çã♦ ✕ ▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠ ▼❛t❡✲ ♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r✲ ❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡
❖r✐❡♥t❛❞♦r❛
Pr♦❢❛✳ ❉r❛✳ ❙✐❞✐♥❡✐❛ ❇❛rr♦③♦
■♥st✐t✉t♦ ❞❡ ◗✉í♠✐❝❛ ✲ ❯◆❊❙P ❆r❛r❛q✉❛r❛
✺✶✻ ❇✶✼✶t
❇❛❧❜✐♥♦ ❏ú♥✐♦r✱ ❱❛❧❝✐ ❘♦❞r✐❣✉❡s
❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✿ ❆♣❧✐❝❛çõ❡s ❡♠ ❖❜❥❡t♦s ❞❡ ❆♣r❡♥❞✐③❛❣❡♠✴ ❱❛❧❝✐ ❘♦❞r✐❣✉❡s ❇❛❧❜✐♥♦ ❏ú♥✐♦r✲ ❘✐♦ ❈❧❛r♦✿ ❬s✳♥✳❪✱ ✷✵✶✺✳
✾✹ ❢✳✿ ✜❣✳✱ t❛❜✳
❉✐ss❡rt❛çã♦ ✭♠❡str❛❞♦✮ ✲ ❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐st❛✱ ■♥st✐✲ t✉t♦ ❞❡ ●❡♦❝✐ê♥❝✐❛s ❡ ❈✐ê♥❝✐❛s ❊①❛t❛s✳
❖r✐❡♥t❛❞♦r❛✿ ❙✐❞✐♥❡✐❛ ❇❛rr♦③♦
■♥st✐t✉t♦ ❞❡ ◗✉í♠✐❝❛ ✲ ❯◆❊❙P ❆r❛r❛q✉❛r❛
✶✳ ●❡♦♠❡tr✐❛✳ ✷✳ ▼❛t❡♠át✐❝❛✳ ✸✳ ❖❜❥❡t♦s ❞❡ ❆♣r❡♥❞✐③❛❣❡♠✳ ✹✳ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✳ ■✳ ❚ít✉❧♦
❚❊❘▼❖ ❉❊ ❆P❘❖❱❆➬➹❖
❱❛❧❝✐ ❘♦❞r✐❣✉❡s ❇❛❧❜✐♥♦ ❏ú♥✐♦r
❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✿ ❆♣❧✐❝❛çõ❡s ❡♠ ❖❜❥❡t♦s ❞❡
❆♣r❡♥❞✐③❛❣❡♠
❉✐ss❡rt❛çã♦ ❛♣r♦✈❛❞❛ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ♥♦ ❈✉rs♦ ❞❡ Pós✲●r❛❞✉❛çã♦ ▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠ ▼❛t❡♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧ ❞♦ ■♥st✐t✉t♦ ❞❡ ●❡♦❝✐ê♥❝✐❛s ❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❞❛ ❯♥✐✲ ✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐st❛ ✏❏ú❧✐♦ ❞❡ ▼❡sq✉✐t❛ ❋✐❧❤♦✑✱ ♣❡❧❛ s❡❣✉✐♥t❡ ❜❛♥❝❛ ❡①❛♠✐♥❛❞♦r❛✿
Pr♦❢❛✳ ❉r❛✳ ❙✐❞✐♥❡✐❛ ❇❛rr♦③♦
■♥st✐t✉t♦ ❞❡ ◗✉í♠✐❝❛ ✲ ❯◆❊❙P ❆r❛r❛q✉❛r❛ ❖r✐❡♥t❛❞♦r❛
Pr♦❢✳ ❉r✳ ◆♦rt❤♦♥ ❈❛♥❡✈❛r✐ ▲❡♠❡ P❡♥t❡❛❞♦ ■●❈❊ ✲ ❯◆❊❙P ❘✐♦ ❈❧❛r♦
Pr♦❢❛✳ ❉r❛✳ ❙✐♠♦♥❡ ❉❛♥✐❡❧❛ ❙❛rtór✐♦ ❈❈❆ ✲ ❯❋❙❈❛r ❆r❛r❛s
❆❣r❛❞❡❝✐♠❡♥t♦s
❆❣r❛❞❡ç♦ ❛ ❉❡✉s✱ q✉❡ ♣❡r♠✐t✐✉ t✉❞♦ ✐ss♦✱ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❡ ♣❡❧♦ ❞♦♠ ❞❛ ✈✐❞❛❀ ❆♦s ♠❡✉s ♣❛✐s ♣❡❧♦ ❡①❡♠♣❧♦ ❞❡ ❞✐❣♥✐❞❛❞❡ ❡ ❧✉t❛❀
➚ ♠✐♥❤❛ ❡s♣♦s❛ ❘♦s❡ ♣❡❧♦ ❛♠♦r✱ ♣❡❧❛ ❞❡❞✐❝❛çã♦✱ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛✱ ♣❡❧❛s r❡✈✐sõ❡s ❞❡ t❡①t♦ ❡ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ♥♦s ♠♦♠❡♥t♦s ❞✐❢í❝❡✐s❀
❆♦s ♠❡✉s ✐r♠ã♦s ❡ à ♠✐♥❤❛ ❢❛♠í❧✐❛ ♣❡❧♦ ❛♣♦✐♦❀
➚ ♠✐♥❤❛ ♦r✐❡♥t❛❞♦r❛ ❡ ❛♦s ♣r♦❢❡ss♦r❡s ❞♦ ♣r♦❣r❛♠❛ P❘❖❋▼❆❚✱ ♣♦r t❡r❡♠ ♠❡ ❛❥✉❞❛❞♦ ♥❡ss❛ ❝❛♠✐♥❤❛❞❛❀
❆♦s ♠❡✉s ❛♠✐❣♦s ❡ ❛♦s ❝♦❧❡❣❛s ❞❡ ♣r♦✜ssã♦ ♣♦r t❡r❡♠ ♣❛rt✐❧❤❛❞♦ ❝♦♠✐❣♦ ❡ss❛ ❜✉s❝❛ ❞❡ r❡❛❧✐③❛çã♦ ♣r♦✜ss✐♦♥❛❧❀
❇❡♠✲❛✈❡♥t✉r❛❞♦ ♦ ❤♦♠❡♠ q✉❡ ❛❝❤❛ s❛❜❡❞♦r✐❛✱ ❡ ♦ ❤♦♠❡♠ q✉❡ ❛❞q✉✐r❡ ❝♦♥❤❡❝✐♠❡♥t♦❀ P♦rq✉❡ é ♠❡❧❤♦r ❛ s✉❛ ♠❡r❝❛❞♦r✐❛ ❞♦ q✉❡ ❛rt✐❣♦s ❞❡ ♣r❛t❛✱ ❡ ♠❛✐♦r ♦ s❡✉ ❧✉❝r♦ q✉❡ ♦ ♦✉r♦ ♠❛✐s ✜♥♦✳ ▼❛✐s ♣r❡❝✐♦s❛ é ❞♦ q✉❡ ♦s r✉❜✐s✱ ❡ t✉❞♦ ♦ q✉❡ ♠❛✐s ♣♦ss❛s ❞❡s❡❥❛r ♥ã♦ s❡ ♣♦❞❡ ❝♦♠♣❛r❛r ❛ ❡❧❛✳
❘❡s✉♠♦
❊st❡ tr❛❜❛❧❤♦ r❡❛❧✐③❛ ✉♠ ❡st✉❞♦ s♦❜r❡ ♦ ❢❛♠♦s♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✱ ❛❜r❛♥❣❡♥❞♦ ❛❧❣✉♠❛s ❞❡♠♦♥str❛çõ❡s✱ ❛♣❧✐❝❛çõ❡s ❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ ♦❜❥❡t♦ ❞❡ ❛♣r❡♥❞✐③❛✲ ❣❡♠✱ ❝✉❥♦ ♦❜❥❡t✐✈♦ é ❛✉①✐❧✐❛r✱ ❞❡ ♠♦❞♦ ❧ú❞✐❝♦✱ ♥❛ ❝♦♠♣r❡❡♥sã♦ ❣❡♦♠étr✐❝❛ ❞♦ ❚❡♦r❡♠❛ ♥♦ ❡♥s✐♥♦ ❜ás✐❝♦✳ P❛r❛ q✉❡ ❛s ❞❡♠♦♥str❛çõ❡s s❡❥❛♠ ♠❡❧❤♦r ❝♦♠♣r❡❡♥❞✐❞❛s✱ s❡rá ❛♣r❡✲ s❡♥t❛❞❛ ❛ ♣❛rt❡ ❞❛ t❡♦r✐❛ ❞❛ ❣❡♦♠❡tr✐❛ ❞♦s tr✐â♥❣✉❧♦s ♥❡❝❡ssár✐❛ ♣❛r❛ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ ❡st✉❞♦ ❡♠ q✉❡stã♦✳ ❆ss✐♠✱ ❡st❡ tr❛❜❛❧❤♦ s❡rá ❞✐✈✐❞✐❞♦ ❡♠ q✉❛tr♦ ♣❛rt❡s✿ ❯♠ ❜r❡✈❡ ❤✐stór✐❝♦❀ ❈♦♥❝❡✐t♦s ❞❡ ●❡♦♠❡tr✐❛❀ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s❀ ❖❜❥❡t♦s ❞❡ ❆♣r❡♥❞✐③❛❣❡♠✳ ❯♠ ❜r❡✈❡ ❤✐stór✐❝♦✿ ❛♣r❡s❡♥t❛ ♦s ❛s♣❡❝t♦s ✜❧♦só✜❝♦s✱ ❝✉❧t✉r❛✐s ❡ ❤✐stór✐❝♦s q✉❡ ✐♥✢✉❡♥✲ ❝✐❛r❛♠ ❞✐✈❡rs❛s ❝✐✈✐❧✐③❛çõ❡s ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞♦ t❡♦r❡♠❛✳ ❈♦♥❝❡✐t♦s ❞❡ ●❡♦♠❡tr✐❛✿ tr❛t❛ ❞❡ ♣r♦♣r✐❡❞❛❞❡s ❡ ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ❞❛ ❣❡♦♠❡tr✐❛✱ ❡♠ ❡s♣❡❝✐❛❧ ❛ ❣❡♦♠❡tr✐❛ ❞♦s tr✐â♥✲ ❣✉❧♦s✱ ❡ss❡♥❝✐❛✐s ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡s❡♥❝❛❞❡❛❞♦ ♣❡❧❛ t❡♦r✐❛✳ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✿ ❛♣r❡s❡♥t❛ ❞❡♠♦♥str❛çõ❡s ❡ r❡s✉❧t❛❞♦s ❞♦ t❡♦r❡♠❛✱ ♦✉ ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞❡st❡✳ ❖❜❥❡t♦ ❞❡ ❆♣r❡♥❞✐③❛❣❡♠✿ ❛❜r❛♥❣❡ ❛s♣❡❝t♦s t❡ór✐❝♦s ❡ ♣rát✐❝♦s ♥❛ ❡❧❛❜♦r❛çã♦ ❞❡ ✉♠ ❖❜❥❡t♦ ❞❡ ❆♣r❡♥❞✐③❛❣❡♠ ❡s❝r✐t♦ ❡♠ ❋❧❛s❤✳
❆❜str❛❝t
❚❤✐s r❡s❡❛r❝❤ st✉❞✐❡s t❤❡ ❢❛♠♦✉s P②t❤❛❣♦r❡❛♥ t❤❡♦r❡♠✱ ✐♥❝❧✉❞✐♥❣ s♦♠❡ ❞❡♠♦♥s✲ tr❛t✐♦♥s✱ ❛♣♣❧✐❝❛t✐♦♥s ❛♥❞ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❛ ❧❡❛r♥✐♥❣ ♦❜❥❡❝t✳ ❚❤❡ ♠❛✐♥ ♣✉r♣♦s❡ ♦❢ t❤✐s ❧❡❛r♥✐♥❣ ♦❜❥❡❝t ✐s t♦ ❤❡❧♣ st✉❞❡♥ts ❢r♦♠ ❜❛s✐❝ ❡❞✉❝❛t✐♦♥ ✇✐t❤ t❤❡ ❣❡♦♠❡tr✐❝ ❝♦♠✲ ♣r❡❤❡♥s✐♦♥ ♦❢ t❤❡ t❤❡♦r❡♠ ✐♥ ❛ ❧✉❞✐❝ ✇❛②✳ ❚❤❡ ♣❛rt ♦❢ t❤❡ t❤❡♦r② ♦❢ t❤❡ ❛♥❣❧❡s ❣❡♦♠❡tr② ♥❡❝❡ss❛r② t♦ t❤❡ ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ t❤✐s st✉❞② ✇✐❧❧ ❜❡ ♣r❡s❡♥t❡❞✱ s♦ t❤❡ ❞❡♠♦♥str❛t✐♦♥s ❝❛♥ ❜❡ ❜❡tt❡r ✉♥❞❡rst♦♦❞✳ ❚❤✐s ✇♦r❦ ✇✐❧❧ ❜❡ ❞✐✈✐❞❡❞ ✐♥ ❢♦✉r ♣❛rts✿ ❆ ❜r✐❡❢ ❤✐st♦r②❀ ●❡✲ ♦♠❡tr✐❝ ❈♦♥❝❡♣ts❀ P②t❤❛❣♦r❡❛♥ ❚❤❡♦r❡♠❀ ▲❡❛r♥✐♥❣ ❖❜❥❡❝ts✳ ❆ ❜r✐❡❢ ❤✐st♦r② ♣r❡s❡♥ts t❤❡ ♣❤✐❧♦s♦♣❤✐❝❛❧✱ ❝✉❧t✉r❛❧ ❛♥❞ ❤✐st♦r✐❝❛❧ ❛s♣❡❝ts t❤❛t ✐♥✢✉❡♥❝❡❞ ♠❛♥② ❝✐✈✐❧✐③❛t✐♦♥s ❛s ❛ r❡s✉❧t ♦❢ t❤❡ t❤❡♦r❡♠✳ ●❡♦♠❡tr✐❝ ❈♦♥❝❡♣ts ✐s ❛❜♦✉t t❤❡ ♣r♦♣❡rt✐❡s ❛♥❞ t❤❡ ❜❛s✐❝ ❝♦♥❝❡♣ts ♦❢ t❤❡ ❣❡♦♠❡tr②✱ ❡s♣❡❝✐❛❧❧② t❤❡ tr✐❛♥❣❧❡ ❣❡♦♠❡tr②✱ ✇❤✐❝❤ ✐s ❡ss❡♥t✐❛❧ t♦ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ✉♥❧❡❛s❤❡❞ ❜② t❤❡ t❤❡♦r②✳ P②t❤❛❣♦r❡❛♥ ❚❤❡♦r❡♠ ♣r❡s❡♥ts ❞❡♠♦♥str❛t✐♦♥s ❛♥❞ r❡s✉❧ts ♦❢ t❤❡ t❤❡♦r❡♠ ♦r t❤❛t ❛r❡ r❡s✉❧t✐♥❣ ❢r♦♠ ✐t✳ ▲❡❛r♥✐♥❣ ❖❜❥❡❝t ❝♦✈❡rs t❤❡ t❤❡♦r❡t✐❝❛❧ ❛♥❞ ♣r❛❝t✐❝❛❧ ❛s♣❡❝ts ✐♥ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❛ ❧❡❛r♥✐♥❣ ♦❜❥❡❝t ❝r❡❛t❡❞ ✐♥ ❋❧❛s❤✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ▼❛♣❛ ❞❛ ❆♥t✐❣❛ ❇❛❜✐❧ô♥✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✷ ❈♦♥t❛❣❡♠ ❇❛❜✐❧ô♥✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✸ ❚á❜✉❧❛ P❧✐♠♣t♦♥ ✸✷✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✹ ❍✐❡r♦❣❧í✜❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✺ P❡❞r❛ ❞❛ ❘♦s❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✻ P❛♣✐r♦ ❘❤✐♥❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✼ ❈♦r❞❛ ❊❣í♣❝✐❛ ❝♦♠ ✶✶ ♥ós ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✽ Pr♦❜❧❡♠❛ ❞♦ P❛♣✐r♦ ❈❛✐r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✾ ❮♥❞✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✶✵ ◗✉❛❞r❛❞♦ ✈❡rsã♦ ❇❛✉❞❤❛②❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✶✶ ❘❡tâ♥❣✉❧♦ ✈❡rsã♦ ❑❛t②❛②❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✶✷ Pr✐♠❡✐r❛ ❡①♣❧✐❝❛çã♦✿ ❉❡s❝♦❜❡rt❛ ❤✐♥❞✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✶✸ ❙❡❣✉♥❞❛ ❡①♣❧✐❝❛çã♦✿ ❉❡s❝♦❜❡rt❛ ❤✐♥❞✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✶✹ ●ré❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✶✺ Pr✐♠❡✐r❛ ❞❡♠♦♥str❛çã♦✿ ❙✉❣❡r✐❞❛ ♣♦r ❊✈❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✶✻ ◗✉❛❞r❛❞♦ ❝♦♠ ♠❡❞✐❞❛ ❞❛ ❞✐❛❣♦♥❛❧ ✐❣✉❛❧ à √2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✸✳✶✻ ➪r❡❛✿ ❚r✐â♥❣✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✶✼ ➪r❡❛✿ ❚r❛♣é③✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✶ ❚r✐â♥❣✉❧♦ q✉❛❧q✉❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✷ ❚r✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✸ ❚r✐â♥❣✉❧♦ ABC✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✹ ❚r✐â♥❣✉❧♦ ❞❡ ❧❛❞♦s ✸✱ ✹ ❡ ✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✺ ◗✉❛❞r✐❝✉❧❛❞♦ ❈❤♦✉✲♣❡✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✻ ❚r✐â♥❣✉❧♦ ✐sós❝❡❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✼ ❚r✐â♥❣✉❧♦ ❞❡ ❇❤❛s❦❛r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✽ ❚r✐â♥❣✉❧♦ ❞❡ ●❛r✜❡❧❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✾ ❉❡❝♦♠♣♦s✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✶✵ ✶♦ ❝❛s♦✿ ❘❡❝í♣r♦❝❛ ❞♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✹✳✶✶ ✷♦ ❝❛s♦✿ ❘❡❝í♣r♦❝❛ ❞♦ t❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✶✾
✷ ❯♠ ❜r❡✈❡ ❍✐stór✐❝♦ ✷✶
✷✳✶ ▼❡s♦♣♦tâ♠✐❛ ✭❇❛❜✐❧ô♥✐♦s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✷ ❊❣í♣❝✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✸ ❍✐♥❞✉s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✹ ●r❡❣♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✺ P✐tá❣♦r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸ ❈♦♥❝❡✐t♦s ❞❡ ●❡♦♠❡tr✐❛ ✸✺
✸✳✶ ❚r✐â♥❣✉❧♦s✿ ❉❡✜♥✐çã♦ ❡ ❡❧❡♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✷ ❈♦♥❣r✉ê♥❝✐❛ ❞❡ tr✐â♥❣✉❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✸ ❚❡♦r❡♠❛ ❞❡ ❚❛❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✹ ❉❡s✐❣✉❛❧❞❛❞❡ tr✐❛♥❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✺ ❙❡♠❡❧❤❛♥ç❛ ❞❡ tr✐â♥❣✉❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✻ ➪r❡❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
✹ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s ✹✾
✹✳✶✶✳✹ ❘❡❧❛çã♦ ❡♥tr❡ ❛❧t✉r❛✱ ❛♣ót❡♠❛ ❞❛ ❜❛s❡ ❡ ❛♣ót❡♠❛ ❞❡ ♣✐râ♠✐❞❡s r❡❣✉❧❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✶✶✳✺ ❘❡❧❛çã♦ ❡♥tr❡ ❛❧t✉r❛✱ ❣❡r❛tr✐③ ❡ r❛✐♦ ❞♦ ❝♦♥❡ r❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✶✶✳✻ ▼ó❞✉❧♦ ❞❡ ♥ú♠❡r♦ ❝♦♠♣❧❡①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✶✶✳✼ ❘❛③õ❡s ❚r✐❣♦♥♦♠étr✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✺ ❖❜❥❡t♦s ❞❡ ❆♣r❡♥❞✐③❛❣❡♠ ✻✾
✺✳✶ ❉❡✜♥✐çã♦ ❞❡ ❖❜❥❡t♦s ❞❡ ❆♣r❡♥❞✐③❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✺✳✷ ❈❛r❛❝t❡ríst✐❝❛s ❞♦s ❖❜❥❡t♦s ❞❡ ❆♣r❡♥❞✐③❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✺✳✸ ❖❜❥❡t♦ ❞❡ ❆♣r❡♥❞✐③❛❣❡♠ P✐tá❣♦r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✺✳✸✳✶ ❖❜❥❡t✐✈♦ ❡ ❝♦♥s✐❞❡r❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✺✳✸✳✷ ■♥t❡r❢❛❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✸✳✸ ◗✉❡❜r❛✲❝❛❜❡ç❛ ❉❡❝♦♠♣♦s✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
✻ ❈♦♥❝❧✉sã♦ ✼✼
❘❡❢❡rê♥❝✐❛s ✼✾
✶ ■♥tr♦❞✉çã♦
P❡r❣✉♥t❡ ❛ q✉❛❧q✉❡r ❛❧✉♥♦ ❞♦ ❡♥s✐♥♦ ❜ás✐❝♦ ♦ ♥♦♠❡ ❞❡ ✉♠ ❣r❛♥❞❡ ♠❛t❡♠át✐❝♦ ❡ ♠✉✐t♦ ♣r♦✈❛✈❡❧♠❡♥t❡ ❡❧❡ ❝✐t❛rá P✐tá❣♦r❛s✳ ❊ss❡ ❢❛♠♦s♦ ♠❛t❡♠át✐❝♦ ❣r❡❣♦✱ ✐♥❞✐s❝✉t✐✲ ✈❡❧♠❡♥t❡✱ ♠✉❞♦✉ ♦ ♠✉♥❞♦✱ ♣♦✐s s✉❛s ❞❡s❝♦❜❡rt❛s ♣❡r♠✐t✐r❛♠ q✉❡ ❛ ❣❡♦♠❡tr✐❛ ❢♦ss❡ s❡♣❛r❛❞❛ ❞❛ ❛r✐t♠ét✐❝❛✳ ❖ ❡st✉❞♦ ❞♦ tr✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦ ❣❡r❛ ✐♥ú♠❡r♦s ♣r♦❜❧❡♠❛s ❡ r❡s✉❧t❛❞♦s✱ ❤✐st♦r✐❝❛♠❡♥t❡ ❞❡s❞❡ ❛♥t✐❣❛s ❝✐✈✐❧✐③❛çõ❡s ❛té ♦s ❞✐❛s ❛t✉❛✐s✱ ❛ ❤✉♠❛♥✐❞❛❞❡ ❞❡❞✐❝♦✉ ❡s❢♦rç♦s ♥❛ t❡♥t❛t✐✈❛ ❞❡ ❡♥❝♦♥tr❛r s♦❧✉çõ❡s ❞❡ ♣r♦❜❧❡♠❛s ♣rát✐❝♦s r❡❧❛❝✐♦♥❛❞♦s ❛ ♠❡❞✐❞❛s ♣♦r ♠❡✐♦ ❞♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✳
◆♦ s❡❣✉♥❞♦ ❝❛♣ít✉❧♦ é ❛♣r❡s❡♥t❛❞♦ ✉♠ ❜r❡✈❡ ❤✐stór✐❝♦ s♦❜r❡ ♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✳ ❊①✐st❡♠ ❡✈✐❞ê♥❝✐❛s q✉❡ ✐♥❞✐❝❛♠ q✉❡ ♦s ❛♥t✐❣♦s ❜❛❜✐❧ô♥✐♦s ❝♦♥❤❡❝✐❛♠ ♦ t❡♦r❡♠❛ ❝❡r❝❛ ❞❡ ♠✐❧ ❛♥♦s ❛♥t❡s ❞❛ é♣♦❝❛ ❞❡ P✐tá❣♦r❛s✱ ❡ ❛❣r✐♠❡♥s♦r❡s ❡❣í♣❝✐♦s ♠❡❞✐❛♠ ❛ t❡rr❛✱ ✉s❛♥❞♦ ❝♦r❞❛s ❡ ♥ós✱ r❡❝r✐❛♥❞♦ tr✐â♥❣✉❧♦s r❡tâ♥❣✉❧♦s✳ ▼❛s ♦s ❣r❡❣♦s s❡❣✉♥❞♦ ❛ tr❛❞✐çã♦ ❤✐stór✐❝❛ ❛♣r❡s❡♥t❛❞❛ ♣♦r ❍♦✇❛r❞ ❊✈❡s✱ ♣♦❞❡♠ t❡r s✐❞♦ ♦s ♣r✐♠❡✐r♦s ❛ ❞❡♠♦♥str❛r ❞❡ ♠❛♥❡✐r❛ ❣❡r❛❧ ♦ ❚❡♦r❡♠❛✳
◆♦ t❡r❝❡✐r♦ ❝❛♣ít✉❧♦ sã♦ ❛♣r❡s❡♥t❛❞♦s ❝♦♥❝❡✐t♦s ❣❡♦♠étr✐❝♦s✱ ♦s q✉❛✐s s❡rã♦ ♥❡❝❡s✲ sár✐♦s ♥❛s ❞❡♠♦♥str❛çõ❡s✿ ❉❡✜♥✐çõ❡s ❡ ❡❧❡♠❡♥t♦s ❞♦s tr✐â♥❣✉❧♦s❀ ❈♦♥❣r✉ê♥❝✐❛ ❞❡ tr✐✲ â♥❣✉❧♦s❀ ❚❡♦r❡♠❛ ❞❡ ❚❛❧❡s❀ ❉❡s✐❣✉❛❧❞❛❞❡ tr✐❛♥❣✉❧❛r❀ ❙❡♠❡❧❤❛♥ç❛ ❞❡ tr✐â♥❣✉❧♦s❀ ➪r❡❛s✳ ❊♠ ❣❡r❛❧✱ ♦s ❧✐✈r♦s ❞✐❞át✐❝♦s ❞♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧ ❡ ▼é❞✐♦ tr❛③❡♠ ❛♣❡♥❛s ❛ ❞❡♠♦♥str❛çã♦ ✈✐❛ s❡♠❡❧❤❛♥ç❛ ❞❡ tr✐â♥❣✉❧♦s✱ ❞❡ss❛ ❢♦r♠❛ ♥♦ q✉❛rt♦ ❝❛♣ít✉❧♦ sã♦ ❛♣r❡✲ s❡♥t❛❞❛s ❛❧❣✉♠❛s ❞❡♠♦♥str❛çõ❡s ❞♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s ❜❛s❡❛❞❛s ♥♦s ❝♦♥❝❡✐t♦s ❞❡ ❞❡❝♦♠♣♦s✐çã♦ ❞❡ ár❡❛s✱ s❡♠❡❧❤❛♥ç❛ ❡ ❝♦♥❣r✉ê♥❝✐❛ ❞❡ ♣♦❧í❣♦♥♦s✱ ✉♠❛ ❢❡✐t❛ ♣❡❧♦ Pr❡s✐✲ ❞❡♥t❡ ❞♦s ❊st❛❞♦s ❯♥✐❞♦s ❏❛♠❡s ❆❜r❛♠ ●❛r✜❡❧❞✱ r❡❝í♣r♦❝❛s ❡ ❣❡♥❡r❛❧✐③❛çã♦ ❞♦ t❡♦✲ r❡♠❛✱ ❡ ✜♥❛❧♠❡♥t❡✱ ❛❧❣✉♠❛s ❛♣❧✐❝❛çõ❡s✳
◆♦ q✉✐♥t♦ ❝❛♣ít✉❧♦✱ sã♦ ❛♣r❡s❡♥t❛❞♦s ❝♦♥❝❡✐t♦ ❞❡ ♦❜❥❡t♦s ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ❡ ✉♠❛ ❛♣❧✐❝❛çã♦✱ ❞❡s❡♥✈♦❧✈✐❞❛ ♣❛r❛ ✐♥tr♦❞✉③✐r ❢❛t♦s ❤✐stór✐❝♦s✱ ❛♣r❡s❡♥t❛r ❞❡♠♦♥str❛çõ❡s ❧ú❞✐✲ ❝❛s ❡ ♣r♦♣♦r ❞❡s❛✜♦s r❡❧❛❝✐♦♥❛❞♦s ❛♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✳ ❆♣❧✐❝❛çõ❡s ❡♠ ♠✉❧t✐♠í❞✐❛ ❝♦st✉♠❛♠ s❡r ✉t✐❧✐③❛❞❛s ♥❛ ❡s❝♦❧❛ ♣❛r❛ ♠❛t❡r✐❛❧✐③❛r ❝♦♥❝❡✐t♦s ❡ ♣r♦♣♦r❝✐♦♥❛r ♠❡❧❤♦r ❝♦♥t❡①t✉❛❧✐③❛çã♦ ❞♦ ❡♥s✐♥♦✱ ♥❡ss❡ ❝❛s♦✱ ♣r♦♣♦r ✉♠❛ ❛❜♦r❞❛❣❡♠ ♠♦❞❡r♥❛ ❞❡st❛s q✉❡s✲ tõ❡s tr❛❞✐❝✐♦♥❛✐s✳
❊♥✜♠✱ ❛t✉❛❧♠❡♥t❡ ❜✉s❝❛✲s❡ ✉♠❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥sã♦ ❞♦ ♣❛ss❛❞♦✱ ❞♦ ♠✉♥❞♦ ❡ ❞❛ ✈✐❞❛✱ ✈❛❧♦r✐③❛♥❞♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❛ ♠❛t❡♠át✐❝❛✱ ♣❡❧❛ s✉❛ r❡❧❡✈â♥❝✐❛ s♦❝✐❛❧ ❡ ❛❝❛❞ê♠✐❝❛✱ ❡ s❡✉ ❞♦♠í♥✐♦ s❡r ❝♦♥s✐❞❡r❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ ❡ ❞❡ ❣r❛♥❞❡ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡ à t❡❝♥♦❧♦❣✐❛✳
✷✵ ■♥tr♦❞✉çã♦
✷ ❯♠ ❜r❡✈❡ ❍✐stór✐❝♦
✷✳✶ ▼❡s♦♣♦tâ♠✐❛ ✭❇❛❜✐❧ô♥✐♦s✮
❈♦♥s✐❞❡r❛❞❛ ♦ ❜❡rç♦ ❞❛ ❝✐✈✐❧✐③❛çã♦✱ ❛ ▼❡s♦♣♦tâ♠✐❛ ❝♦♠♣r❡❡♥❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣♦✈♦s q✉❡ ✈✐✈❡r❛♠ ♥♦s ✈❛❧❡s ❞♦s r✐♦s ❚✐❣r❡s ❡ ❊✉❢r❛t❡s✱ ♥♦ q✉❡ ❤♦❥❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ t❡rr✐tór✐♦ ❞♦ ■r❛q✉❡ ❡ r❡❣✐õ❡s ❛❞❥❛❝❡♥t❡s✱ ❋✐❣✉r❛✶ ✷✳✶✳ ❉❡♥tr❡ ♦s r❡✐♥♦s ♠❡s♦♣♦tâ♠✐❝♦s✱
❇♦②❡r ✭✶✾✼✹✮✱ ❊✈❡s ✭✷✵✶✶✮✱ ❘♦q✉❡ ✭✷✵✶✷✮ ❡ ▼♦❧ ✭✷✵✶✸✮ ❞❡st❛❝❛♠ ❛q✉❡❧❡ ❜❛s❡❛❞♦ ♥❛ ❝✐❞❛❞❡ ❞❡ ❇❛❜✐❧ô♥✐❛✱ ♣♦r ✐ss♦✱ ❤á ❛ ❝♦♥✈❡♥çã♦ ❞❡ s❡ r❡❢❡r✐r ❝♦♠♦ ❜❛❜✐❧ô♥✐❝❛ à ❝✐✈✐❧✐③❛çã♦ ♠❡s♦♣♦tâ♠✐❝❛✱ ❛♦ ♠❡♥♦s ♥♦ ♣❡rí♦❞♦ ❞❡ ✷✵✵✵ ❛✳❈✳ ❛ ✻✵✵ ❛✳❈✳✳
❋✐❣✉r❛ ✷✳✶✿ ▼❛♣❛ ❞❛ ❆♥t✐❣❛ ❇❛❜✐❧ô♥✐❛
❆ss✐♠ ❝♦♠♦ ♦s ❡❣í♣❝✐♦s✱ ❛ ❣❡♦♠❡tr✐❛ ❜❛❜✐❧ô♥✐❝❛ ❡♠ s❡✉s ♣r✐♠ór❞✐♦s ❡st❡✈❡ ✐♥t✐♠❛✲ ♠❡♥t❡ ❧✐❣❛❞❛ ❝♦♠ ❛ ♠❡♥s✉r❛çã♦ ♣rát✐❝❛ ♥❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞♦ ❞✐❛ ❛ ❞✐❛✳
▼♦❧ ✭✷✵✶✸✱ ♣✳ ✶✹✮ ❞❡st❛❝❛ q✉❡ ❛ ♠❛♥❡✐r❛ ❞❡ ❝♦♥t❛r ♦s ❞❡❞♦s ❢♦✐ ❞❡t❡r♠✐♥❛♥t❡ ♥❛
✶❋✐❣✉r❛s✿ ❚♦❞❛s ❛s ✐♠❛❣❡♥s ❞❡st❡ ❞♦❝✉♠❡♥t♦ sã♦ ❞❡ ❞♦♠í♥✐♦ ♣ú❜❧✐❝♦ ❛❞q✉❡r✐❞❛s ❡♠ r❡♣♦s✐tór✐♦s
❝♦♠♦ ❤tt♣✿✴✴✇✐❦✐♠❡❞✐❛✳♦r❣ ♦✉ ❤tt♣s✿✴✴♣✐①❛❜❛②✳❝♦♠✳ ❆❧❣✉♠❛s ✜❣✉r❛s ❢♦r❛♠ ❝r✐❛❞❛s ❝♦♠ s♦❢t✇❛r❡ ❞❡ ❣❡♦♠❡tr✐❛ ❞✐♥â♠✐❝❛ ♣❡❧♦ ♣ró♣r✐♦ ❛✉t♦r✳
✷✷ ❯♠ ❜r❡✈❡ ❍✐stór✐❝♦
❡s❝♦❧❤❛ ❞❛ ❜❛s❡ ♥✉♠ér✐❝❛ ❛❞♦t❛❞❛ ♣♦r ❡st❛s ❝✐✈✐❧✐③❛çã♦✳ ❆ ❜❛s❡ ✶✵ ✉s❛❞❛ ♥♦ s✐st❡♠❛ ❞❡ ♥✉♠❡r❛çã♦✱ q✉❡ ❤♦❥❡ ✉t✐❧✐③❛♠♦s ❡ q✉❡ ❡r❛ ❡♠♣r❡❣❛❞❛ ♣❡❧♦s ❡❣í♣❝✐♦s ❛♥t✐❣♦s✱ t❡r✐❛ ♦r✐❣❡♠ ♥♦s ✶✵ ❞❡❞♦s ❞❛s ♠ã♦s✳ ❆ ❜❛s❡ ✷✵✱ ✉s❛❞❛ ♣❡❧♦s ♠❛✐❛s ♣ré✲❝♦❧♦♠❜✐❛♥♦s✱ t❡r✐❛ s✐❞♦ ♠♦t✐✈❛❞❛ ♣❡❧♦ ✉s♦ ❞♦s ✶✵ ❞❡❞♦s ❞❛s ♠ã♦s ❡ ❞♦s ✶✵ ❞❡❞♦s ❞♦s ♣és✳
❆ ❝♦♥t❛❣❡♠ ❡♠ ❞ú③✐❛s✱ ♦✉ s❡❥❛✱ ♥❛ ❜❛s❡ ✶✷✱ ♣♦❞❡ t❛♠❜é♠ s❡r ✈✐st❛ ❝♦♠♦ ❞❡ ♥❛t✉r❡③❛ ❛♥tr♦♣♦♠ór✜❝❛✿ ❡♠ ✉♠❛ ♠ã♦✱ ♦ ❞❡❞♦ ♣♦❧❡❣❛r é ✉s❛❞♦ ♣❛r❛ ❝♦♥t❛r ❛s ✶✷ ❢❛❧❛♥❣❡s ❞♦s ♦✉tr♦s q✉❛tr♦ ❞❡❞♦s✳ ❆ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❝♦♥t❛r ✶✷ ✉♥✐❞❛❞❡s ❡♠ ✉♠❛ ❞❛s ♠ã♦s✱ ❝♦♥❥✉❣❛❞❛ ❝♦♠ ♦s ❝✐♥❝♦ ❞❡❞♦s ❞❛ ♦✉tr❛ ♠ã♦✱ ♣♦❞❡ ❡st❛r ♥❛ ♦r✐❣❡♠ ❞❡ s✐st❡♠❛s ❞❡ ❝♦♥t❛❣❡♠ ♥❛ ❜❛s❡ ✻✵✱ ❝♦♠♦ ❡r❛ ♦ s✐st❡♠❛ ❜❛❜✐❧ô♥✐❝♦ ❡ ✐❧✉str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✷✳
❋✐❣✉r❛ ✷✳✷✿ ❈♦♥t❛❣❡♠ ❇❛❜✐❧ô♥✐❝❛
❖s ❛rq✉❡ó❧♦❣♦s ❥á ❞❡s❝♦❜r✐r❛♠ ♠❛✐s ❞❡ ♠❡✐♦ ♠✐❧❤ã♦ ❞❡ tá❜✉❧❛s✷ ❞❡ ❛r❣✐❧❛ ❝♦♠ ❡s❝r✐✲
t❛s ❝✉♥❡✐❢♦r♠❡s✱ ♠❛s s❡❣✉♥❞♦ ❇♦②❡r ✭✶✾✼✹✱ ♣✳ ✷✵✮ ❡ ❘♦q✉❡ ✭✷✵✶✷✱ ♣✳ ✹✾✮ ❛ ♠❛✐♦r✐❛ ❞❛s tá❜✉❧❛s ❡♥❝♦♥tr❛❞❛s sã♦ ❞♦ ♣❡rí♦❞♦ ❡♠ t♦r♥♦ ❞♦ ❛♥♦ ✶✼✵✵ ❛✳❈✳✱ q✉❛♥❞♦ ❛ ♠❛t❡♠át✐❝❛ ❥á ❡r❛ ❜❛st❛♥t❡ ❞❡s❡♥✈♦❧✈✐❞❛✳ ❙❡❣✉♥❞♦ ❊✈❡s ✭✷✵✶✶ ♣✳ ✻✷✮✱ ♥❡ss❡ ♣❡rí♦❞♦ ❛ ❝✐✈✐❧✐③❛çã♦ ❜❛❜✐❧ô♥✐❝❛ ❥á ❡st❛✈❛ ❢❛♠✐❧✐❛r✐③❛❞❛ ❝♦♠ ❛s r❡❣r❛s ❣❡r❛✐s ❞❛ ár❡❛ ❞❡ ✜❣✉r❛s ❝♦♠♦✿ r❡tâ♥✲ ❣✉❧♦✱ tr✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦✱ tr✐â♥❣✉❧♦ ✐sós❝❡❧❡s ✭❡ t❛❧✈❡③ tr✐â♥❣✉❧♦ ❣❡♥ér✐❝♦✮ ❡ tr❛♣é③✐♦ r❡tâ♥❣✉❧♦✳
❈♦♥s✐❞❡r❛✈❛✲s❡ ❛ ♠❡❞✐❞❛ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ✉♠❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ❝♦♠♦ ♦ tr✐♣❧♦ ❞❡ s❡✉ ❞✐â♠❡tr♦ ✭r❡❣r❛ ❝♦rr❡t❛ ♣❛r❛ π = 3✮✳ ❖s ❜❛❜✐❧ô♥✐♦s t❛♠❜é♠ t✐♥❤❛♠ ❝♦♥❤❡❝✐♠❡♥t♦
❞❡ q✉❡ ♦s ❧❛❞♦s ❝♦rr❡s♣♦♥❞❡♥t❡s ❞❡ ❞♦✐s tr✐â♥❣✉❧♦s r❡tâ♥❣✉❧♦s s❡♠❡❧❤❛♥t❡s sã♦ ♣r♦✲ ♣♦r❝✐♦♥❛✐s✱ q✉❡ ❛ ♣❡r♣❡♥❞✐❝✉❧❛r ❜❛✐①❛❞❛ ❞♦ ✈ért✐❝❡ ❞❡ ✉♠ tr✐â♥❣✉❧♦ ✐sós❝❡❧❡s ❡♠ q✉❡ ✐♥❝✐❞❡♠ ♦s ❧❛❞♦s ❝♦♥❣r✉❡♥t❡s ❞✐✈✐❞❡ ❛♦ ♠❡✐♦ ❛ ❜❛s❡ ❡ q✉❡ ✉♠ â♥❣✉❧♦ ✐♥s❝r✐t♦ ♥✉♠❛ s❡♠✐❝✐r❝✉♥❢❡rê♥❝✐❛ é r❡t♦✳
❇♦②❡r ✭✶✾✼✹✱ ♣✳ ✷✼✮ ❡ ❊✈❡s ✭✷✵✶✶✱ ♣✳ ✻✹✮✱ ❝♦♥❝♦r❞❛♠ q✉❡ ♦s ❜❛❜✐❧ô♥✐♦s ❝♦♥❤❡❝✐❛♠ ♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✸ ❡ ❛❜♦r❞❛✈❛♠✲♦ ❞❡ ♠❛♥❡✐r❛ ❛❧❣é❜r✐❝❛✱ ❝♦♠♦ ❡✈✐❞❡♥❝✐❛ ❛ tá✲
❜✉❧❛ P❧✐♠♣t♦♥ ✸✷✷✱ ❝❛t❛❧♦❣❛❞❛ s♦❜ ♦ ♥ú♠❡r♦ ✸✷✷ ♣❡❧❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❈♦❧ú♠❜✐❛✱ ❡ss❡
✷❚á❜✉❧❛s ❞❡ ❛r❣✐❧❛ ❝♦♠ ❡s❝r✐t❛ ❝✉♥❡✐❢♦r♠❡✿ ❖s ♠✉s❡✉s ❞❡ P❛r✐s✱ ❇❡r❧✐♠ ❡ ▲♦♥❞r❡s ❡ ❛s ❯♥✐✈❡rs✐❞❛❞❡s
❞❡ ❨❛❧❡✱ ❈♦❧ú♠❜✐❛ ❡ P❡♥s✐❧✈â♥✐❛ tê♠ ❡①❝❡❧❡♥t❡s ❝♦❧❡çõ❡s ❞❡ss❛s tá❜✉❧❛s✳ ❆❧❣✉♥s ❝❛tá❧♦❣♦s sã♦ ♦♥❧✐♥❡ ❝♦♠♦ ♦ ❞✐s♣♦♥✐❜✐❧✐③❛❞♦ ❡♠ ❤tt♣✿✴✴❝❝♣✳②❛❧❡✳❡❞✉✴❝❛t❛❧♦❣✉❡✴
✸❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✿ ❊♠ t♦❞♦ tr✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦✱ ❛ ♠❡❞✐❞❛ ❞♦ q✉❛❞r❛❞♦ ❞❛ ❤✐♣♦t❡♥✉s❛ é ✐❣✉❛❧
▼❡s♦♣♦tâ♠✐❛ ✭❇❛❜✐❧ô♥✐♦s✮ ✷✸
❛rt❡❢❛t♦ ❞❡ ❜❛rr♦ trás ❡ss❛ r❡❧❛çã♦ ❣r❛✈❛❞❛✱ ❋✐❣✉r❛ ✷✳✸✳
❋✐❣✉r❛ ✷✳✸✿ ❚á❜✉❧❛ P❧✐♠♣t♦♥ ✸✷✷
❆ tá❜✉❧❛ ❢♦✐ ❡s❝r✐t❛ ♥♦ ♣❡rí♦❞♦ ❇❛❜✐❧ô♥✐❝♦ ❆♥t✐❣♦ ✭❛♣r♦①✐♠❛❞❛♠❡♥t❡ ❡♥tr❡ ✶✾✵✵ ❡ ✶✻✵✵ ❛✳❈✳✮✳ ❈♦♥té♠ três ❝♦❧✉♥❛s ♣r❛t✐❝❛♠❡♥t❡ ❝♦♠♣❧❡t❛s ❞❡ ❝❛r❛❝t❡r❡s q✉❡✱ ♣♦r ❝♦♥✈❡✲ ♥✐ê♥❝✐❛✱ ❢♦r❛♠ ❝♦♠♣❧❡t❛❞❛s ❡ r❡♣r❡s❡♥t❛❞❛s ♥❛ ❚❛❜❡❧❛ ✷✳✶ ❡♠ ♥♦ss❛ ♥♦t❛çã♦ ❞❡❝✐♠❛❧✳
❛ ❜ ❝ ✉ ✈
✶✷✵ ✶✶✾ ✶✻✾ ✶✷ ✺
✸✹✺✻ ✸✸✻✼ ✹✽✷✺ ✻✹ ✷✼ ✹✽✵✵ ✹✻✵✶ ✻✻✹✾ ✼✺ ✸✷ ✶✸✺✵✵ ✶✷✼✵✾ ✶✽✺✹✶ ✶✷✺ ✺✹
✼✷ ✻✺ ✾✼ ✾ ✹
✸✻✵ ✸✶✾ ✹✽✶ ✷✵ ✾
✷✼✵✵ ✷✷✾✶ ✸✺✹✶ ✺✹ ✷✺
✾✻✵ ✼✾✾ ✶✷✹✾ ✸✷ ✶✺
✻✵✵ ✹✽✶ ✼✻✾ ✷✺ ✶✷
✻✹✽✵ ✹✾✻✶ ✽✶✻✶ ✽✶ ✹✵
✻✵ ✹✺ ✼✺ ✷ ✶
✷✹✵✵ ✶✻✼✾ ✷✾✷✾ ✹✽ ✷✺
✷✹✵ ✶✻✶ ✷✽✾ ✶✺ ✽
✷✼✵✵ ✶✼✼✶ ✸✷✷✾ ✺✵ ✷✼
✾✵ ✺✻ ✶✵✻ ✾ ✺
✷✹ ❯♠ ❜r❡✈❡ ❍✐stór✐❝♦
❍á ✉♠❛ q✉❛rt❛✱ ♠❛s ✐♥❝♦♠♣❧❡t❛✱ ❝♦❧✉♥❛ ❞❡ ❝❛r❛❝t❡r❡s ❛♦ ❧♦♥❣♦ ❞♦ ❧❛❞♦ q✉❡❜r❛❞♦ q✉❡ ❝♦♠♣❧❡t❛♠♦s✹✳ ❆ ❣r❛♥❞❡ ♠❛✐♦r✐❛ ❞❡ss❡s t❡r♥♦s✱ ❡①❝❡t♦ ♦s ❞❛s ❧✐♥❤❛s ✶✶ ❡ ✶✺✱ sã♦
♣r✐♠✐t✐✈♦s✺✳ ❆ss✐♠ ✭✸✱✹✱✺✮ é ✉♠ t❡r♥♦ ♣✐t❛❣ór✐❝♦ ♣r✐♠✐t✐✈♦✱ ❛♦ ♣❛ss♦ q✉❡ ✭✻✱✽✱✶✵✮ ♥ã♦
é✳
6 = 3×2✱ 8 = 4×2 ❡ 10 = 5×2 ⑤ ❢❛t♦r ❝♦♠✉♠ é ♦ ✷
◆❛ t❛❜❡❧❛ ✷✳✶ ❤á ✉♠❛ ❧✐st❛ ❞♦s ✈❛❧♦r❡s ❞♦s ♣❛râ♠❡tr♦s u ❡ v q✉❡ ❧❡✈❛♠ ❛ ❡ss❡s t❡r♥♦s ♣✐t❛❣ór✐❝♦s✳ ❍✐st♦r✐❛❞♦r❡s ❝♦♠♦ ❊✈❡s✱ ❢✉♥❞❛♠❡♥t❛r❛♠ s✉❛s ♣❡sq✉✐s❛s ❛❧✐♥❤❛❞❛s ❛s ✐❞❡✐❛s ❞❡ ❛✉t♦r✐❞❛❞❡s ❝♦♠♦ ❖tt♦ ◆❡✉❣❡❜❛✉❡r✻✱ s❡♥❞♦ ❛ss✐♠✱ ❛❝r❡❞✐t❛✈❛♠ q✉❡ ♦s
❜❛❜✐❧ô♥✐♦s ❞❡ss❡ r❡♠♦t♦ ♣❡rí♦❞♦ t✐♥❤❛♠ ❝♦♥s❝✐ê♥❝✐❛ ❞❛ r❡♣r❡s❡♥t❛çã♦ ♣❛r❛♠étr✐❝❛ ❣❡r❛❧ ❞♦s t❡r♥♦s ♣✐t❛❣ór✐❝♦s ♣r✐♠✐t✐✈♦s ❝♦♠♦ ❢♦✐ ❞❛❞❛ ❛♥t❡r✐♦r♠❡♥t❡✳
❯♠ ❞♦s ❣r❛♥❞❡s ❢❡✐t♦s ♠❛t❡♠át✐❝♦s ❞♦s ❣r❡❣♦s✱ ♣♦st❡r✐♦r ♠✉✐t♦s sé❝✉❧♦s à tá❜✉❧❛ P❧✐♠♣t♦♥ ✸✷✷✱ ❢♦✐ ♠♦str❛r q✉❡ t♦❞♦s ♦s t❡r♥♦s ♣✐t❛❣ór✐❝♦s ♣r✐♠✐t✐✈♦s(a, b, c)sã♦ ❞❛❞♦s
♣❛r❛♠❡tr✐❝❛♠❡♥t❡ ♣♦r✿
a = 2uv ✱ b=u2−v2 ❡ c=u2+v2✳
❊♥tr❡t❛♥t♦✱ tr❛❜❛❧❤♦s ✐♥♦✈❛❞♦r❡s ❝♦♠♦ ♦s ❞❡ ❘♦❜s♦♥✼✭✷✵✵✶✮ ❝♦♥s✐❞❡r❛♠ ❡✈✐❞ê♥❝✐❛s
t❡①t✉❛✐s✱ ♥ã♦ só ♠❛t❡♠át✐❝❛s✱ ♠❛s ❞❡ ♦✉tr❛s ♠❛♥✐❢❡st❛çõ❡s q✉❡ ♣♦ss❛♠ ❛❥✉❞❛r ♥❛ ❝♦♠♣r❡❡♥sã♦ ❞❛ é♣♦❝❛ ❡st✉❞❛❞❛✱ tr❛♥s❢♦r♠❛r❛♠ ❞❡ ♠♦❞♦ ✐rr❡✈❡rsí✈❡❧ ❛ ✐♠❛❣❡♠ ❞❛ ♠❛t❡♠át✐❝❛ ♠❡s♦♣♦tâ♠✐❝❛✱ ❛♥t❡s ❡st✉❞❛❞❛ ♣♦r ♠❡✐♦ ❞❡ r❡❝♦♥str✉çõ❡s ❛♥❛❝rô♥✐❝❛s✳
❈♦♠♣❛rt✐❧❤❛♥❞♦ ❞❡ss❛ ♥♦✈❛ ❛❜♦r❞❛❣❡♠✱ ❘♦q✉❡ ✭✷✵✶✷✮ s✉❣❡r❡ q✉❡ ❛s tá❜✉❧❛s ♣♦✲ ❞❡♠ ♦r❛ s❡r✈✐r ❝♦♠♦ ✧t❛❜✉❛❞❛s✧✱ ❝♦♥t❡♥❞♦ r❡s✉❧t❛❞♦s ❞❡ ♦♣❡r❛çõ❡s✱ ❡ ♦✉tr❛s tá❜✉❧❛s ❝♦♥t❡♥❞♦ ♣r♦❝❡❞✐♠❡♥t♦s✱ ❝♦♠♦ s❡ ❢♦ss❡♠ ❡①❡r❝í❝✐♦s r❡s♦❧✈✐❞♦s✳
❆ss✐♠✱ ♦s ♣r♦❜❧❡♠❛s ❛♥t❡r✐♦r♠❡♥t❡ ❡♥❝❛r❛❞♦s ❝♦♠♦ ❛r✐t♠ét✐❝♦s ♣❡❧♦s ❤✐st♦r✐❛❞♦r❡s ❛♥t✐❣♦s✱ ❛❣♦r❛ ♣♦❞❡♠ s❡r ✐♥t❡r♣r❡t❛❞♦s ❝♦♠♦ ♣r♦❜❧❡♠❛s ❣❡♦♠étr✐❝♦s✳
✷✳✷ ❊❣í♣❝✐♦s
❆ ❛♥t✐❣❛ ❝✐✈✐❧✐③❛çã♦ ❡❣í♣❝✐❛ ❞❡s❡♥✈♦❧✈❡✉✲s❡ ♥♦ ♥♦r❞❡st❡ ❛❢r✐❝❛♥♦ às ♠❛r❣❡♥s ❞♦ r✐♦ ◆✐❧♦✱ ♠✐❧❤❛r❡s ❞❡ ❛♥♦s ❛♥t❡s ❞❡ ❈r✐st♦✳ ❈♦♠♦ ❛ r❡❣✐ã♦ é ❢♦r♠❛❞❛ ♣❡❧♦ ❞❡s❡rt♦ ❙❛❛r❛✱ ♦ ✈❛❧❡ ❞♦ r✐♦ ❢♦✐ ❞❡ ❡①tr❡♠❛ ✐♠♣♦rtâ♥❝✐❛ ♣❛r❛ ❛ ❛❣r✐❝✉❧t✉r❛ ❡ ❛ ❡❝♦♥♦♠✐❛ ❞❡ss❡ ♣♦✈♦✳ ❙❡❣✉♥❞♦ r❡❧❛t♦s tr❛❞✐❝✐♦♥❛✐s✱ ♦ ❤✐st♦r✐❛❞♦r ❣r❡❣♦ ❍❡ró❞♦t♦ ✭✹✽✹✲✹✷✵ ❛✳❈✳✮ ❛tr✐❜✉✐✉ ❛
✹❚❛❜❡❧❛✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ P❧✐♠♣t♦♥ ✸✷✷ ❝♦♠ ❞❛❞♦s ❡♠ r❡♣r❡s❡♥t❛çã♦ ❞❡❝✐♠❛❧ ❡ ❝♦♠♣❧❡t❛❞♦s ♣❛r❛
❛♥á❧✐s❡ ❡ ❝♦♠♣❛r❛çã♦✳ ❖❜s❡r✈❛♠♦s q✉❡ ♥♦ ♦r✐❣✐♥❛❧ ❤á q✉❛tr♦ ❡rr♦s ♥❛ ❡①✐❜✐çã♦ ❞♦s t❡r♥♦s ♥❛s ❧✐♥❤❛s ✷✱ ✾✱ ✶✸ ❡ ✶✺✱ ♣♦ss✐✈❡❧♠❡♥t❡ ❣❡r❛❞♦s ♥❛ tr❛♥s❝r✐çã♦✳
✺❚❡r♥♦s ♣r✐♠✐t✐✈♦s✿ ❙❡ ♦ ú♥✐❝♦ ❢❛t♦r ✐♥t❡✐r♦ ♣♦s✐t✐✈♦ ❝♦♠✉♠ ❛♦s ❡❧❡♠❡♥t♦s ❞❡ ✉♠ t❡r♥♦ ♣✐t❛❣ór✐❝♦
é ❛ ✉♥✐❞❛❞❡✱ ❡♥tã♦ ❡ss❡ t❡r♥♦ s❡ ❞✐③ ♣r✐♠✐t✐✈♦✳
✻❖tt♦ ◆❡✉❣❡❜❛✉❡r✿ ❘❡♥♦♠❛❞♦ ❤✐st♦r✐❛❞♦r ♠❛t❡♠át✐❝♦ q✉❡ ♣✉❜❧✐❝♦✉ ♥♦s ❛♥♦s ✶✾✸✵ ❡ ✹✵ ❛s ♣r✐♠❡✐r❛s
tr❛❞✉çõ❡s✳
✼❉r❛✳ ❊❧❡❛♥♦r ❘♦❜s♦♥ é ✉♠❛ ❛rq✉❡♦❧♦❣✐st❛ ❡s♣❡❝✐❛❧✐③❛❞❛ ❡♠ ❤✐stór✐❛ ❞❛ ❝✐ê♥❝✐❛✳ ❊❧❛ é ❛ ❛✉t♦r❛ ♦✉
❊❣í♣❝✐♦s ✷✺
♦r✐❣❡♠ ❞❛ ❣❡♦♠❡tr✐❛ ❡❣í♣❝✐❛ à ♥❡❝❡ss✐❞❛❞❡ ❞❡✱ ❛♣ós ❝❛❞❛ ✐♥✉♥❞❛çã♦ ❞♦ r✐♦ ◆✐❧♦✱ r❡❞✐s✲ tr✐❜✉✐r ❝❛♠♣♦s ❝✉❧t✐✈á✈❡✐s ❛ s❡✉s ♣r♦♣r✐❡tár✐♦s ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ ❞✐♠✐♥✉✐r ❛s t❛①❛s ❞❡ ✐♠♣♦st♦s ❛♦s ♣r❡❥✉❞✐❝❛❞♦s✱ ❝♦♥❢♦r♠❡ ❘♦q✉❡ ✭✷✵✶✷✱ ♣✳ ✾✷✮✳
❆ ♠❛✐♦r✐❛ ❞♦s ❛✉t♦r❡s ❝♦♠♦ ❇♦②❡r ✭✶✾✼✹✮✱ ❊✈❡s ✭✷✵✶✶✮ ❡ ♦✉tr♦s ❛♥t❡r✐♦r❡s ❛ ❡st❡s✱ ♣r♦♣õ❡ q✉❡ ❛ ♠❛t❡♠át✐❝❛ ❡❣í♣❝✐❛ ❛♥t✐❣❛ s❡ tr❛t❛✈❛ ❞❡ ✉♠❛ ♠❛t❡♠át✐❝❛ ❡ss❡♥❝✐❛❧♠❡♥t❡ ♣rát✐❝❛✱ ❜❛s❡❛❞❛ ❡♠ ♠ét♦❞♦s ❡♠♣ír✐❝♦s ❞❡ t❡♥t❛t✐✈❛ ❡ ❡rr♦ ✭♠ét♦❞♦ ❞❛ ❢❛❧s❛✲♣♦s✐çã♦✽✮✳
P♦ré♠✱ ♥✉♠❛ ❛♥á❧✐s❡ ♠❛✐s ❛♣r♦❢✉♥❞❛❞❛✱ s❡❣✉♥❞♦ ❘♦q✉❡ ✭✷✵✶✷ ♣✳ ✽✶✮✱ t❛❧ ❡♥t❡♥❞✐♠❡♥t♦ ♣♦❞❡ r❡✈❡❧❛r ✉♠ t✐♣♦ ❞❡ ❛♥❛❝r♦♥✐s♠♦✳ ❆ ❜✉s❝❛ ❞❡ ❣❡♥❡r❛❧✐❞❛❞❡ ❡ ✉♥✐✈❡rs❛❧✐❞❛❞❡ q✉❡ ❝❛r❛❝t❡r✐③❛ ❛ ❝✐❡♥t✐✜❝✐❞❛❞❡ ❞❛s ♥♦ss❛s ♣rát✐❝❛s ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛ ♥❛ ♠❛t❡♠át✐❝❛ ❡❣í♣❝✐❛✱ ♠❛s ❞❡ ✉♠ ♠♦❞♦ ❞✐st✐♥t♦✳
❆té q✉❡ s❡ ❞❡❝✐❢r❛ss❡♠ t❛♥t❛s tá❜✉❧❛s ♠❛t❡♠át✐❝❛s ❜❛❜✐❧ô♥✐❝❛s✱ ♦ ❊❣✐t♦ ❢♦✐ ♣♦r ♠✉✐t♦ t❡♠♣♦ ♦ ♠❛✐s r✐❝♦ ❝❛♠♣♦ ❞❡ ♣❡sq✉✐s❛s ❤✐stór✐❝❛s s♦❜r❡ ❛ ❆♥t✐❣✉✐❞❛❞❡ ❡ ❝♦♥s✐❞❡r❛❞♦ ❡rr♦♥❡❛♠❡♥t❡ ♠❛✐s ❞❡s❡♥✈♦❧✈✐❞♦ ♠❛t❡♠❛t✐❝❛♠❡♥t❡✳ ▼❛s ❛ ♠❛t❡♠át✐❝❛ ♥♦ ❊❣✐t♦ ❛♥t✐❣♦ ♥✉♥❝❛ ❛❧❝❛♥ç♦✉ ♦ ♥í✈❡❧ ♦❜t✐❞♦ ♣❡❧❛ ♠❛t❡♠át✐❝❛ ❜❛❜✐❧ô♥✐❝❛✱ t❛❧✈❡③ ✐ss♦ s❡ ❞❡✈❛ ❛♦ ❢❛t♦ ❞❛ ❇❛❜✐❧ô♥✐❛ t❡r ❛❧❝❛♥ç❛❞♦ ♠❛✐♦r ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡❝♦♥ô♠✐❝♦✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ❊❣✐t♦ s❡ ♠❛♥t❡✈❡ ❡♠ s❡♠✐ ✐s♦❧❛♠❡♥t♦✱ s❡❣✉♥❞♦ ❊✈❡s ✭✷✵✶✶ ♣✳ ✻✼✮✳
❆s ❝♦♥str✉çõ❡s ♣❡r❡♥❡s ❞❡ t✉♠❜❛s ❡ t❡♠♣❧♦s✱ ❝♦♠ ♣❛r❡❞❡s ❣r❛✈❛❞❛s ❝♦♠ r✐❝❛s ✐♥s❝r✐✲ çõ❡s✱ ❡ ♦ ❝❧✐♠❛ s❡❝♦ ❞❛ r❡❣✐ã♦ ❢♦r❛♠ ❞❡t❡r♠✐♥❛♥t❡s ♥❛ ♣r❡s❡r✈❛çã♦ ❞❡ ♣❛♣✐r♦s✳ ▼✉✐t♦s ❞♦s r❡❣✐str♦s ♠❛t❡♠át✐❝♦s ❞❡ss❛ ❝✐✈✐❧✐③❛çã♦✱ s❡❣✉♥❞♦ ▼♦❧ ✭✷✵✶✸✮✱ ❝❤❡❣❛r❛♠ ❛♦s ♥♦ss♦s ❞✐❛s ❡♠ ♣❛♣✐r♦s q✉❡ ❡r❛♠ ♣r♦❞✉③✐❞♦s ❛ ♣❛rt✐r ❞♦ ❝❛✉❧❡ ❞❛ ♣❧❛♥t❛ ❞❡ ♠❡s♠♦ ♥♦♠❡✳ ❖s ♣❛♣✐r♦s ❡r❛♠ ❣r❛❢❛❞♦s ♣♦r ❡s❝r✐❜❛s ❡♠ ❡s❝r✐t❛ ❤✐❡rát✐❝❛ ✭❢♦r♠❛t♦ ❝✉rs✐✈♦ ❡ ✉s❛❞❛ ♥♦r✲ ♠❛❧♠❡♥t❡ ♣❛r❛ ✜♥s ❝♦♠❡r❝✐❛✐s✮✱ ✉♠❛ s✐♠♣❧✐✜❝❛çã♦ ❞❛ ❡s❝r✐t❛ ❤✐❡r♦❣❧í✜❝❛ ♠❛✐s ❛❞❡q✉❛❞❛ ❛ ❡s❝r✐t❛ ❝♦rr❡♥t❡✳ ❆♠❜❛s ❡r❛♠ ❝♦♠♣♦st❛s ❞❡ sí♠❜♦❧♦s✱ ♣♦ré♠ ❛ ❡s❝r✐t❛ ❤✐❡r♦❣❧í✜❝❛ t✐♥❤❛ ❝❛rát❡r ♣✐❝tór✐❝♦ ❡ ❡r❛ ♠❛✐s ✉s❛❞❛ ❡♠ ♠♦♥✉♠❡♥t♦s✱ ❋✐❣✉r❛ ✷✳✹✳
❋✐❣✉r❛ ✷✳✹✿ ❍✐❡r♦❣❧í✜❝♦s
❇♦②❡r ✭✶✾✼✹✮ ❡ ❊✈❡s ✭✷✵✶✶✮ ❞❡st❛❝❛♠ ❛❧❣✉♠❛s ❣r❛♥❞❡s ❢♦♥t❡s ❞❡ ✐♥❢♦r♠❛çõ❡s q✉❡
✽▼ét♦❞♦ ❞❛ ❢❛❧s❛✲♣♦s✐çã♦ é ✉♠ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ✉s❛❞♦ ♣❛r❛ r❡s♦❧✈❡r ❡q✉❛çõ❡s ❧✐♥❡❛r❡s✱ ♣❛rt✐♥❞♦
✷✻ ❯♠ ❜r❡✈❡ ❍✐stór✐❝♦
♣♦ss✐❜✐❧✐t❛r❛♠ ❛ ❝♦♠♣r❡❡♥sã♦ ❞❛ ♠❛t❡♠át✐❝❛ ❡❣í♣❝✐❛ ❛♥t✐❣❛✱ ❛ P❡❞r❛ ❞❛ ❘♦s❡t❛✱ ♦ P❛♣✐r♦ ❞❡ ❈❛✐r♦✱ ♦ P❛♣✐r♦ ❞❡ ▼♦s❝♦✉ ❡ ♦ P❛♣✐r♦ ❞❡ ❘❤✐♥❞✾✳
❊♠ ✶✼✾✾✱ ❞✉r❛♥t❡ ❛ ❝❛♠♣❛♥❤❛ ❞❡ ◆❛♣♦❧❡ã♦ ❛♦ ❊❣✐t♦✱ ❡♥❣❡♥❤❡✐r♦s ❢r❛♥❝❡s❡s ❡♥❝♦♥✲ tr❛r❛♠ ❡♠ ❘♦s❡t❛✶✵ ✉♠ ❢r❛❣♠❡♥t♦✱ ❝♦♥❤❡❝✐❞♦ ❤♦❥❡ ❝♦♠♦ ❛ P❡❞r❛ ❞❛ ❘♦s❡t❛✱ q✉❡ ✐r✐❛
♣r♦♣✐❝✐❛r ❛ ❞❡❝✐❢r❛çã♦ ❞♦s ❝❛r❛❝t❡r❡s ❤✐❡r♦❣❧í✜❝♦s ❡ ❞❡♠ót✐❝♦s✳ ❊ss❛ ♣❡❞r❛✱ q✉❡ ♠❡❞❡ três ♣és ❡ s❡t❡ ♣♦❧❡❣❛❞❛s ✭✶✵✾✱✷ ❝♠✮ ♣♦r ❞♦✐s ♣és ❡ s❡✐s ♣♦❧❡❣❛❞❛s ✭✼✻✱✷ ❝♠✮✱ ❡♥❝♦♥tr❛✲ s❡ ❡①♣♦st❛ ♥♦ ▼✉s❡✉ ❇r✐tâ♥✐❝♦ ❡ ❝♦♥té♠ ✐♥s❝r✐çõ❡s ❝♦♠ ✉♠❛ ♠❡♥s❛❣❡♠ r❡♣❡t✐❞❛ ❡♠ ❤✐❡ró❣❧✐❢♦s ❡❣í♣❝✐♦s✱ ❡♠ ❝❛r❛❝t❡r❡s ❞❡♠ót✐❝♦s ❡❣í♣❝✐♦s ❡ ❡♠ ❣r❡❣♦✱ ❋✐❣✉r❛ ✷✳✺✳
❋✐❣✉r❛ ✷✳✺✿ P❡❞r❛ ❞❛ ❘♦s❡t❛
❏❡❛♥ ❋r❛♥ç♦✐s ❈❤❛♠♣♦❧❧✐♦♥✶✶ ✉t✐❧✐③♦✉ ♦ ❣r❡❣♦ ❝♦♠♦ ❝❤❛✈❡ ♣❛r❛ ❞❡❝✐❢r❛r ❛ ❡s❝r✐t❛
❡❣í♣❝✐❛ ❛♥t✐❣❛✳ ❖ s✐st❡♠❛ ❞❡ ♥✉♠❡r❛çã♦ ❢♦✐ ❢❛❝✐❧♠❡♥t❡ ❞❡❝✐❢r❛❞♦ ❡ ♦ ❝♦♥t❡①t♦ ♠❛✲ t❡♠át✐❝♦ ❛❣♦r❛ ♣♦❞❡r✐❛ s❡r ❝♦♥❢r♦♥t❛❞♦✳ ❖ ♣❛♣✐r♦ ❞❡ ▼♦s❝♦✉ ❝♦♥t❡♠ ✷✺ ♣r♦❜❧❡♠❛s ♠❛t❡♠át✐❝♦s ❡ ❢♦✐ ❛❞q✉✐r✐❞♦ ♣❡❧♦ ❝♦❧❡❝✐♦♥❛❞♦r r✉ss♦ ●♦❧❡♥✐s❝❤❡✈ ❡♠ ✶✽✾✸✱ ❤♦❥❡ s❡ ❡♥✲ ❝♦♥tr❛ ♥♦ ▼✉s❡✉ ❞❡ ❇❡❧❛s✲❆rt❡s ❞❡ ▼♦s❝♦✉✳
❊♥tã♦ ❡♠ ✶✽✺✽✱ ✉♠ ❛♥t✐q✉ár✐♦ ❡s❝♦❝ês✱ ❆❧❡①❛♥❞❡r ❍❡♥r② ❘❤✐♥❞✱ ❝♦♠♣r❛ ✉♠ ♣❛♣✐r♦ ❞❡ ✶✻✺✵ ❛✳❈✳ q✉❡ s❡ t♦r♥❛r✐❛ ✉♠❛ ❞❛s ❢♦♥t❡s ♣r✐♠ár✐❛s ♠❛✐s r✐❝❛ ❡♠ ♠❛t❡♠át✐❝❛ ❡❣í♣❝✐❛ ❛♥t✐❣❛✳ ❖ ❡s❝r✐❜❛ ❆❤♠❡s ❝♦♣✐♦✉ ❡ss❡ ❞♦❝✉♠❡♥t♦ q✉❡ ❞❡t❛❧❤❛ ❛ r❡s♦❧✉çã♦ ❞❡ ♦✐t❡♥t❛ ♣r♦❜❧❡♠❛s ♠❛t❡♠át✐❝♦s✳
✾❖ ♠✉s❡✉ ❇r✐tâ♥✐❝♦ ❞✐s♣♦♥✐❜✐❧✐③❛ ✐♠❛❣❡♥s ❞♦s ♣❛♣✐r♦s ❡♠ ❤tt♣✿✴✴✇✇✇✳❜r✐t✐s❤♠✉s❡✉♠✳♦r❣✴ ✶✵❘♦s❡t❛✿ P♦rt♦ ♥♦ ♠❛r ▼❡❞✐t❡rrâ♥❡♦✱ ❝✐❞❛❞❡ q✉❡ ❢♦✐ ❢✉♥❞❛❞❛ ♣♦r ✈♦❧t❛ ❞♦ ❛♥♦ ✽✵✵ ❞✳❈✳✳
✶✶❏❡❛♥✲❋r❛♥ç♦✐s ❈❤❛♠♣♦❧❧✐♦♥ ✭✶✼✾✵✲✶✽✸✷✮ ❢♦✐ ✉♠ ❧✐♥❣✉✐st❛✱ ❡❣✐♣tó❧♦❣♦ ❢r❛♥❝ês ❢❛♠♦s♦ ❞♦ sé❝✉❧♦ ❳■❳✱
❊❣í♣❝✐♦s ✷✼
❋✐❣✉r❛ ✷✳✻✿ P❛♣✐r♦ ❘❤✐♥❞
❙❡❣✉♥❞♦ ❊✈❡s ✭✷✵✶✶✱ ♣✳ ✽✻✮✱ ♦s ❛♥t✐❣♦s ❛❣r✐♠❡♥s♦r❡s ❡❣í♣❝✐♦s✱ ❞♦ t❡♠♣♦ ❞♦s ❢❛r❛ós✱ ❝♦♥str✉í❛♠ tr✐â♥❣✉❧♦s✶✷ ✭✸✱✹✱✺✮ ❝♦♠ ✉♠❛ ❝♦r❞❛ ❞✐✈✐❞✐❞❛ ❡♠ ✶✷ ♣❛rt❡s ✐❣✉❛✐s ♣♦r ✶✶
♥ós ♣❛r❛ ❞❡♠❛r❝❛r â♥❣✉❧♦s r❡t♦s✳ ❊ss❛ té❝♥✐❝❛ ❡r❛ ❡♠♣r❡❣❛❞❛ ♣❛r❛ ♠❡❞✐r ár❡❛s✱ t❡rr❛s ❢ért❡✐s✱ q✉❡ ♣♦r r❛③õ❡s ♦❜✈✐❛s ❡r❛♠ ♠✉✐t♦ ✈❛❧✐♦s❛s✳
❋✐❣✉r❛ ✷✳✼✿ ❈♦r❞❛ ❊❣í♣❝✐❛ ❝♦♠ ✶✶ ♥ós
❖ ❝❤❛♠❛❞♦ ♣❛♣✐r♦ ♠❛t❡♠át✐❝♦ ❈❛✐r♦ ❢♦✐ ❡♥❝♦♥tr❛❞♦ ❡♠ ✶✾✸✽ ❡ ✐♥✈❡st✐❣❛❞♦ ❡♠ ✶✾✻✷✳ ❖ ♣❛♣✐r♦✱ q✉❡ ❞❛t❛ ❞❡ ✸✵✵ ❛✳❈✳ ❛♣r♦①✐♠❛❞❛♠❡♥t❡✱ ❝♦♥té♠ ✹✵ ♣r♦❜❧❡♠❛s ❞❡ ♠❛t❡♠át✐❝❛✱ ✾ ❞♦s q✉❛✐s ❧✐❞❛♠ ❡①❝❧✉s✐✈❛♠❡♥t❡ ❝♦♠ ♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s ❡ ♠♦str❛ q✉❡ ♦s ❡❣í♣❝✐♦s ❞❡ss❛ é♣♦❝❛ ♥ã♦ só s❛❜✐❛♠ q✉❡ ♦ tr✐❛♥❣✉❧♦ ✸✱✹✱✺ ❡r❛ r❡tâ♥❣✉❧♦✱ ♠❛s q✉❡ t❛♠❜é♠ ❛❝♦♥t❡❝✐❛ ♦ ♠❡s♠♦ ♣❛r❛ ♦s tr✐â♥❣✉❧♦s ✺✱✶✷✱✶✸ ❡ ✷✵✱✷✶✱✷✾✳
✷✽ ❯♠ ❜r❡✈❡ ❍✐stór✐❝♦
❊①❡♠♣❧♦ ✷✳✶✳ ✭P❛♣✐r♦ ❈❛✐r♦✮ Pr♦❜❧❡♠❛ ♣r♦♣♦st♦ ♣♦r ❊✈❡s ✭✷✵✶✶✱ ♣✳ ✽✼✮ ❯♠❛ ❡s❝❛❞❛ ❞❡ ✶✵ ❝ú❜✐t♦s ❡stá ❝♦♠ s❡✉s ♣és ❛ ✻ ❝ú❜✐t♦s ❞❛ ♣❛r❡❞❡✳ ◗✉❡ ❞✐stâ♥❝✐❛ ❛ ❡s❝❛❞❛ ❛❧❝❛♥ç❛❄
❋✐❣✉r❛ ✷✳✽✿ Pr♦❜❧❡♠❛ ❞♦ P❛♣✐r♦ ❈❛✐r♦
✷✳✸ ❍✐♥❞✉s
❆ ❮♥❞✐❛ ❛♥t✐❣❛ q✉❛s❡ s❡♠♣r❡ s❡ ❝♦♠♣ôs ❞❡ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ♣❡q✉❡♥♦s ♣r✐♥❝✐✲ ♣❛❞♦s ❞❡s✉♥✐❞♦s ❡ s♦❢r❡✉ ❝♦♠ ♥✉♠❡r♦s❛s ✐♥✈❛sõ❡s✳ ❖s ✐♥❞✐❛♥♦s ❞♦s ♣r✐♠❡✐r♦s t❡♠♣♦s ❢♦r❛♠ ❡①t❡r♠✐♥❛❞♦s ♣♦r ✐♥✈❛s♦r❡s ♥ô♠❛❞❡s ♣♦r ✈♦❧t❛ ❞❡ ✶✺✵✵ ❛✳❈✳ ❡ ❛ r❡❣✐ã♦ ❢♦✐ t♦✲ ♠❛❞❛ ♣❡❧♦s ❛r✐❛♥♦s q✉❡ ❞❡s❡♥✈♦❧✈❡r❛♠ ♦ ❤✐♥❞✉ís♠♦✶✸✳ ❙♦♠❡♥t❡ r❡st♦s ❛rq✉❡♦❧ó❣✐❝♦s ❞❡
❛❧❣✉♠❛s ❝✐❞❛❞❡s ❡✈✐❞❡♥❝✐❛♠ ❛ ❡①✐stê♥❝✐❛ ❞❡ss❡ ♣♦✈♦ q✉❡ s❡ s✐t✉❛✈❛♠ ♣ró①✐♠♦ à r❡❣✐ã♦ ❞❡ ▼♦❤❡♥❥♦ ❉❛r♦ ❡ ❍❛r❛♣♣❛✱ s❡❣✉♥❞♦ ❊✈❡s ✭✷✵✶✶✱ ♣✳ ✷✸✻✮✳
❋✐❣✉r❛ ✷✳✾✿ ❮♥❞✐❛
✶✸❍✐♥❞✉ís♠♦ é ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❞❡ r❡❧✐❣✐ã♦✱ ✜❧♦s♦✜❛ ❡ ❡str✉t✉r❛ s♦❝✐❛❧ q✉❡ ✈❡✐♦ ❛ ❢♦r♠❛r ❛ ♣❡❞r❛
❍✐♥❞✉s ✷✾
P♦✉❝♦ s❡ s❛❜❡ s♦❜r❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ♠❛t❡♠át✐❝❛ ❤✐♥❞✉ ❛♥t✐❣❛✱ ❡♠ ✈✐rt✉❞❡ ❞❛ ❢❛❧t❛ ❞❡ r❡❣✐str♦s ❤✐stór✐❝♦s✳ ❆ ❢♦♥t❡ ❤✐stór✐❝❛ ♣r❡s❡r✈❛❞❛ ♠❛✐s ❛♥t✐❣❛ sã♦ ❛s r✉í♥❛s ❞❡ ✉♠❛ ❝✐❞❛❞❡ ❞❡ ✺✵✵✵ ❛♥♦s✱ ❡♥❝♦♥tr❛❞❛s ❡♠ ▼♦❤❡♥❥♦ ❉❛r♦✳ ❱❡stí❣✐♦s ✐♥❞✐❝❛♠ q✉❡ ❡ss❛ ❝✐✈✐❧✐③❛çã♦ ❝♦♥t❛✈❛ ❝♦♠ ✉♠❛ ♠❛t❡♠át✐❝❛ ❡ ✉♠❛ ❡♥❣❡♥❤❛r✐❛ tã♦ ❛✈❛♥ç❛❞❛ q✉❛♥t♦ q✉❛❧q✉❡r ♦✉tr❛ ❞♦ ❖r✐❡♥t❡ ❛♥t✐❣♦✱ ❊✈❡s ✭✷✵✶✶✱ ♣✳ ✷✹✼✮✳
❆s ♣r✐♠❡✐r❛s ❢♦♥t❡s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦ ❞❛ ❮♥❞✐❛ q✉❡ ❞✐s♣♦♠♦s sã♦ ♦s ❙✉❧❜❛s✉tr❛s✶✹ q✉❡ sã♦ ❞♦ ♣❡rí♦❞♦ ❡♥tr❡ ✽✵✵ ❛✳❈✳ ❡ ✺✵✵ ❛✳❈✳✳ ❆s ✜❣✉r❛s ❣❡♦♠étr✐❝❛s
✉t✐❧✐③❛❞❛s ♣❛r❛ ❝♦♥str✉✐r ❛❧t❛r❡s ❞❡✈❡r✐❛♠ s❡ ❛❥✉st❛r ❛ ❞✐♠❡♥sõ❡s ❡ ár❡❛s ❡s♣❡❝✐✜❝❛s✳ ❆ ♦r✐❡♥t❛çã♦✱ ❛s ❢♦r♠❛s ❡ ❛s ár❡❛s t✐♥❤❛♠ q✉❡ ♦❜❡❞❡❝❡r ✉♠❛ r✐❣♦r♦s❛ ❡①❛t✐❞ã♦✱ ❡ ❡ss❛ ❡①❛t✐❞ã♦ ❡r❛ tã♦ ✐♠♣♦rt❛♥t❡ q✉❛♥t♦ ❛ ♣r♦♥ú♥❝✐❛ ❝♦rr❡t❛ ❞♦s ❝â♥t✐❝♦s ❡ r❡❝✐t❛✐s ✈é❞✐❝♦s✱ ●❛s♣❛r ✭✷✵✶✺✮✳
❊♠ ✶✽✼✺✱ ●✳ ❚❤✐❜❛✉t tr❛❞✉③✐✉ ✉♠❛ ❣r❛♥❞❡ ♣❛rt❡ ❞♦s ❙✉❧❜❛s✉tr❛s ❡ ♠♦str♦✉ q✉❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦ ❞♦s s❛❝❡r❞♦t❡s ❤✐♥❞✉s ♥ã♦ ❡r❛ ♣❡q✉❡♥♦✱ ❡ ✐♥❝❧✉s✐✈❡✱ ❝♦♥❤❡✲ ❝✐❛♠ ♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✳ ❖s ❤✐♥❞✉s r❡❧❛❝✐♦♥❛✈❛♠ q✉❛❞r❛❞♦s ❝♦♥str✉í❞♦s s♦❜r❡ ❞✐❛❣♦♥❛❧ ❡ ❧❛❞♦s ❞❡ r❡tâ♥❣✉❧♦s✱ ❡ ❡①✐st❡ ♣❡❧♦ ♠❡♥♦s três ❡①♣❧✐❝❛çõ❡s ❞❡ ❝♦♠♦ ♦s ❤✐♥❞✉s ❞❡s❝♦❜r✐r❛♠ ♦ ❚❡♦r❡♠❛✱ ●❛s♣❛r ✭✷✵✶✺✮✳
✶♦ ❱❡rsã♦✿ ✭✈❡rsã♦ ❇❛✉❞❤❛②❛♥❛✮
❆ ❝♦r❞❛ q✉❡ s❡ ❡st✐❝❛ ♥♦ s❡♥t✐❞♦ ❞❛ ❞✐❛❣♦♥❛❧ ❞❡ ✉♠ q✉❛❞r❛❞♦ ♣r♦❞✉③ ✉♠❛ ár❡❛ ❞❡ t❛♠❛♥❤♦ ✐❣✉❛❧ ❛♦ ❞♦❜r♦ ❞❛ ár❡❛ ❞♦ q✉❛❞r❛❞♦ ♦r✐❣✐♥❛❧✳
❋✐❣✉r❛ ✷✳✶✵✿ ◗✉❛❞r❛❞♦ ✈❡rsã♦ ❇❛✉❞❤❛②❛♥❛ ✷❛ ❱❡rsã♦✿ ✭✈❡rsã♦ ❑❛t②❛②❛♥❛✮
❆ ❝♦r❞❛ ❡st✐❝❛❞❛ ❛♦ ❧♦♥❣♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❞✐❛❣♦♥❛❧ ❞❡ ✉♠ r❡tâ♥❣✉❧♦ ♣r♦❞✉③ ❛♠❜♦s ✉♠❛ ár❡❛ ✐❣✉❛❧ à ♦❜t✐❞❛ ❝♦♥❥✉♥t❛♠❡♥t❡ ♣❡❧♦s ❧❛❞♦s ❤♦r✐③♦♥t❛✐s ❡ ✈❡rt✐❝❛✐s✳
✶✹❖s ❙✉❧❜❛s✉tr❛s ❡r❛♠ ❛♣ê♥❞✐❝❡s ❞♦s ❱❡❞❛s✱ ❝♦♥❥✉♥t♦ ❞❡ t❡①t♦s s❛❣r❛❞♦s✱ ❡ ✐♥❞✐❝❛✈❛♠ ❛s r❡❣r❛s
✸✵ ❯♠ ❜r❡✈❡ ❍✐stór✐❝♦
❋✐❣✉r❛ ✷✳✶✶✿ ❘❡tâ♥❣✉❧♦ ✈❡rsã♦ ❑❛t②❛②❛♥❛
◆❛s ✈❡rsõ❡s ❛♥t❡r✐♦r❡s tr❛t❛♠ ❞❡ r❡tâ♥❣✉❧♦s ❡ ♥ã♦ ❞❡ tr✐â♥❣✉❧♦s r❡tâ♥❣✉❧♦s✳ ❆ ♣r✐✲ ♠❡✐r❛ ✈❡rsã♦ é r❡❧❛t✐✈❛ à q✉❛❞r❛❞♦s ❡ é ♠❛✐s ❡s♣❡❝í✜❝❛✱ ❡♥q✉❛♥t♦ q✉❡ ❛ s❡❣✉♥❞❛ ✈❡rsã♦ r❡❢❡r❡✲s❡ ❛♦ ❝❛s♦ ❣❡r❛❧✳ P♦r ❝♦♥t❛ ❞✐ss♦✱ ●❛s♣❛r ✭✷✵✶✺✮ ✐♥❢❡r❡ q✉❡ ❤á ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ t❡r ♦❝♦rr✐❞♦ ❞✉❛s ❡t❛♣❛s ♥❛ ❞❡s❝♦❜❡rt❛ ❞♦ ❚❡♦r❡♠❛ ♣❡❧♦s ❤✐♥❞✉s✳
❆ ♣r✐♠❡✐r❛ ❡①♣❧✐❝❛çã♦✿ ❖s ❤✐♥❞✉s ♣♦❞❡♠ t❡r ♦❜s❡r✈❛❞♦ q✉❡ ♦ q✉❛❞r❛❞♦ ♠❛✐♦r s♦❜r❡ ❛ ❞✐❛❣♦♥❛❧ ❞♦ q✉❛❞r❛❞♦ ♠❡♥♦r ♣♦❞❡ s❡r ❞✐✈✐❞✐❞♦ ❡♠ q✉❛tr♦ tr✐â♥❣✉❧♦s ✐sós❝❡❧❡s✱ ❝❛❞❛ ✉♠ ❞❡❧❡s ❝♦♠ ❛ ♠❡❞✐❞❛ ❞❡ ár❡❛ ✐❣✉❛❧ ❛ ♠❡t❛❞❡ ❞❛ ♠❡❞✐❞❛ ❞❛ ár❡❛ ❞♦ q✉❛❞r❛❞♦ ♠❡♥♦r✱ ❋✐❣✉r❛ ✷✳✶✷✳
❋✐❣✉r❛ ✷✳✶✷✿ Pr✐♠❡✐r❛ ❡①♣❧✐❝❛çã♦✿ ❉❡s❝♦❜❡rt❛ ❤✐♥❞✉
❆ s❡❣✉♥❞❛ ❡①♣❧✐❝❛çã♦✿ ❆ ♣❛rt✐r ❞❛ ❝♦♥str✉çã♦ ❞♦ ❛t♠❛♥✱ q✉❡ é ✉♠ q✉❛❞r❛❞♦ ❝♦♠ ♠❡❞✐❞❛ ✐❣✉❛❧ ❛ ✹ ♣✉r✉s❤❛s✶✺ ❞❡ ár❡❛ ❡ é ❢❡✐t♦ ✉♥✐♥❞♦ q✉❛tr♦ q✉❛❞r❛❞♦s ❝♦♠ ♠❡❞✐❞❛
✐❣✉❛❧ ❛ ✉♠❛ ♣✉r✉s❤❛ ❞❡ ❧❛❞♦✳ ❙❡ tr❛ç❛r♠♦s ❛s ❞✐❛❣♦♥❛✐s ✭d1✱d2✱d3 ❡d4✮ ❞♦s q✉❛❞r❛❞♦s
♠❡♥♦r❡s ❝♦♠♦ ♥❛ s❡❣✉✐♥t❡ ❋✐❣✉r❛ ✷✳✶✸✱ ❢♦r♠❛♠♦s ✉♠ q✉❛❞r❛❞♦ q✉❡ ❡stá ❞✐✈✐❞✐❞♦ ❡♠ q✉❛tr♦ tr✐â♥❣✉❧♦s ❞❡ ár❡❛ ♠❡❞✐♥❞♦ ♠❡✐❛ ♣✉r✉s❤❛s✳ ❆♦ ♦❜s❡r✈❛r q✉❡ ♦ q✉❛❞r❛❞♦ s♦❜r❡ ❛ ❞✐❛❣♦♥❛❧ ❞❡ ✉♠ q✉❛❞r❛❞♦ t❡♠ ár❡❛ ✐❣✉❛❧ ❛♦ ❞♦❜r♦ ❞❛ ♠❡❞✐❞❛ ❞❛ ár❡❛ ❞❡ss❡ q✉❛❞r❛❞♦✱ ♣♦❞❡ ♣❡r❝❡❜❡r ♦ ❚❡♦r❡♠❛✱ s❡❣✉♥❞♦ ●❛s♣❛r ✭✷✵✶✺✮✳
●r❡❣♦s ✸✶
❋✐❣✉r❛ ✷✳✶✸✿ ❙❡❣✉♥❞❛ ❡①♣❧✐❝❛çã♦✿ ❉❡s❝♦❜❡rt❛ ❤✐♥❞✉
❆ t❡r❝❡✐r❛ ❡①♣❧✐❝❛çã♦✿ ◆❛ ❝♦♥str✉çã♦ ❞♦ ❛❧t❛r ♣❛✐tr❦②✈❡❞✐✱ q✉❡ é ❢❡✐t♦ ❛ ♣❛rt✐r ❞❡ ✉♠ q✉❛❞r❛❞♦ ❞❡ ❞✉❛s ♣✉r✉s❤❛s ❡ ❛s q✉✐♥❛s ❞♦ ❱❡❞✐ ✜❝❛♠ s♦❜r❡ ♦s ♣♦♥t♦s ♠é❞✐♦s ❞❡ ❧❛❞♦s✳ ❖ ❞✐❛❣r❛♠❛ ❞❛ ❝♦♥str✉çã♦ é ♦ ♠❡s♠♦ q✉❡ ❞❛ ❋✐❣✉r❛ ✷✳✶✸✱ só q✉❡ ❛❣♦r❛ ❛ ❝♦♥str✉çã♦ s❡ ✐♥✐❝✐❛ ♣❡❧♦ q✉❛❞r❛❞♦ ❞❡ ❧❛❞♦ ✷ ♣✉r✉s❤❛s✳
❊ss❛s três ❡①♣❧✐❝❛çõ❡s✱ ♣♦❞❡♠ ❡st❛r r❡❧❛❝✐♦♥❛❞❛s ❝♦♠ ❛ ❞❡s❝♦❜❡rt❛ ❞♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s ♣❡❧♦s ✐♥❞✐❛♥♦s✱ s❡❣✉♥❞♦ ❡st✉❞♦s ❞❡ ●❛s♣❛r ✭✷✵✶✺✮✳
✷✳✹ ●r❡❣♦s
❆s ❝✐✈✐❧✐③❛çõ❡s ♠✐♥♦✐❝❛ ❡ ♠✐❝ê♥✐❝❛ ❢♦r❛♠ ❛s ♣r✐♠❡✐r❛s ❛ ♦❝✉♣❛r ❛ r❡❣✐ã♦ ❞❛ ●ré❝✐❛✱ ❡♥tr❡t❛♥t♦ ❢♦r❛♠ ❡①t❡r♠✐♥❛❞❛s ♥♦ ♣❡rí♦❞♦ ❡♥tr❡ ✶✷✵✵ ❛✳❈✳ ❡ ✶✶✺✵ ❛✳❈✳✱ ♣♦r ✐♥✈❛s♦r❡s ❜ár❜❛r♦s✱ ♦s ❞ór✐♦s✱ ✉♠❛ tr✐❜♦ ❛♣❛r❡♥t❛❞❛ ❝♦♠ ♦s ❛r✐❛♥♦s✳
✸✷ ❯♠ ❜r❡✈❡ ❍✐stór✐❝♦
❆ ❡s❝r✐t❛ q✉❡ ❤❛✈✐❛ ❞❡s❛♣❛r❡❝✐❞❛ ❢♦✐ r❡✐♥tr♦❞✉③✐❞❛ ♣♦r ✈♦❧t❛ ❞❡ ✽✵✵ ❛✳❈✳ ♣❡❧♦s ♠❡r✲ ❝❛❞♦r❡s ❢❡♥í❝✐♦s✱ s❡❣✉♥❞♦ ❊✈❡s ✭✷✵✶✶✱ ♣✳ ✾✵✮✳ ❇♦②❡r ✭✶✾✼✹✱ ♣✳ ✸✸✮✱ ❡①❛❧t❛ ❛ ❝❛♣❛❝✐❞❛❞❡ ❡ ♦ ❡♠♣❡♥❤♦ ❡♠ ❛♣r❡♥❞❡r ❞♦s ❣r❡❣♦s ♣ré✲❤❡❧ê♥✐❝♦s✶✻✳ ❆♣❡s❛r ❞♦s ✐♥✈❛s♦r❡s ♥ã♦ t❡r❡♠
tr❛❞✐çã♦ ❝♦♠ ❛ ❡s❝r✐t❛ ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ♠❛t❡♠át✐❝♦✱ t✐✈❡r❛♠ ❞❡s❡❥♦ ❡♠ ❛♣r❡♥❞❡r ❡ ♥ã♦ ❞❡♠♦r❛r❛♠ ❛ ♠❡❧❤♦r❛r ♦ q✉❡ ❧❤❡ ❡♥s✐♥❛r❛♠✳ ❆♣♦s ❛♣r❡♥❞❡r❡♠ ❛ ❡s❝r✐t❛ ❡ ❛ ♠❛t❡✲ ♠át✐❝❛ ❝♦♠ ♠❡r❝❛❞♦r❡s✱ ❡st✉❞✐♦s♦s ♣❛ss❛r❛♠ ❛ ✈✐❛❥❛r ❛té ♦s ❣r❛♥❞❡s ❝❡♥tr♦s ❞❡ ❝✉❧t✉r❛ ❝♦♠♦ ❊❣✐t♦ ❡ ❇❛❜✐❧ô♥✐❛ ♣❛r❛ s❡ ❛♣r♦♣r✐❛r ❞❡ ♠❛✐s ❝♦♥❤❡❝✐♠❡♥t♦✳
❖ ♣❡rí♦❞♦ s❡❣✉✐♥t❡ é ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❍❡❧ê♥✐❝♦ ✭❝♦♠♣r❡❡♥❞✐❞♦ ❡♥tr❡ ✽✵✵ ❛✳❈✳ ❡ ✸✸✻ ❛✳❈✳✮ ♣❡❧♦s ❤✐st♦r✐❛❞♦r❡s✱ ❛♣r❡s❡♥t♦✉ ✉♠ ❣r❛♥❞❡ ❛✈❛♥ç♦ ❝✐❡♥tí✜❝♦ ❡ ✐♥t❡❧❡❝t✉❛❧✳
❚r❛❞✐❝✐♦♥❛❧♠❡♥t❡✱ ❝♦♥❢♦r♠❡ ❘♦q✉❡ ✭✷✵✶✷✱ ♣✳ ✾✷✮✱ ❤✐st♦r✐❛❞♦r❡s ❛♥t✐❣♦s s✉❣❡r❡♠ q✉❡ ❛ ♣rát✐❝❛ ❞❛ ❛❣r✐♠❡♥s✉r❛ ❞♦s ❡❣í♣❝✐♦s t❡r✐❛ ❞❛❞♦ ♦r✐❣❡♠ à ✐♥✈❡♥çã♦ ❞❛ ❣❡♦♠❡✲ tr✐❛✶✼✱ ✉♠ ❝♦♥❤❡❝✐♠❡♥t♦ q✉❡ s❡r✐❛ ✐♠♣♦rt❛❞♦ ♣❡❧♦s ❣r❡❣♦s✳ ❚❛❧❡s ❞❡ ▼✐❧❡t♦ ✭✻✷✵ ❛✳❈✳
à ✺✺✵ ❛✳❈✳✮✱ ♠❛t❡♠át✐❝♦ ❡ ✜❧ós♦❢♦✱ ✐♥tr♦❞✉③✐✉ ❛ ❣❡♦♠❡tr✐❛ ♥♦ t❡rr✐tór✐♦ ●r❡❣♦✳ ◆❡ss❡ ♣❡rí♦❞♦ ❤♦✉✈❡ ✉♠❛ tr❛♥s✐çã♦ ❞❛ ❣❡♦♠❡tr✐❛ ❡♠♣ír✐❝❛ ♣❛r❛ ❛ t❡ór✐❝❛✱ ♦♥❞❡ ♦ ❢♦❝♦ ♣❛ss♦✉ ❛ s❡r ❛s ❞❡♠♦♥str❛çõ❡s✳ ❆✐♥❞❛ ❝♦♠♦ r❡sq✉í❝✐♦s ❞❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❡ss❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❛♥t✐❣♦✱ ♦❜s❡r✈❛♠♦s ❛ ✐❞❡✐❛ ❞❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ♠❡❞✐❞❛s ✐♥❛❝❡ssí✈❡✐s✳ P♦r ❡①❡♠♣❧♦✱ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ♠❡❞✐❞❛ ❞❛ ❛❧t✉r❛ ❞❡ ✉♠❛ ❞❛s ♣✐râ♠✐❞❡s ❞♦ ❊❣✐t♦ ♣♦r ❚❛❧❡s ❞❡ ♠❛♥❡✐r❛ ♣rát✐❝❛ ❡ ❛♣❧✐❝❛❞❛✳
❆ ♠❛t❡♠át✐❝❛ s♦❢r❡✉ ✉♠❛ ♠✉❞❛♥ç❛ ❞❡ r✉♠♦ ♥❛ ●ré❝✐❛ ❆♥t✐❣❛✱ ❞❡✐①♦✉ ❞❡ s❡r ✉♠❛ ❝♦❧❡çã♦ ❞❡ r❡s✉❧t❛❞♦s ❡♠♣ír✐❝♦s ❡ ♣❛ss♦✉ ❛ t❡r ♦ ❢♦r♠❛t♦ ❞❡ ✉♠❛ ❝✐ê♥❝✐❛ ♦r❣❛♥✐③❛❞❛✱ ❞❡ ♠❛♥❡✐r❛ s✐st❡♠át✐❝❛ ❡ ♣♦r ❡❧❡♠❡♥t♦s r❛❝✐♦♥❛✐s✳ ❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ ❛ ♠❛t❡♠á✲ t✐❝❛ ❛tr❛✈és ❞❡ ❞❡♠♦♥str❛çõ❡s✱ ♣❛ss♦✉ ❛ s❡r ❡ss❡♥❝✐❛❧♠❡♥t❡ ❛❜str❛t❛✱ ❝♦♠ ✉♠❛ ❝❡rt❛ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❡♠ r❡❧❛çã♦ às ❛♣❧✐❝❛çõ❡s ♣rát✐❝❛s✱ ❝♦♥❢♦r♠❡ ▼♦❧ ✭✷✵✶✸✱ ♣✳ ✷✾✮✳
❉❡✈❡♠♦s r❡ss❛❧t❛r q✉❡ ♦s ❣r❡❣♦s s❡ ❡s❢♦rç❛✈❛♠ ❡♠ ❜✉s❝❛r ♠❛♥❡✐r❛s ❞❡ ❞✐st✐♥❣✉✐r ♣❡♥s❛♠❡♥t♦s ❢❛❧s♦s ❞♦s ❝♦rr❡t♦s✱ ♦✉ s❡❥❛✱ ❡st❛❜❡❧❡❝✐❛♠ ❝r✐tér✐♦s ♣❛r❛ ❞❡❝✐❞✐r q✉❡♠ t✐♥❤❛ r❛③ã♦✳ ❋✐❧ós♦❢♦s ❝♦♠♦ ❙ó❝r❛t❡s ❡ ❆r✐stót❡❧❡s ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ❞❡s❡♥✈♦❧✈❡r ✉♠ ♥♦✈♦ t✐♣♦ ❞❡ ❛r❣✉♠❡♥t❛çã♦✳ ❆ ✜❧♦s♦✜❛ ♥❛s❝❡✉ ♥❛ ●ré❝✐❛✱ ♣♦r ✈♦❧t❛ ❞♦ sé❝✉❧♦ ❱■■ ❛✳❈✳✳ ◆♦ ❡♥t❛♥t♦✱ ❛ ♣❛❧❛✈r❛ ✜❧♦s♦✜❛✶✽✱ ✐♥✈❡♥t❛❞❛ ♣❡❧♦ ✜❧ós♦❢♦ P✐tá❣♦r❛s ❞❡ ❙❛♠♦s✱ ❛♣❛r❡❝❡✉
❛♣❡♥❛s ♥♦ s❡❝✉❧♦ ❱ ❛✳❈✳✱ ♣❛r❛ ❞❡s✐❣♥❛r ✉♠ s❛❜❡r q✉❡ ❤❛✈✐❛ s❡ ❡str✉t✉r❛❞♦ ❡♠ ❢✉♥çã♦ ❞❡ ♣r✐♥❝í♣✐♦s r❛❝✐♦♥❛✐s✱ ✭❋❆▲❆❇❘❊❚❚■✱ ❖▲■❱❊■❘❆✱ ✷✵✶✶ ♣✳ ✷✹✮✳
◆❡ss❛ é♣♦❝❛✱ ❚❛❧❡s ❞❡ ▼✐❧❡t♦ ✉♥✐✉ ♦ ❡st✉❞♦ ❞❛ ❛str♦♥♦♠✐❛ ❛♦ ❞❛ ❣❡♦♠❡tr✐❛ ❡ ❞❛ t❡♦r✐❛ ❞♦s ♥ú♠❡r♦s✱ ❢✉♥❞❛♥❞♦ ❛ ❝❤❛♠❛❞❛ ❊s❝♦❧❛ ■♦♥✐❛♥❛✳ ❈♦♥s✐❞❡r❛❞♦ ♦ ❝r✐❛❞♦r ❞❛ ❣❡♦♠❡tr✐❛ ❞❡❞✉t✐✈❛✱ s❡♥❞♦ ❛ ❚❛❧❡s ❛tr✐❜✉í❞❛s ❛s ♣r✐♠❡✐r❛s ❞❡♠♦♥str❛çõ❡s ♠❛t❡♠át✐❝❛s q✉❡ ❢✉♥❞❛♠❡♥t❛r✐❛♠ ♦✉tr♦s ♣❡♥s❛❞♦r❡s✱ ▼♦❧ ✭✷✵✶✸✱ ♣✳ ✸✷✮✳
✶✻Pré✲❍❡❧ê♥✐❝♦ é ♦ ♣❡rí♦❞♦ ❛♥t❡r✐♦r ❛♦ ❤❡❧ê♥✐❝♦✱ ❛♥t❡s ❞❡ ✽✵✵ ❛✳❈✳
✶✼●❡♦♠❡tr✐❛✿ ❱❡♠ ❞♦ ●r❡❣♦ ❣❡♦♠❡tr✐❛✱ ♠❡❞✐❞❛ ❞❛ t❡rr❛✱ ❞❡ ❣❡♦✱ t❡rr❛✱ ♠❛✐s ♠❡tr❡✐♥✱ ♠❡❞✐r ✭❞❡
♠❡tr♦♥✱ ♠❡❞✐❞❛✮✳ ❊ss❛ ♠❛tér✐❛ t❡✈❡ ✐♥í❝✐♦ ❛ ♣❛rt✐r ❞❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❞❡✜♥✐r ❝♦♠ ♣r❡❝✐sã♦ ♦s t❡rr❡♥♦s ❝✉❧t✐✈á✈❡✐s✱ q✉❛♥❞♦ ❛ ❡s♣é❝✐❡ ❤✉♠❛♥❛ ♣❛ss♦✉ ❛ s❡ ♦❝✉♣❛r ❝♦♠ ❛ ❛❣r✐❝✉❧t✉r❛✳
✶✽P❤✐❧♦s♦♣❤✐❛ é ❝♦♠♣♦st❛ ♣♦r ❞✉❛s ♣❛❧❛✈r❛s✿ P❤í❧✐❛ ✭❛♠♦r✱ ❛♠✐③❛❞❡✮ ❡ ❙♦♣❤✐❛ ✭s❛❜❡❞♦r✐❛✮✳ P♦rt❛♥t♦
P✐tá❣♦r❛s ✸✸
✷✳✺ P✐tá❣♦r❛s
❆s ♣r✐♥❝✐♣❛✐s ❢♦♥t❡s ❞❡ ✐♥❢♦r♠❛çõ❡s ❛ r❡s♣❡✐t♦ ❞♦ ✐♥í❝✐♦ ❞❛ ♠❛t❡♠át✐❝❛ ❣r❡❣❛ q✉❡ r❡❧❛❝✐♦♥❛ P✐tá❣♦r❛s sã♦ ♦ ❝❤❛♠❛❞♦ ❉❡ ❝♦♠♠✉♥✐ ♠❛t❤❡♠❛t✐❝❛ s❝✐❡♥t✐❛ ❞❡ ❏â♠❜❧✐❝♦✶✾ ❡
♦ ❙✉♠ár✐♦ ❊✉❞❡♠✐❛♥♦ ❞❡ Pr♦❝❧♦✷✵✱ s❡❣✉♥❞♦ ❊✈❡s ✭✷✵✶✶✱ ♣✳ ✾✼✮ ❡ ❘♦q✉❡ ✭✷✵✶✷✱ ♣✳ ✶✵✷✮✳
P✐tá❣♦r❛s ❞❡ ❙❛♠♦s ✭✺✼✷ ❛✳❈✳ ✲ ✹✾✻ ❛✳ ❈✳✮✱ ♠❛t❡♠át✐❝♦ ❣r❡❣♦ ♥❛s❝✐❞♦ ♥❛ ✐❧❤❛ ❞❡ ❙❛♠♦s✱ ♣❛r❡❝❡ q✉❡ r❡s✐❞✐✉ ♣♦r ❛❧❣✉♠ t❡♠♣♦ ♥♦ ❊❣✐t♦ ❡ t❡r♠✐♥♦✉ ♣♦r ❡st❛❜❡❧❡❝❡r✲s❡ ♥❛ ❝✐❞❛❞❡ ❞❡ ❈r♦t♦♥❛✱ ♥❛ ❝♦st❛ s✉❞❡st❡ ❞❛ ■tá❧✐❛✳ ❋♦r♠♦✉✲s❡ ❡♠ t♦r♥♦ ❞❡ P✐tá❣♦r❛s ✉♠❛ ✐r♠❛♥❞❛❞❡ r❡❧✐❣✐♦s❛✱ ✜❧♦só✜❝❛ ❡ ❝✐❡♥tí✜❝❛✱ ✉♠❛ ❡s❝♦❧❛ ❞❡ ♣❡♥s❛❞♦r❡s ❝♦♠ ❡❧❡♠❡♥t♦s ❞❡ ♠✐st✐❝✐s♠♦✱ ❊✈❡s ✭✷✵✶✶✮ ❡ ▼♦❧ ✭✷✵✶✸✮✳
❆ ✜❧♦s♦✜❛ ♣✐t❛❣ór✐❝❛ ❜❛s❡❛✈❛✲s❡ ♥❛ s✉♣♦s✐çã♦ ❞❡ q✉❡ ❛ ❝❛✉s❛ ú❧t✐♠❛ ❞❛s ✈ár✐❛s ❝❛r❛❝✲ t❡ríst✐❝❛s ❞♦ ❤♦♠❡♠ ❡ ❞❛ ♠❛tér✐❛ sã♦ ♦s ♥ú♠❡r♦s ✐♥t❡✐r♦s✳ ■ss♦ ❧❡✈❛✈❛ ❛ ✉♠❛ ❡①❛❧t❛çã♦ ❡ ❛♦ ❡st✉❞♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❞♦s ♥ú♠❡r♦s ❡ ❞❛ ❛r✐t♠ét✐❝❛ ✭t❡♦r✐❛ ❞♦s ♥ú♠❡r♦s✮✱ ❥✉♥t♦ ❝♦♠ ❛ ❣❡♦♠❡tr✐❛✱ ❛ ♠ús✐❝❛ ❡ ❛ ❛str♦♥♦♠✐❛✱ q✉❡ ❝♦♥st✐t✉í❛♠ ❛s ❛rt❡s ❧✐❜❡r❛✐s ❜ás✐❝❛s ❞♦ ♣r♦❣r❛♠❛ ❞❡ ❡st✉❞♦s ♣✐t❛❣ór✐❝♦✱ s❡❣✉♥❞♦ ❊✈❡s ✭✷✵✶✶✮✳
❆ tr❛❞✐çã♦ é ✉♥â♥✐♠❡ ❡♠ ❛tr✐❜✉✐r ❛ P✐tá❣♦r❛s ❛ ❞❡s❝♦❜❡rt❛ ❞♦ t❡♦r❡♠❛ s♦❜r❡ tr✐â♥✲ ❣✉❧♦s r❡tâ♥❣✉❧♦s✱ ❝♦♥❤❡❝✐❞♦ ✉♥✐✈❡rs❛❧♠❡♥t❡ ♣❡❧♦ s❡✉ ♥♦♠❡✳ ❊♥tr❡t❛♥t♦✱ ❡ss❡ t❡♦r❡♠❛ ❥á ❡r❛ ❛♣❧✐❝❛❞♦ ♣♦r ❝✐✈✐❧✐③❛çõ❡s ❛♥t❡r✐♦r❡s à ♠❛✐s ❞❡ ✉♠ ♠✐❧ê♥✐♦ ❛♥t❡s ❞♦s ♣r✐♠❡✐r♦s tr❛❜❛❧❤♦s ❣r❡❣♦s ♥❡ss❛ ár❡❛ s❡r❡♠ ❞❡s❡♥✈♦❧✈✐❞♦s✳
❆ ♣r✐♠❡✐r❛ ❞❡♠♦♥str❛çã♦ ❢♦r♠❛❧ ♣♦❞❡ t❡r s✐❞♦ ❞❛❞❛ ♣♦r P✐tá❣♦r❛s ❡ ✐♥❝❧✉s✐✈❡ ♣♦❞❡ t❡r ✉t✐❧✐③❛❞♦ ✉♠❛ ❞❡♠♦♥str❛çã♦ ❝♦♠ ❞❡❝♦♠♣♦s✐çã♦ ❝♦♠♦ ♥❛ ❋✐❣✉r❛ ✷✳✶✺✱ s❡❣✉♥❞♦ ❊✈❡s ✭✷✵✶✶✱ ♣✳ ✶✵✸✮✳ ▼❛s ❘♦q✉❡ ✭✷✵✶✷✱ ♣✳ ✶✶✷✮✱ r❡❢♦rç❛ ❛ t❡s❡ q✉❡ ♥ã♦ ❤á ❡✈✐❞ê♥❝✐❛s q✉❡ ♣♦ss❛♠ ❝♦♠♣r♦✈❛r q✉❡ r❡❛❧♠❡♥t❡ ❛❧❣✉♠ P✐t❛❣ór✐❝♦ t❡♥❤❛ ❞❡♠♦♥str❛❞♦ ❡ss❡ t❡♦r❡♠❛✳
❋✐❣✉r❛ ✷✳✶✺✿ Pr✐♠❡✐r❛ ❞❡♠♦♥str❛çã♦✿ ❙✉❣❡r✐❞❛ ♣♦r ❊✈❡s
❆ ❋✐❣✉r❛ ✷✳✶✺✱ s✉❣❡r❡ ❛♦ r❡t✐r❛r ♣❛rt❡s ❝♦♠✉♥s ✭tr✐â♥❣✉❧♦s✮ q✉❡ ♦ q✉❛❞r❛❞♦ ♠❛✐♦r t❡♠ ❛ ♠❡s♠❛ ár❡❛ q✉❡ ❛ s♦♠❛ ❞❛s ár❡❛s ❞♦s q✉❛❞r❛❞♦s ♠❡♥♦r❡s✳
c2 =a2+b2
