❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ P✐❛✉í ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❞❛ ◆❛t✉r❡③❛
Pós ●r❛❞✉❛çã♦ ❡♠ ▼❛t❡♠át✐❝❛
▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠ ▼❛t❡♠át✐❝❛ ✲ P❘❖❋▼❆❚
❚❡♦❞♦❧✐t♦✿ ❯♠❛ ❛♥á❧✐s❡ ❞♦ ❊♥s✐♥♦ ❞❡
▼❛t❡♠át✐❝❛ ♥❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛ ❡ ❆♣❧✐❝❛çõ❡s
❋r❛♥❝✐s❝♦ ❚❡✐①❡✐r❛ ❊stê✈❡s
❘❡❧❛tór✐♦ ♣❛r❛ ♦ ❊①❛♠❡ ●❡r❛❧ ❞❡ ◗✉❛❧✐✜❝❛çã♦ ❛♣r❡✲ s❡♥t❛❞♦ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ✕ ▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠ ▼❛t❡♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧
❖r✐❡♥t❛❞♦r❛
Pr♦❢❛✳ ❉r❛✳ ▲✐❛♥❡ ▼❡♥❞❡s ❋❡✐t♦s❛ ❙♦❛r❡s
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ P✐❛✉í ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❞❛ ◆❛t✉r❡③❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ▼❛t❡♠át✐❝❛
❚❡♦❞♦❧✐t♦✿ ❯♠❛ ❛♥á❧✐s❡ ❞♦ ❊♥s✐♥♦ ❞❡
▼❛t❡♠át✐❝❛ ♥❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛ ❡ ❆♣❧✐❝❛çõ❡s
❋r❛♥❝✐s❝♦ ❚❡✐①❡✐r❛ ❊stê✈❡s
❉✐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❛✳ ▲✐❛♥❡ ▼❡♥❞❡s ❋❡✐t♦s❛ ❙♦❛r❡s
1
FICHA CATALOGRÁFICA
Serviço de Processamento Técnico da Universidade Federal do Piauí Biblioteca Setorial do CCN
E81t Estêves, Francisco Teixeira.
Teodolito: uma análise do ensino de matemática na educação básica e aplicações / Francisco Teixeira Estêves.
– Teresina, 2015. 64f. il.: color
Dissertação (Mestrado Profissional) – Pós-Graduação em Matemática, Universidade Federal do Piauí, 2015.
Orientadora: Prof. Dra. Liane Mendes Feitosa Soares 1. Geometria. 2. Trigonometria Plana. 3. Matemática –
Estudo e Ensino. I. Título
❆❣r❛❞❡❝✐♠❡♥t♦s
❘❡s✉♠♦
❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ t❡♠ ♣♦r ♦❜❥❡t✐✈♦ ❛♣r❡s❡♥t❛r ❛❧❣✉♠❛s ❢♦r♠❛s ♠❛✐s ❡✜❝❛③❡s ❞♦ ❡♥s✐♥♦ ❞❡ ♠❛t❡♠át✐❝❛ ♣❛r❛ ❛❧✉♥♦s ❞♦ ❡♥s✐♥♦ ❜ás✐❝♦✳ P❛r❛ ✐ss♦✱ ♦ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠❛ ♣❡sq✉✐s❛ q✉❡ ❜✉s❝❛ ❝♦♠♣❛r❛r ❞✐❞át✐❝❛s ❞❡ ❡♥s✐♥♦ ❞❡ ♠❛t❡♠át✐❝❛ ❡ ❛♣r❡s❡♥t❛r ❛❧✲ t❡r♥❛t✐✈❛s q✉❡ ✈✐s❛♠ ♠❡❧❤♦r ❛♣r❡♥❞✐③❛❞♦✳ ❆ ♣❡sq✉✐s❛ ❢♦✐ ❜❛s❡❛❞♦ ❡♠ ❧✐✈r♦s q✉❡ tr❛t❛♠ ❞❡ t❛❧ ✜♠✱ ❞❡ ♦❜s❡r✈❛çõ❡s ❢❡✐t❛ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ❡♠ três ❡s❝♦❧❛s ❞✐❢❡r❡♥t❡s✱ ❝♦♠♦ t❛♠❜é♠ ❝♦♥✈❡rs❛s ❝♦♠ ♣r♦❢❡ss♦r❡s q✉❡ ❡stã♦ ❤á t❡♠♣♦s ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ❡ ❝♦♥✈✐✈❡♠ ❞✐❛r✐❛♠❡♥t❡ ❝♦♠ ♣r♦❜❧❡♠❛s ❞❡ ❛♣r❡♥❞✐③❛❞♦✳ ❆s ♦❜s❡r✈❛çõ❡s ❢♦r❛♠ r❡❛❧✐③❛❞❛s ♥♦ ✐♥t❡rstí❝✐♦ ✷✵✶✸ ❡ ✷✵✶✺✱ ❡♥q✉❛♥t♦ ❛ ♣❡sq✉✐s❛ ✉s❛♥❞♦ ❧✐✈r♦s ❞❡❞✐❝❛❞♦s ❛♦ ❡♥s✐♥♦ ❢♦✐ r❡❛❧✐③❛❞❛ ♥♦ ❛♥♦ ❞❡ ✷✵✶✺✳
❈♦♥st❛ ♥♦ tr❛❜❛❧❤♦✱ ❛✐♥❞❛ ✉♠❛ ❛♣❧✐❝❛çã♦ ❞✐❞át✐❝❛ ❝♦♠ ❛❧✉♥♦s ❞♦ ✾♦ ❛♥♦ ❞♦ ❡♥s✐♥♦
❢✉♥❞❛♠❡♥t❛❧ ❞❛ ❯♥✐❞❛❞❡ ❊s❝♦❧❛ ❉❡s❡♠❜❛r❣❛❞♦r ❖❞✐❧♦ ❈♦st❛ ❋✐❧❤♦✱ s✐t✉❛❞❛ ♥❛ ❝✐❞❛❞❡ ❞❡ ❚✐♠♦♥✱ ▼❛r❛♥❤ã♦❀ ♦♥❞❡ é ✉s❛❞♦ ♠❡t♦❞♦❧♦❣✐❛s ❛❧t❡r♥❛t✐✈❛s ♣❛r❛ tr❛♥s♠✐t✐r ❝♦♥❤❡❝✐✲ ♠❡♥t♦ ❞✐❞át✐❝♦✳ ❚❛♠❜é♠ é ❛♣r❡s❡♥t❛❞♦ ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ✉♠❛ ❛♣❧✐❝❛çã♦ ❝♦♠ ❛❧✉♥♦s ❞♦ ✾♦ ❛♥♦ ❞♦ ❡♥s✐♥♦ ♠é❞✐♦ ❞❛ ❯♥✐❞❛❞❡ ■♥t❡❣r❛❞❛ ▼✉♥✐❝✐♣❛❧ ✧▲✉ís ❋❛❧❝ã♦✧✱ ❧♦❝❛❧✐③❛❞❛
❡♠ ❈❛①✐❛s ✲ ▼❛r❛♥❤ã♦❀ ♦♥❞❡ é ✉s❛❞♦ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❛❞q✉✐r✐❞♦ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ♥❛ ♠❡❞✐çã♦ ❞❡ ♦❜❥❡t♦s ✐♥❛❧❝❛♥çá✈❡✐s✳ P♦r ✜♠✱ é ❛♣r❡s❡♥t❛❞♦ ❛s ❝♦♥❝❧✉sõ❡s✱ ❧❡✈❛♥❞♦ ❡♠ ❝♦♥s✐❞❡r❛çã♦ t✉❞♦ q✉❡ ❢♦✐ ❛♣r❡s❡♥t❛❞♦✳ ❖ tr❛❜❛❧❤♦ ✈✐s❛ s❡r✈✐r ❝♦♠♦ ❜❛s❡ ♣❛r❛ ❢✉t✉r❛s ❛♣❧✐❝❛çõ❡s ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ♣❛r❛ t♦❞♦ ❡ q✉❛❧q✉❡r ❡❞✉❝❛❞♦r✳
❆❜str❛❝t
❚❤✐s ♣❛♣❡r ❛✐♠s t♦ ♣r❡s❡♥t s♦♠❡ ♠♦r❡ ❡✛❡❝t✐✈❡ ✇❛②s ♦❢ t❡❛❝❤✐♥❣ ♠❛t❤ t♦ ❡❧❡♠❡♥t❛r② s❝❤♦♦❧ st✉❞❡♥ts✳ ❋♦r t❤✐s✱ t❤❡ ♣❛♣❡r ♣r❡s❡♥ts ❛ s✉r✈❡② t❤❛t s❡❡❦s t♦ ❝♦♠♣❛r❡ t❡❛❝❤✐♥❣ ♦❢ ♠❛t❤ ❛♥❞ ♣r❡s❡♥t ❛❧t❡r♥❛t✐✈❡s t❤❛t ❛✐♠ t♦ ❜❡tt❡r ❧❡❛r♥✐♥❣✳ ❚❤❡ r❡s❡❛r❝❤ ✇❛s ❜❛s❡❞ ♦♥ ❜♦♦❦s ❞❡❛❧✐♥❣ ✇✐t❤ t❤✐s ♣✉r♣♦s❡✱ ♦❜s❡r✈❛t✐♦♥s ♠❛❞❡ ✐♥ ❝❧❛ss ✐♥ t❤r❡❡ ❞✐✛❡r❡♥t s❝❤♦♦❧s✱ ❛s ✇❡❧❧ ❛s ❝♦♥✈❡rs❛t✐♦♥s ✇✐t❤ t❡❛❝❤❡rs ✇❤♦ ❤❛✈❡ ❜❡❡♥ t✐♠❡s ✐♥ t❤❡ ❝❧❛ssr♦♦♠ ❛♥❞ ❢❛❝❡ ❞❛✐❧② ✇✐t❤ ❧❡❛r♥✐♥❣ ♣r♦❜❧❡♠s✳ ❚❤❡ ♦❜s❡r✈❛t✐♦♥s ✇❡r❡ ♠❛❞❡ ✐♥ t❤❡ ✐♥t❡rst✐t✐❛❧ s♣❛❝❡ ❜❡t✇❡❡♥ ✷✵✶✸ ❛♥❞ ✷✵✶✺✱ ✇❤✐❧❡ t❤❡ r❡s❡❛r❝❤ ❜♦♦❦s ❞❡✈♦t❡❞ t♦ t❡❛❝❤✐♥❣ ✇❛s ❝❛rr✐❡❞ ♦✉t ✐♥ ✷✵✶✺✳
■♥ t❤✐s ✇♦r❦ t❤❡r❡ ✐s ❛ ❞✐❞❛❝t✐❝ ❛♣♣❧✐❝❛t✐♦♥ ✇✐t❤ st✉❞❡♥ts ❢r♦♠ ✾t❤ ❣r❛❞❡ ♦❢ ❡❧❡✲ ♠❡♥t❛r② s❝❤♦♦❧ ❯♥✐t ❙❝❤♦♦❧ ❏✉❞❣❡ ❖❞✐❧♦ ❈♦st❛ ❋✐❧❤♦✱ ✐♥ t❤❡ ❝✐t② ♦❢ ❚✐♠♦♥✱ ▼❛r❛♥❤❛♦❀ ✇❤❡r❡ ✐t ✐s ✉s❡❞ ❛❧t❡r♥❛t✐✈❡ ♠❡t❤♦❞s t♦ ❝♦♥✈❡② ❞✐❞❛❝t✐❝ ❦♥♦✇❧❡❞❣❡✳ ■t ✐s ❛❧s♦ ♣r❡s❡♥t❡❞ ✐♥ t❤✐s ✇♦r❦ ❛ ♣r♦❣r❛♠ ✇✐t❤ st✉❞❡♥ts ❢r♦♠ ✾t❤ ❣r❛❞❡ ♦❢ ❤✐❣❤ s❝❤♦♦❧ ♦❢ t❤❡ ▼✉♥✐❝✐♣❛❧ ■♥t❡❣r❛t❡❞ ❯♥✐t ✧▲✉✐s ❋❛❧❝ã♦✧✱ ❧♦❝❛t❡❞ ✐♥ ❈❛①✐❛s ✲ ▼❛r❛♥❤ã♦❀ ✇❤❡r❡ ✐t ✐s ✉s❡❞ t❤❡ ❦♥♦✲ ✇❧❡❞❣❡ ❣❛✐♥❡❞ ✐♥ t❤❡ ❝❧❛ssr♦♦♠ ✐♥ t❤❡ ♠❡❛s✉r❡♠❡♥t ♦❢ ✉♥r❡❛❝❤❛❜❧❡ ♦❜❥❡❝ts✳ ❋✐♥❛❧❧②✱ ✐t ✐s ♣r❡s❡♥t❡❞ t❤❡ ✜♥❞✐♥❣s✱ t❛❦✐♥❣ ✐♥t♦ ❛❝❝♦✉♥t ❛❧❧ t❤❛t ❤❛s ❜❡❡♥ ♣r❡s❡♥t❡❞✳ ❚❤❡ ✇♦r❦ ❛✐♠s t♦ s❡r✈❡ ❛s ❛ ❜❛s✐s ❢♦r ❢✉t✉r❡ ❛♣♣❧✐❝❛t✐♦♥s ✐♥ t❤❡ ❝❧❛ssr♦♦♠ ❢♦r ❡❛❝❤ ❛♥❞ ❡✈❡r② ❡❞✉❝❛t♦r✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❊st✉❞❛r ① ❋❛❝❡❜♦♦❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✶ ❯♥✐❞❛❞❡ ❊s❝♦❧❛r ❉❡s❡♠❜❛r❣❛❞♦r ❖❞✐❧♦ ❈♦st❛ ❋✐❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✹✳✶ ❈❧❛ss✐✜❝❛çã♦ ❞♦s ❚r✐â♥❣✉❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✷ ❚r✐â♥❣✉❧♦ ❘❡tâ♥❣✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✸ ❚r✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦ ❝♦♠ ➶♥❣✉❧♦ ❛❣✉❞♦θ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✹✳✹ ❚r✐â♥❣✉❧♦ ❊q✉✐❧át❡r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✺ ❚r✐â♥❣✉❧♦ ❘❡tâ♥❣✉❧♦ ❞❡ ➶♥❣✉❧♦s ❛❣✉❞♦s ✸✵♦ ❡ ✻✵♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✹✳✻ ❚r✐â♥❣✉❧♦ ❘❡tâ♥❣✉❧♦ ■só❝❡❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✼ ❚❛❜❡❧❛ ❚r✐❣♦♥♦♠étr✐❝❛ ❞❡ ➶♥❣✉❧♦s ◆♦tá✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✽ ❚❛❜❡❧❛ ❚r✐❣♦♥♦♠étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✺✳✶ ❯■▼ ▲✉ís ❋❛❧❝ã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✺✳✷ ❚❡♦❞♦❧✐t♦ Pr♦✜ss✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✺✳✸ ❚❡♦❞♦❧✐t♦ ❈❛s❡✐r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✺✳✹ ■❧✉str❛çã♦ ❞❡ ✉s♦ ❞♦ ❚❡♦❞♦❧✐t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✺✳✺ ▼é❞✐❛ ❇✐♠❡str❛❧ ❆❧✉♥♦s ✾♦ ❆♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✶✾
✷ ❊♥s✐♥♦ ❞❡ ▼❛t❡♠át✐❝❛ ♥❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛ ✷✶
✷✳✶ ❊♠ s❛❧❛ ❞❡ ❛✉❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✷ ❊❞✉❝❛çã♦ ♥❛ ❩♦♥❛ ❘✉r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✸ ❆♣❧✐❝❛çã♦ ❉✐❞át✐❝❛ ✷✺
✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✷ ❆ ❊s❝♦❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✸ ❉✐♥â♠✐❝❛ ❞♦ ❏♦❣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✹ ❏✉st✐✜❝❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✺ ❈♦♥❝❧✉sçã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
✹ ❆ ❚r✐❣♦♥♦♠❡tr✐❛ ✷✾
✹✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✹✳✷ ❈♦♥t❡①t♦ ❍✐stór✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✹✳✸ ❉❡✜♥✐çõ❡s Pr❡❧✐♠✐♥❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✹ ❋✉♥çõ❡s ❚r✐❣♦♥♦♠étr✐❝❛ ♥♦ ❚r✐â♥❣✉❧♦ ❘❡tâ♥❣✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✺ ❘❡❧❛çã♦ ❚r✐❣♦♥♦♠étr✐❝❛ ❋✉♥❞❛♠❡♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✻ ❙❡♥♦✱ ❈♦ss❡♥♦ ❡ ❚❛♥❣❡♥t❡ ❞❡ ➶♥❣✉❧♦s ◆♦tá✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✺ ❆♣❧✐❝❛çã♦ ❞❡ ❚r✐❣♦♥♦♠❡tr✐❛ ✸✾
✺✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✺✳✷ ❆ ❊s❝♦❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✺✳✸ ❚❡♦❞♦❧✐t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✺✳✹ ❈♦♥str✉✐♥❞♦ ✉♠ ❚❡♦❞♦❧✐t♦ ❈❛s❡✐r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✺✳✺ ❆♣❧✐❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✺✳✻ ❏✉st✐✜❝❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✺✳✼ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✻ ◗✉❛❞r❛❞♦ ▼á❣✐❝♦ ✹✼
✶ ■♥tr♦❞✉çã♦
◆❡st❡ ♠✉♥❞♦ ♠♦❞❡r♥♦✱ ❝❛❞❛ ✈❡③ ✜❝❛ ❞✐❢í❝✐❧ ♣❛r❛ ♦ ♣r♦❢❡ss♦r✱ s❡❥❛ ❞❡ q✉❛❧ ❢♦r ❛ ❞✐s❝✐♣❧✐♥❛✱ ❝♦♥s❡❣✉✐r r❡♣❛ss❛r ♦ ❝♦♥t❡ú❞♦ ♣❛r❛ ♦ s❡✉ ❛❧✉♥❛❞♦✳ ❖s ❥♦✈❡♥s ❡ ❛❞♦❧❡s❝❡♥t❡s ♣♦ss✉❡♠ ✐♥ú♠❡r❛s ❛t✐✈✐❞❛❞❡s q✉❡ ♣♦❞❡♠ t✐r❛r s✉❛ ❛t❡♥çã♦ ❞✉r❛♥t❡ ❛s ❛✉❧❛s✱ s❡❥❛♠ ❡❧❛s ❝♦♠♣✉t❛❞♦r❡s✱ ❝❡❧✉❧❛r❡s✱ t❛❜❧❡ts✱ r❡✈✐st❛s✱ ❡t❝✳ ◆❛ ♠❛✐♦r✐❛ ❞❛s ❡s❝♦❧❛s é ♣r♦✐❜✐❞♦ ♦ ✉s♦ ❞❡ ❛♣❛r❡❧❤♦s ❡❧❡trô♥✐❝♦s ♥❛s ❞❡♣❡♥❞ê♥❝✐❛s ❞❛ ❡s❝♦❧❛✱ ♣♦ré♠ ✜❝❛ ❞✐❢í❝✐❧ ❞❡ ✜s❝❛❧✐③❛r✱ ❥á q✉❡ ♣❛r❛ ✐ss♦ s❡r✐❛ ♥❡❝❡ssár✐♦ ✉♠❛ r❡✈✐st❛ ❡♠ ❝❛❞❛ ❛❧✉♥♦✳ ❖ ♣r♦❢❡ss♦r t❡♠ q✉❡ s❡ ✈✐r❛r ❡♠ ✶✵ ♣❛r❛ ❝❤❛♠❛r ❛ ❛t❡♥çã♦ ❞♦ ❛❧✉♥♦✱ ❛❥✉❞❛r ❛q✉❡❧❡ q✉❡ t❡♠ ♠❛✐s ❞✐✜❝✉❧❞❛❞❡s✱ ✐♥❝❡♥t✐✈❛r ❛q✉❡❧❡ q✉❡ ❝♦♥s❡❣✉❡ ♣❡❣❛r ♦ ❝♦♥t❡ú❞♦ ❢á❝✐❧ ❡ ❛✐♥❞❛ ✜❝❛ r❡s♣♦♥sá✈❡❧ ♣❡❧♦ r❡❣✐str♦ ❞❡ ❛✉❧❛✱ ❢❛❧t❛s✱ ❡♥tr❡ ♦✉tr♦s❀ ✜s❝❛❧✐③❛r ♦ ✉s♦ ❞❡ ❛♣❛r❡❧❤♦s ❡❧❡trô♥✐❝♦s ♣❡❧♦s ❛❧✉♥♦s é ✉♠❛ t❛r❡❢❛ ❛ ♠❛✐s✱ q✉❡ ♥❛ ♠❛✐♦r✐❛ ❞❛s ✈❡③❡s é ✐❣♥♦r❛❞❛ ♣❡❧♦ ❞♦❝❡♥t❡✳ ➱ ✉♠❛ ❝❛r❣❛ ♠✉✐t♦ ♣❡s❛❞❛ ♣❛r❛ ✉♠❛ ♣❡ss♦❛ só✱ ❛✐♥❞❛ ♠❛✐s q✉❛♥❞♦ s❡ t❡♠ ♠❛✐s ❞❡ ✸✵ ❛❞♦❧❡s❝❡♥t❡s ❡♠ s❛❧❛ ❞❡ ❛✉❧❛✱ ♦♥❞❡ ❛ ♠❛✐♦r✐❛ ❝♦♥t❛ ♦s ♠✐♥✉t♦s ♣❛r❛ s❛✐r✳ ❖ ✐❞❡❛❧ s❡r✐❛ ❝♦❧♦❝❛r ♠❛✐s ✉♠❛ ♣❡ss♦❛ ♣❛r❛ ❛❥✉❞❛r ♦ ♣r♦❢❡ss♦r ❞❡♥tr♦ ❞❡ s❛❧❛ ❞❡ ❛✉❧❛❄ ❈♦❧♦❝❛r ❛♣❛r❡❧❤♦s q✉❡ ❜❧♦q✉❡✐❛♠ s✐♥❛✐s ❡❧❡trô♥✐❝♦s✱ ❝♦♠♦ ❡♠ ♣r✐sõ❡s❄
❋✐❣✉r❛ ✶✳✶✿ ❊st✉❞❛r ① ❋❛❝❡❜♦♦❦
P❛r❛ ❝♦♥t♦r♥❛r ❡ss❛ s✐t✉❛çã♦ ♦ ♣r♦✜ss✐♦♥❛❧ ❞❡ ❡❞✉❝❛çã♦ ♣♦ss✉✐ ✈ár✐♦s ❛rt✐❢í❝✐♦s✱ ♣♦ré♠ t♦❞♦s ❡❧❡s ❞❡♣❡♥❞❡ ❞❡ ✉♠ ❡s❢♦rç♦ ❡①tr❛ ❞❡❧❡✱ s❡❥❛ ♥❛ ♣r❡♣❛r❛çã♦ ♦✉ ♥❛ ❡①❡❝✉çã♦ ❞❛ t❛r❡❢❛ ♣r♦♣♦st❛✳ ❖ ❞♦❝❡♥t❡ t❡♠ q✉❡ ✉s❛r s❡✉ t❡♠♣♦ ❧✐✈r❡ ♣❛r❛ ❡❧❛❜♦r❛r ❡ ♦r❣❛♥✐③❛r ❡①❡r❝í❝✐♦s q✉❡ ♣♦ss✐❜✐❧✐t❡♠ ♦ ♠❡❧❤♦r ❛♣r❡♥❞✐③❛❞♦ ❞❡ s❡✉ ❛❧✉♥❛❞♦✱ ❛❧é♠ ❞♦ ❣r❛♥❞❡ ❡s❢♦rç♦
✷✵ ■♥tr♦❞✉çã♦
❡♠ s❛❧❛ ❞❡ ❛✉❧❛✳ ❈❧❛r♦ q✉❡ t❛♠❜é♠ é ♥❡❝❡ssár✐❛ ❛ ❛❥✉❞❛ ❞❛ ❞✐r❡çã♦ ❞❛ ❡s❝♦❧❛✱ s❡❥❛ ❝♦♠ ♠❛t❡r✐❛✐s ♦✉ ❝♦♠ ♣❡ss♦❛❧✳ ❆❧❣✉♠❛s ❛t✐✈✐❞❛❞❡s sã♦ ♠✉✐t♦ ✐♥t❡r❡ss❛♥t❡s✱ ♣♦ré♠ ❞❡♣❡♥❞❡ ❞❡ ♠❛✐s ❞❡ ✉♠❛ ♣❡ss♦❛ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ♣❛r❛ s❡r ❡①❡❝✉t❛❞❛s✱ ♦ q✉❡ ❣❡r❛❧♠❡♥t❡ é ❝♦♠♣❧✐❝❛❞♦ ❞❡ s❡ t❡r✱ ❥á q✉❡ ❝❛❞❛ ✉♠ ❡♠ ✉♠❛ ❡s❝♦❧❛ t❡♠ ✉♠❛ t❛r❡❢❛ ❡s♣❡❝í✜❝❛ ❡ ♥ã♦ ♣♦❞❡ ❧❛r❣á✲❧❛ q✉❛♥❞♦ q✉✐s❡r✳ ❆❧é♠ ❞✐ss♦✱ é ♥❡❝❡ssár✐♦ ♠❛t❡r✐❛✐s ♣❛r❛ r❡❛❧✐③❛r ❛s ❛t✐✈✐❞❛❞❡s✳ ❆❧❣✉♠❛s ❡s❝♦❧❛s ♣♦ss✉❡♠ ♠❛t❡r✐❛✐s ❡♠ s❡✉s ❞❡♣ós✐t♦s ♣❛r❛ s❡r ✉s❛❞♦ ♣♦r s❡✉s ♣r♦❢❡ss♦r❡s✱ ♦ q✉❡ ❛❥✉❞❛ ♠✉✐t♦❀ ♣♦ré♠✱ q✉❛♥❞♦ s❡ ♣r❡❝✐s❛ ❞❡ ✉♠ ♠❛t❡r✐❛❧ q✉❡ ❛ ❡s❝♦❧❛ ♥ã♦ ♣♦ss✉✐✱ ♦ ♣r♦❢❡ss♦r t❡♠ q✉❡ t✐r❛r ❞♦ ♣ró♣r✐♦ ❜♦❧s♦ ♣❛r❛ ♣♦❞❡r r❡❛❧✐③❛r ❛ t❛r❡❢❛ ❝♦♠ s❡✉ ❛❧✉♥❛❞♦✳
◗✉❛❧ s❡r✐❛ ❡♥tã♦ ❛ s♦❧✉çã♦ ♣❛r❛ t♦❞♦s ❡st❡s ♣r♦❜❧❡♠❛s❄ ❈♦♠♦ ❢❛③❡r ❝♦♠ q✉❡ ♦ ❛❧✉♥❛❞♦ ✐♥t❡r❡ss❡✲s❡ ♠❛✐s ♣❡❧♦s ❡st✉❞♦s✱ q✉❡ ❡❧❡s ❡♥t❡♥❞❛♠ q✉❡ ❡st✉❞❛r é ❛ ú♥✐❝❛ ❢♦r♠❛ ❞❡ t❡r ✉♠❛ ❜♦❛ ♣r♦✜ssã♦ ♥♦ ❢✉t✉r♦❄ ❖♥❞❡ ♦ ♣r♦❢❡ss♦r ❞❡✈❡ ♣r♦❝✉r❛r ❛t✐✈✐❞❛❞❡s q✉❡ ✈✐s❡♠ ♣r❡♥❞❡r ❛ ❛t❡♥çã♦ ❞♦ s❡✉ ❛❧✉♥♦ ❡ ❝♦♠♦ ❡❧❡s ❞❡✈❡♠ ❡①❡❝✉t❛r ❡ss❛ t❛r❡❢❛❄ ❖ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ é t❡♥t❛r r❡s♣♦♥❞❡r ❛❧❣✉♠❛s ♣❡r❣✉♥t❛s ❞❡st❛s✱ ❛♣r❡s❡♥t❛r t❛r❡❢❛s q✉❡ ♣♦ss❛♠ s❡r ❛♣❧✐❝❛❞❛s ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ❡ ♠♦str❛r ❛♦ ❞♦❝❡♥t❡ ❝♦♠♦ ❞r✐❜❧❛r t♦❞❛s ❛s ❞✐✜❝✉❧❞❛❞❡s ❡♥❢r❡♥t❛❞❛s ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ♥♦s ❞✐❛s ❛t✉❛✐s✳
❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❡stá ❞✐✈✐❞✐❞♦ ❡♠ três ♣❛rt❡s ♣r✐♥❝✐♣❛✐s✳ ◆❛ ♣r✐♠❡✐r❛ é ❛♣r❡✲ s❡♥t❛❞♦ ♠❡t♦❞♦❧♦❣✐❛s ❡ ❡st✉❞♦s q✉❡ ♣♦ss✐❜✐❧✐t❡♠ ♦ ❞♦❝❡♥t❡ ❛♣❡r❢❡✐ç♦❛r ♦ ❡♥s✐♥❛♠❡♥t♦ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛✳ ❙ã♦ ❛♣r❡s❡♥t❛❞❛s ❛t✐✈✐❞❛❞❡s q✉❡ ♣♦❞❡♠ s❡r ❛♣❧✐❝❛❞❛s ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ♣❛r❛ ❛❥✉❞❛r ♥♦ ❛♣r❡♥❞✐③❛❞♦ ❡ sã♦ ❛♣r❡s❡♥t❛❞❛s ❡♠ ❞❡t❛❧❤❡s ♥♦s ❧✐✈r♦s q✉❡ s❡r✈✐r❛♠ ❞❡ ❜❛s❡ ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❖ ♦❜❥❡t✐✈♦ ❞❡st❛ ♣r✐♠❡✐r❛ ♣❛rt❡ é ❢❛③❡r ♦ ❞♦❝❡♥t❡ ❛❞♦t❛r ♠ét♦❞♦s ♣rát✐❝♦s ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ❡ ❛ss✐♠ tr❛♥s♠✐t✐r ♦ ❝♦♥t❡ú❞♦ ❞✐✲ ❞át✐❝♦ ♠❛✐s ❢❛❝✐❧♠❡♥t❡✳ ❆ s❡❣✉♥❞❛ ♣❛rt❡ ❞♦ tr❛❜❛❧❤♦ é ✉♠❛ ♥♦✈❛ ❛❜♦r❞❛❣❡♠ s♦❜r❡ tr✐❣♦♥♦♠❡tr✐❛✱ ♠❛✐s ❡s♣❡❝✐✜❝❛♠❡♥t❡✱ ❛ tr✐❣♦♥♦♠❡tr✐❛ q✉❡ é r❡♣❛ss❛❞❛ ♣❛r❛ ❛❧✉♥♦s ❞♦ ✾♦ ❛♥♦ ❞♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧✳ ➱ ✉♠❛ ♥♦✈❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❝♦♠♦ ❧❡❝✐♦♥❛r ❛♦ ❛❧✉♥❛❞♦
❞♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧ ❡st❡ ❝♦♥t❡ú❞♦ q✉❡ ♣❛r❡❝❡ tã♦ ❝♦♠♣❧✐❝❛❞♦ ♣❛r❛ ❡❧❡s✳ ❖ ♦❜❥❡t✐✈♦ é ♦❢❡r❡❝❡r ✉♠❛ ❛❧t❡r♥❛t✐✈❛ ♣❛r❛ ♦ ❞♦❝❡♥t❡ ❛❧é♠ ❞❛ ❡♥❝♦♥tr❛❞❛ ♥♦s ❧✐✈r♦s ❞✐❞át✐❝♦s✱ q✉❡ ❣❡r❛❧♠❡♥t❡ é ♠❛✐s ❝♦♠♣❧✐❝❛❞♦ ❡ ♥ã♦ ❢❛③ ✉♠❛ ❧✐❣❛çã♦ ❝♦♠♦ ♦ ❝♦t✐❞✐❛♥♦ ❞♦ ❛❧✉♥♦✱ ♦ q✉❡ é ✐♥❞✐s♣❡♥sá✈❡❧ ♣❛r❛ ✉♠ ♠❡❧❤♦r ❛♣r❡♥❞✐③❛❞♦✳ P♦r ✜♠✱ ❛ t❡r❝❡✐r❛ ♣❛rt❡ é ✉♠❛ ❛♣❧✐❝❛çã♦ ❞❡ tr✐❣♦♥♦♠❡tr✐❛ ❝♦♠ ❛❧✉♥♦s ❞♦ ✾♦ ❛♥♦ ❞❡ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧✳ ➱ ♠♦str❛❞♦ ❝♦♠♦ ✉s❛r
♦ ❚❡♦❞♦❧✐t♦ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❢❛③❡r ❛ ♠❡❞✐çã♦ ❞❡ ❛❧t✉r❛s ✐♥❛❧❝❛♥çá✈❡✐s✳ ❖ ♦❜❥❡t✐✈♦ ❞❡st❛ ❡t❛♣❛ é ❛♣r❡s❡♥t❛r ✉♠❛ ❛♣❧✐❝❛çã♦ ❞❛ ❚r✐❣♦♥♦♠❡tr✐❛ q✉❡ ♣r❡♥❞❡ ❛ ❛t❡♥çã♦ ❞♦ ❛❧✉♥♦✱ ❛❧é♠ ❞❡ ❞❡s♣❡rt❛r ♣❛r❛ ❛ ❜❡❧❡③❛ ❞❛ ♠❛t❡♠át✐❝❛✳
✷ ❊♥s✐♥♦ ❞❡ ▼❛t❡♠át✐❝❛ ♥❛ ❊❞✉❝❛çã♦
❇ás✐❝❛
✷✳✶ ❊♠ s❛❧❛ ❞❡ ❛✉❧❛
❖s ♣r♦❜❧❡♠❛s ❡♥❢r❡♥t❛❞♦s ❞✐❛r✐❛♠❡♥t❡ ♣❡❧♦s ❞♦❝❡♥t❡s ❞♦ ❡♥s✐♥♦ ❜ás✐❝♦ sã♦ ✐♥ú✲ ♠❡r♦s✱ ✈ã♦ ❞❡s❞❡ ❛ ❝❤❡❣❛❞❛ ❛ ❡s❝♦❧❛ ❛té ♦ ♠♦♠❡♥t♦ q✉❡ ❡stã♦ ❡♠ s✉❛s r❡s✐❞ê♥❝✐❛s ❝♦rr✐❣✐♥❞♦ tr❛❜❛❧❤♦s ❡ ❛✈❛❧✐❛çõ❡s✳ ❖ ❞♦❝❡♥t❡ é r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ❡❧❛❜♦r❛çã♦ ❞❛s ❛✉❧❛s✱ ❞❛s ❛✈❛❧✐❛çõ❡s✱ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❛❧✉♥♦ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛✱ ❞❛ ✜s❝❛❧✐③❛çã♦ ❞❡ ♠❛t❡r✐✲ ❛✐s ♣r♦✐❜✐❞♦s✱ ❡♥tr❡ ♦✉tr♦s❀ ❛❧é♠ ❞✐ss♦✱ t❡♠ q✉❡ s❡ ❛❞❡q✉❛r ❛s ♥♦r♠❛s ❞❡ ❝❛❞❛ ❡s❝♦❧❛ ❡ ❢❛③❡r ❝♦♠ q✉❡ ❛s ♠❡t❛s ❞❛ s❡❝r❡t❛r✐❛ ❞❡ ❡❞✉❝❛çã♦ s❡❥❛♠ ❛❧❝❛♥ç❛❞❛s✳ ❊♠ s❛❧❛ ❞❡ ❛✉❧❛ ❝♦♠ ♠❛✐s ❞❡ ✸✵ ❛❞♦❧❡s❝❡♥t❡s✱ ♦ ❞♦❝❡♥t❡ t♦r♥❛✲s❡ q✉❛s❡ ✐♥út✐❧ s❡ ♥ã♦ t✐✈❡r tr❛ç❛❞♦ ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ❡✜❝✐❡♥t❡ ❡ ❛❞♦t❛❞♦ ♠ét♦❞♦s q✉❡ t♦r♥❡♠ ♣♦ssí✈❡✐s s✉❛s ❛✉❧❛s✳ P❛r❛ ✉♠ ❞♦✲ ❝❡♥t❡ ✐♥❡①♣❡r✐❡♥t❡ ♣♦❞❡ s❡r ❝♦♠♣❧✐❝❛❞♦ tr❛♥s♠✐t✐r ❛♦ s❡✉ ❛❧✉♥❛❞♦ ♦ ❝♦♥t❡ú❞♦ ❞✐❞át✐❝♦ ❞♦ ❛♥♦ ❧❡t✐✈♦✱ ♠❡s♠♦ q✉❡ t❡♥❤❛ ❢❡✐t♦ ✉♠ ❜♦♠ ♣❧❛♥❡❥❛♠❡♥t♦ ♣ré✈✐♦✳ ➱ ♥❡❝❡ssár✐♦ q✉❡ ♦ ❞♦❝❡♥t❡ ❞♦♠✐♥❡ ❝♦♠♣❧❡t❛♠❡♥t❡ ♦ ❝♦♥t❡ú❞♦✱ q✉❡ t❡♥❤❛ ♣❧❛♥❡❥❛❞♦ ♣❛ss♦ ❛ ♣❛ss♦ s✉❛ ❛✉❧❛ ❡✱ ❛❧é♠ ❞✐ss♦✱ ♣r♦❝✉r❛r ❢♦r♠❛s ❞❡ ♣r❡♥❞❡r ❛ ❛t❡♥çã♦ ❞❡ s❡✉ ❛❧✉♥♦✳ ▼♦②sés ✭✶✾✾✼✮ ❢❛❧❛ ❡♠ s❡✉ ❧✐✈r♦ ❆♣❧✐❝❛çõ❡s ❞❡ ❱②❣♦ts❦② à ❡❞✉❝❛çã♦ ♠❛t❡♠át✐❝❛✿
✏■♠♣r❡s❝✐♥❞í✈❡❧ é ❛ ❢♦r♠❛çã♦ ❞♦ ♣r♦❢❡ss♦r✳ ❙❡♠ ✉♠ ❡♠❜❛s❛♠❡♥t♦ t❡ór✐❝♦ ❝♦♥s✐st❡♥t❡✱ ❝r❡✐♦ q✉❡ ❞✐✜❝✐❧♠❡♥t❡ s❛❜❡rá ♣ôr ❡♠ ♣rát✐❝❛ ❛ t❡♦r✐❛✳ ❊♠❜♦r❛ ❛ ♣❡sq✉✐s❛ t✐✈❡ss❡ ❞❡♠♦♥str❛❞♦ q✉❡ ❡ss❡ ❡♠❜❛s❛♠❡♥t♦ ♣♦❞❡ s❡r ❢❡✐t♦ ♣♦r ❛❧❣✉é♠ q✉❡ ✈á ♦r✐❡♥t❛♥❞♦ ♠✉✐t♦ ❞❡ ♣❡rt♦ ♦ tr❛❜❛❧❤♦ ❞♦ ♣r♦❢❡ss♦r✱ ♦ ✐❞❡❛❧ é q✉❡ ❡❧❡ s❡ ❛♣r♦♣r✐❡ ❞❡ss❡ ❝♦♥❤❡❝✐♠❡♥t♦✳ ❊ ♠❛✐s✱ q✉❡✱ ♥❡ss❡ ❛♣r♦♣r✐❛r✲s❡✱ ❡❧❡ r❡❝♦♥str✉❛ ♦ ♣ró♣r✐♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ ■❣✉❛❧♠❡♥t❡ ✐♠♣r❡s❝✐♥❞í✈❡❧ é q✉❡ ❡❧❡ q✉❡✐r❛ ❛❞♦t❛r ❡ss❡ ♥♦✈❛ ❜❛s❡ t❡ór✐❝❛ ♣❛r❛ s✉❛ ❛t✐✈✐❞❛❞❡ ♣❡❞❛❣ó❣✐❝❛✱ ✉♠❛ ✈❡③ ❝♦♥✈❡♥❝✐❞♦ ❞❡ s✉❛ r✐q✉❡③❛✳✑
P❛r❛ ✉♠ ♣r♦✜ss✐♦♥❛❧ ❞❡ ❡❞✉❝❛çã♦ q✉❡ ♥ã♦ t❡♥❤❛ s✐❞♦ ❝❛♣❛❝✐t❛❞♦ ❝♦rr❡t❛♠❡♥t❡ ♣❛r❛ ❛ ❞♦❝ê♥❝✐❛✱ tr❛♥s♠✐t✐r ❝♦♥❤❡❝✐♠❡♥t♦ ♣♦❞❡ s❡r ✉♠❛ t❛r❡❢❛ ❝♦♠♣❧✐❝❛❞❛ ❡ tr❛✉♠át✐❝❛✱ ♣♦✉❝♦s sã♦ ❝❛♣❛③❡s ❞❡ s✉♣♦rt❛r ❛ t❡♥sã♦ ❡♠ ✉♠❛ s❛❧❛ ❞❡ ❛✉❧❛ ❧♦t❛❞❛ ❞❡ ❛❞♦❧❡s❝❡♥t❡s✱ ♦♥❞❡ ❛ ♠❛✐♦r✐❛ ♣r❡❢❡r✐❛ ❡stá ❡♠ s✉❛ ❝❛s❛ ❛ss✐st✐♥❞♦ ❚❱ ♦✉ ✉s❛♥❞♦ ❛ ✐♥t❡r♥❡t✳ ▼✉✐t♦s
✷✷ ❊♥s✐♥♦ ❞❡ ▼❛t❡♠át✐❝❛ ♥❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛
❞❡❧❡s ♦ ❢❛③❡♠ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛✱ ✉s❛♥❞♦ ❞❡ ❛♣❛r❡❧❤♦s ❞✐❣✐t❛✐s q✉❡ ❛ ❝❛❞❛ ❞✐❛ ❡stã♦ ♠❡♥♦r❡s ❡ t❡❝♥♦❧ó❣✐❝♦s✳ ❋✐❝❛ ❞✐❢í❝✐❧ ♣❛r❛ ♦ ♣r♦❢❡ss♦r ❝♦♠♣❡t✐r ❝♦♠ ✉♠ ❝❛♠♣♦ tã♦ ❣r❛♥❞❡ q✉❡ é ❛ ✐♥t❡r♥❡t✱ ❝❤❡✐♦ ❞❡ ❝✉r✐♦s✐❞❛❞❡s ❡ ❡♥tr❡t❡♥✐♠❡♥t♦s✳ ❖ ❞♦❝❡♥t❡ ❞❡✈❡ ✉s❛r ❡st❡ ❝❛♠♣♦ ❛ s❡✉ ❢❛✈♦r✱ ✉t✐❧✐③❛♥❞♦ ❛ ✐♥t❡r♥❡t ❡♠ s✉❛ ❝❛s❛ ♣❛r❛ ❡♥❝♦♥tr❛r ♠ét♦❞♦s ❛❧t❡r♥❛t✐✈♦s ❛♦s tr❛❞✐❝✐♦♥❛✐s ❞❡ ❡♥s✐♥♦✱ s❡❥❛ ❡st❡s ❝♦♠ ✉s♦ ❞❡ ❝❛rt❛③❡s✱ r❡tr♦♣r♦❥❡t♦r❡s ♦✉ ♠❛t❡r✐❛❧ ♣❛r❛ ❧❡✐t✉r❛✳ ❈♦♠ ✉♠❛ ❜♦❛ ♣❡sq✉✐s❛ ❡ s❛❜❡♥❞♦ ❜❡♠ ♦ q✉❡ ❡stá ♣r♦❝✉r❛♥❞♦✱ t♦❞♦ ♣r♦❢❡ss♦r é ❝❛♣❛③ ❞❡ ❛❝❤❛r ❛❧❣♦ q✉❡ ♣♦ss❛ ❡♥tr❡t❡r ♦ ❛❧✉♥♦ ❡ ❛♦ ♠❡s♠♦ t❡♠♣♦ ❢❛③❡r ❝♦♠ q✉❡ ❡st❡ ❛♣r❡♥❞❛✳ ➱ s✉r♣r❡❡♥❞❡♥t❡ ❛ ❞✐❢❡r❡♥ç❛ q✉❡ ♦ ✉s♦ ❞❡ ✉♠ s✐♠♣❧❡s r❡tr♦♣r♦❥❡t♦r ❢❛③ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛✱ ♦ ❛❧✉♥♦ ♣r♦❝✉r❛ ❛❧❣♦ ♥♦✈♦✱ ❛❧❣♦ q✉❡ ❝❤❛♠❡ s✉❛ ❛t❡♥çã♦ ❡✱ ❝❛❜❡ ❛ ♣r♦❢❡ss♦r✱ ❧❡✈❛r ♣❛r❛ ❝❧❛ss❡ ❛❧❣♦ q✉❡ ❡❧❡s ❛✐♥❞❛ ♥ã♦ t✐♥❤❛♠ ❝♦♥❤❡❝✐♠❡♥t♦✳
✷✳✷ ❊❞✉❝❛çã♦ ♥❛ ❩♦♥❛ ❘✉r❛❧
❙❡ é ♣r♦❜❧❡♠át✐❝♦ tr❛♥s♠✐t✐r ❝♦♥t❡ú❞♦ ♣❛r❛ ❛❧✉♥♦s ❞❛ ③♦♥❛ ✉r❜❛♥❛✱ q✉❛♥❞♦ s❡ tr❛t❛ ❞❡ ✉♠❛ ❡s❝♦❧❛ ♣ú❜❧✐❝❛ ❞❛ ③♦♥❛ r✉r❛❧ ♦ ♣r♦❜❧❡♠❛ é ♠❛✐♦r ❛✐♥❞❛✳ ❆ ♠❛✐♦r✐❛ ❞❛s ❡s❝♦❧❛s ❞❛ ③♦♥❛ r✉r❛❧ ♣♦ss✉✐ ❛♣❡♥❛s ♦ ❢✉♥❞❛♠❡♥t❛❧ ■ ❡ ■■✱ ♦♥❞❡ ❛❧✉♥♦s q✉❡ ❞❡✈❡r✐❛♠ ❡st❛r ♥❛ ♠♦❞❛❧✐❞❛❞❡ ❊❏❆ s❡ ❥✉♥t❛ ❝♦♠ ♦✉tr♦s q✉❡ ❡stã♦ ♥❛ ✐❞❛❞❡ ❝❡rt❛✳ ❆s ❡s❝♦❧❛s ♥ã♦ ♣♦ss✉❡♠ ♦ ❛♣♦✐♦ ♥❡❝❡ssár✐♦ ❞❛ s❡❝r❡t❛r✐❛ ❞❡ ❡❞✉❝❛çã♦✱ ❥á q✉❡ ❡stã♦ ❛❢❛st❛❞❛s ❞❛ ❝✐❞❛❞❡✳ ❋❛❧t❛ ♠❡r❡♥❞❛ ❡s❝♦❧❛r✱ ❝❛rt❡✐r❛s✱ ♣✐♥❝❡✐s ♦✉ ❣✐③✱ ❡t❝✳ P♦✉❝❛s ♣♦ss✉❡♠ ♠áq✉✐♥❛s ❞❡ ❳❡r♦① ❡✱ q✉❛♥❞♦ ❛s ♣♦ss✉✐✱ ♥ã♦ ❤á ♠❛♥✉t❡♥çã♦✱ ♣❛♣❡❧ ♦✉ t✐♥t❛✳ ❚✉❞♦ ✐st♦ ❛tr❛♣❛❧❤❛ ❛✐♥❞❛ ♠❛✐s ❛ ✈✐❞❛ ❞♦ ❞♦❝❡♥t❡ q✉❡✱ ❛❧é♠ ❞❡ ❧✐❞❛r ❝♦♠ t♦❞♦s ❡st❡s ♣r♦❜❧❡♠❛s✱ ❛✐♥❞❛ t❡rã♦ q✉❡ ❧❡❝✐♦♥❛r ♣❛r❛ ❛❧✉♥♦s q✉❡ ♥ã♦ t✐✈❡r❛♠ ✉♠❛ ❜♦❛ ❜❛s❡ ❡ ♥ã♦ ♣♦ss✉✐ ✉♠ ❛♣♦✐♦ ❡♠ ❝❛s❛✳ Pr♦❢❡ss♦r❡s ❞❡st❛ ③♦♥❛ ❡s❝✉t❛♠ ❝♦♠ ❢r❡q✉ê♥❝✐❛ ❞♦ s❡✉ ❛❧✉♥❛❞♦ q✉❡ ❡st❡s ♣r❡❢❡r✐❛♠ ❡stá ❡♠ ❛❧❣✉♠ tr❛❜❛❧❤♦ ❜r❛ç❛❧ ❝♦♠ s❡✉s ♣❛✐s ♦✉ ♣❛r❡♥t❡s✳ ❙❛❧✈♦ ✉♠❛ ♣❡q✉❡♥❛ ♠✐♥♦r✐❛✱ ❡st❡s ❞✐s❝❡♥t❡s ♥ã♦ ♣♦ss✉❡♠ ✉♠❛ ❛♠❜✐çã♦ ♣❛r❛ ♠❡❧❤♦r❛r ❞❡ ✈✐❞❛✱ t❡r♠✐♥❛r ♦ ❡♥s✐♥♦ ♠é❞✐♦ ❡ ❝♦♥s❡❣✉✐r ✉♠ tr❛❜❛❧❤♦ q✉❡ ♣❛❣✉❡ ✉♠ s❛❧ár✐♦ ♠í♥✐♠♦✱ ♦✉ ❛té ♠❡♥♦s q✉❡ ✐ss♦✱ ❥á é s✉✜❝✐❡♥t❡ ♣❛r❛ ❡❧❡s✳
❚❡♥t❛r ♠✉❞❛r ❛ ✐❞❡✐❛ q✉❡ ❛❧✉♥♦s ❞❛ ③♦♥❛ r✉r❛❧ ♣♦ss✉✐ é ✉♠ tr❛❜❛❧❤♦ ár❞✉♦ ♣❛r❛ ♦ ❞♦❝❡♥t❡✱ ♣♦ssí✈❡❧ s♦♠❡♥t❡ ❝♦♠ ✉♠❛ ❜♦❛ ♠❡t♦❞♦❧♦❣✐❛✱ ✉♠❛ ❛❞♠✐♥✐str❛çã♦ q✉❡ ❛❥✉❞❡ ❜❛st❛♥t❡ ❡ ♠✉✐t❛ ♣❛❝✐ê♥❝✐❛✳ ❖s ❞❡s❛✜♦s sã♦ ❡♥♦r♠❡s ❡ ❛♥t❡s ❞❡ t❡♥t❛r r❡♣❛ss❛r ❝♦♥❤❡✲ ❝✐♠❡♥t♦✱ é ♥❡❝❡ssár✐♦ ♠❡①❡r ❝♦♠ ❛s ♣❡rs♣❡❝t✐✈❛ ❞❡st❡s ❛❧✉♥♦s✳ ❆❧é♠ ❞✐ss♦✱ ♦ ♣r♦❢❡ss♦r ❛✐♥❞❛ ❡♥❢r❡♥t❛rá ♦ ❢❛t♦ ❞❡ q✉❡ ❡st❡s ❛❧✉♥♦s ♥ã♦ s❡ ❡①♣r❡ss❛♠ ❝♦♠♦ ❛❧✉♥♦s ❞❡ ③♦♥❛ ✉r❜❛♥❛✱ ♣r❛ ❡❧❡s sã♦ ♥❛t✉r❛❧ ♥ã♦ ❡♥t❡♥❞❡r ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❝♦♥t❡ú❞♦✳ ❆❧❣✉♥s ♣r❡❢❡r❡♠ ✜❝❛r ❡♠ s✐❧ê♥❝✐♦ q✉❡ ♣❡r❣✉♥t❛r ❛❧❣♦ q✉❡ t❡✈❡ ❞ú✈✐❞❛✱ s❡❥❛ ♣♦r ♠❡❞♦ ❞♦ ♣r♦❢❡ss♦r✱ ♠❡❞♦ ❞♦ q✉❡ ♦s ❝♦❧❡❣❛s ✐rã♦ ♣❡♥s❛r ♦✉ s✐♠♣❧❡s♠❡♥t❡ t✐♠✐❞❡③✳
❊❞✉❝❛çã♦ ♥❛ ❩♦♥❛ ❘✉r❛❧ ✷✸
❜❛✐①❛r ♦ ♥í✈❡❧ ❞❛s ❛✉❧❛s✱ ♣❛r❛ q✉❡ ❡st❡s ♣♦ss❛♠ ❛❝♦♠♣❛♥❤❛r✳ P❛r❛ ❡❧❡s✱ ❛❧❣✉é♠ q✉❡ ❝♦♥s❡❣✉❡ ❞♦♠✐♥❛r ❛ ♠❛t❡♠át✐❝❛ é ♠✉✐t♦ ✐♥t❡❧✐❣❡♥t❡✱ s❡♥❞♦ ✐♠♣♦ssí✈❡❧ t❛❧ ❢❛ç❛♥❤❛✳ ❈❛r✲ ✈❛❧❤♦ ✭✶✾✾✹✮ ❡♠ s❡✉ ❧✐✈r♦ ▼❡t♦❞♦❧♦❣✐❛ ❞♦ ❊♥s✐♥♦ ❞❛ ▼❛t❡♠át✐❝❛ ❢❛❧❛✿
✏ ❖✉tr❛ ❝♦♥s❡q✉ê♥❝✐❛ ❡✱ t❛❧✈❡③✱ ❛ ❞❡ r❡s✉❧t❛❞♦s ♠❛✐s ♥❡❢❛st♦s✱ é ❛ ❞❡ q✉❡ ♦ s✉❝❡ss♦ ❡♠ ▼❛t❡♠át✐❝❛ r❡♣r❡s❡♥t❛ ❝r✐tér✐♦ ❛✈❛❧✐❛❞♦r ❞❛ ✐♥t❡❧✐❣ê♥❝✐❛ ❞♦s ❛❧✉♥♦s✱ ♥❛ ♠❡❞✐❞❛ ❡♠ q✉❡ ✉♠❛ ❝✐ê♥❝✐❛ tã♦ ♥♦❜r❡ ❡ ♣❡r❢❡✐t❛ só ♣♦❞❡ s❡r ❛❝❡ssí✈❡❧ ❛ ♠❡♥t❡s ♣r✐✈✐❧❡❣✐❛❞❛s✱ ♦s ❝♦♥t❡ú❞♦s ♠❛t❡♠át✐❝♦s sã♦ ❛❜str❛t♦s ❡ ♥❡♠ t♦❞♦s tê♠ ❝♦♥❞✐çõ❡s ❞❡ ♣♦ss✉í✲❧♦s✳✑
❖s ❛❧✉♥♦s ❛❝❤❛♠ ❛s q✉❡stõ❡s ♠✉✐t♦ ❞✐❢í❝❡✐s ❡ s❡ ♣♦r ❛❝❛s♦ ♦ ♣r♦❢❡ss♦r ❢❛❧❛r q✉❡ é ❢á❝✐❧✱ q✉❡ ❡❧❡s só ♣r❡❝✐s❛♠ tr❡✐♥❛r ✉♠ ♣♦✉❝♦ ♠❛✐s✱ ❛ r❡s♣♦st❛ ❞❡❧❡s é s❡♠♣r❡ ❛ ♠❡s♠❛✿ ✧❋á❝✐❧ ♣❛r❛ ♦ s❡♥❤♦r✱ q✉❡ s❛❜❡ ❞❡ t✉❞♦✳✧▼❛♥❞❛r ❞❡✈❡r❡s ♣❛r❛ ❝❛s❛ t❛♠❜é♠ é q✉❛s❡ ✐♥út✐❧✱ ♣♦✉❝♦s tê♠ ❛ t❡♥❞ê♥❝✐❛ ❞❡ ❡st✉❞❛r ❡♠ ❝❛s❛✱ s❡❥❛ ♣♦r t❡r ♦❜r✐❣❛çõ❡s ❛ ❢❛③❡r ♦✉ ♣♦r ♣r❡❣✉✐ç❛✳ ❆❧é♠ ❞✐ss♦✱ sã♦ ♣♦✉❝♦s ♦s ♣❛✐s q✉❡ s❡ ♣r❡♦❝✉♣❛♠ ❡♠ s❛❜❡r ❝♦♠♦ ❡stá ♦ r❡♥❞✐♠❡♥t♦ ❞♦ s❡✉ ✜❧❤♦✱ ❡♠ ♦❧❤❛r ♦ ❝❛❞❡r♥♦ ❞❡st❡s ♣❛r❛ s❛❜❡r s❡ t❡♠ ❛❧❣♦ ❛ s❡r ❢❡✐t♦ ♦✉ ♠❡s♠♦ ✈✐s✐t❛r ❛ ❡s❝♦❧❛ ♣❛r❛ ❝♦♥✈❡rs❛r ❝♦♠ ❛ ❞✐r❡çã♦ ❡ ♦s ♣r♦❢❡ss♦r❡s✳ ◆❛s r❡✉♥✐õ❡s ❝♦♠ ♦s ♣❛✐s✱ ❛♣❛r❡❝❡♠ ♣♦✉❝❛s ♣❡ss♦❛s ❡ ❛s q✉❡ ❛♣❛r❡❝❡♠ sã♦ ♣❛✐s ❞❛q✉❡❧❡s ♠❡❧❤♦r❡s ❛❧✉♥♦s✳
➱ ♥❡❝❡ssár✐❛ ✉♠❛ ❝♦♥s❝✐❡♥t✐③❛çã♦ ❞❡st❛s ❢❛♠í❧✐❛s ❞❛ ③♦♥❛ r✉r❛❧✱ ❢❛③❡r ❝♦♠ q✉❡ ❡❧❡s ❡♥t❡♥❞❛♠ q✉❡ s♦♠❡♥t❡ ✉♠❛ ❜♦❛ ❡❞✉❝❛çã♦ ♠❡❧❤♦r❛rá ❛ q✉❛❧✐❞❛❞❡ ❞❡ ✈✐❞❛s ❞♦s s❡✉s ✜❧❤♦s✳ ▼♦str❛r ❛ ❡❧❡s ❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ✉♠❛ ❝r✐❛♥ç❛ q✉❡ t❡♠ t♦t❛❧ ✐♥t❡r❡ss❡ ♥❛ ❡s❝♦❧❛ ❡ ♦✉tr❛ q✉❡ ✈❛✐ s❡♠ ♥❡♥❤✉♠❛ ❛♠❜✐çã♦✱ ♠♦str❛r q✉❡ ♥❛ ✈✐❞❛ ❛❞✉❧t❛ ❡st❡ ✐♥t❡r❡ss❡ ♥❛ ❡s❝♦❧❛ ❢❛rá t♦❞❛ ❛ ❞✐❢❡r❡♥ç❛✳ ▼❡s♠♦ ❝♦♠ ♦ ❛❝❡ss♦ ❛ ✐♥❢♦r♠❛çã♦ tã♦ ❢á❝✐❧ ❛✐♥❞❛ ❡①✐st❡ ❢❛♠í❧✐❛s ♥❛ ③♦♥❛ r✉r❛❧ ❝♦♠ ♣❡♥s❛♠❡♥t♦s ❛tr❛s❛❞♦s✱ ❛❝❤❛♠ q✉❡ s✉❛s ❝r✐❛♥ç❛s ❞❡✈❡♠ ❝♦♥t✐♥✉❛r ❛ ✈✐❞❛ ❞❡ s❡✉s ♣❛✐s✱ s❡♥❞♦ tr❛❜❛❧❤❛❞♦r❡s ❜r❛ç❛✐s ♦✉ tr❛❜❛❧❤❛r ♣❛r❛ ❛❧❣✉♠ ❣r❛♥❞❡ ❢❛③❡♥❞❡✐r♦✳ ◗✉❛♥t♦ ❛ ✐ss♦✱ ❛t✐✈✐❞❛❞❡s ❝♦♠♦ ❡st❛s q✉❡ s❡rã♦ ♠♦str❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦ é ❡ss❡♥❝✐❛❧ ♣❛r❛ ♠✉❞❛r ❡ss❡s ♣❡♥s❛♠❡♥t♦s✱ ♦ ❛❧✉♥♦ ❝❤❡❣❛♥❞♦ ❡♠ ❝❛s❛ ❝♦♠ ❛❧❣♦ ♣❛r❛ ♠♦str❛r ❛ s✉❛ ❢❛♠í❧✐❛ ♣♦❞❡rá ❝♦♥✈❡♥❝ê✲❧♦s ❞❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ ✉♠❛ ❜♦❛ ❡❞✉✲ ❝❛çã♦✳ ◗✉❛♥❞♦ ❛ ❡ss❡ ❢❡❡❞❜❛❝❦✱ ▼♦②sés ✭✶✾✾✼✮ ❢❛❧❛✿
✏❆♦ q✉❡ ♣❛r❡❝❡✱ ♥ã♦ ❤á ♠✉✐t❛ ❝♦♥t✐♥✉✐❞❛❞❡ ❡♥tr❡ ♦ q✉❡ s❡ ❛♣r❡♥❞❡ ♥❛ ❡s❝♦❧❛ ❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ q✉❡ ❡①✐st❡ ❢♦r❛ ❞❡❧❛✳ ❍á ❝r❡s❝❡♥t❡ ❡✈✐❞ê♥❝✐❛ ❞❡ q✉❡ ❛ ❡s❝♦❧❛r✐③❛çã♦ ❡stá ❝♦♥tr✐❜✉✐♥❞♦ ♠✉✐t♦ ♣♦✉❝♦ ♣❛r❛ ♦ ❞❡s❡♠♣❡♥❤♦ ❢♦r❛ ❞❡❧❛ ❡s❝♦❧❛✳ ❉✐✜❝✐❧♠❡♥t❡ s❡ ♠♦str❛ ♣❛r❛ ♦ ❛❧✉♥♦ ❛ r❡❧❛çã♦ ❞✐r❡t❛ ❡ ó❜✈✐❛ q✉❡ ❤á ❡♥tr❡ ❛ ❡s❝♦❧❛ ❡ ❛ ✈✐❞❛✳✑
✷✹ ❊♥s✐♥♦ ❞❡ ▼❛t❡♠át✐❝❛ ♥❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛
✸ ❆♣❧✐❝❛çã♦ ❉✐❞át✐❝❛
✸✳✶ ■♥tr♦❞✉çã♦
❈♦♠♦ ❞✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ✉♠❛ ❛✉❧❛ ❞✐❢❡r❡♥t❡ é ❝❛♣❛③ ❞❡ ❢❛③❡r ♠✐❧❛❣r❡s ♥♦ q✉❡ s❡ r❡❢❡r❡ ❛ ♣r❡♥❞❡r ❛t❡♥çã♦ ❞♦s ❛❧✉♥♦s✳ ❯♠❛ s✐♠♣❧❡s ❜r✐♥❝❛❞❡✐r❛ ❡♥tr❡ ❡❧❡s ♣♦❞❡ r❡s✉❧t❛r ❡♠ ✉♠ ❡♥♦r♠❡ ❛♣r❡♥❞✐③❛❞♦✱ q✉❡ ♥ã♦ s❡r✐❛ ♣♦ssí✈❡❧ ❡♠ ✉♠❛ ❛✉❧❛ tr❛❞✐❝✐♦♥❛❧✳ ❆ ❛♣❧✐✲ ❝❛çã♦ ❞❡s❝r✐t❛ ❛q✉✐ ❢♦✐ ❜❛s❡❛❞❛ ♥❛ ❡①♣❧❛♥❛❞❛ ♥♦ ❧✐✈r♦ ▼❡✉ ♣r♦❢❡ss♦r ❞❡ ▼❛t❡♠át✐❝❛ ❡ ♦✉tr❛s ❍✐stór✐❛s✱ ❞❡ ❊❧♦♥ ▲❛❣❡s ▲✐♠❛✳ ➱ ✉♠❛ ❜r✐♥❝❛❞❡✐r❛ q✉❡ ✈✐s❛ ❛ ❝♦♠♣❡t✐çã♦ ❡♥tr❡ ❞♦✐s ❣r✉♣♦s ❡♠ ✉♠❛ ♠❡s♠❛ s❛❧❛ ❞❡ ❛✉❧❛✳ ❋♦✐ ❢❡✐t♦ ♣❡q✉❡♥❛s ❛❞❛♣t❛çõ❡s✱ ♠❛s ♦ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ é ♦ ♠❡s♠♦✳ ❯t✐❧✐③❛♥❞♦✲s❡ ❞❡ss❡ ❥♦❣♦✱ ♦s ❛❧✉♥♦s t❡rã♦ ✉♠❛ ♠♦t✐✈❛çã♦ ❛ ♠❛✐s ♣❛r❛ ❡st✉❞❛r✱ ♣♦✐s ❝❛s♦s ❝♦♥trár✐♦s ♣r❡❥✉❞✐❝❛rã♦ ♦ t✐♠❡ ❛ q✉❛❧ ♣❛rt✐❝✐♣❛♠✱ ❡ ❡st❛rã♦ ❛t❡♥t♦s ❛ r❡s♦❧✉çã♦ ❞♦s ❡①❡r❝í❝✐♦s✱ ♣♦✐s só ❛ss✐♠ s❛❜❡rã♦ q✉❡♠ ❢♦✐ ♦ ✈❡♥❝❡❞♦r ❡♠ ❝❛❞❛ ❡t❛♣❛✳
✸✳✷ ❆ ❊s❝♦❧❛
❋✐❣✉r❛ ✸✳✶✿ ❯♥✐❞❛❞❡ ❊s❝♦❧❛r ❉❡s❡♠❜❛r❣❛❞♦r ❖❞✐❧♦ ❈♦st❛ ❋✐❧❤♦
✷✻ ❆♣❧✐❝❛çã♦ ❉✐❞át✐❝❛
❆ ❛t✐✈✐❞❛❞❡ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞❛ ♥❛ ❯♥✐❞❛❞❡ ❊s❝♦❧❛r ❉❡s❡♠❜❛r❣❛❞♦r ❖❞✐❧♦ ❈♦st❛ ❋✐✲ ❧❤♦✱ ❡s❝♦❧❛ ❞♦ ♠✉♥✐❝í♣✐♦ ❞❡ ❚✐♠♦♥✱ ▼❛r❛♥❤ã♦✱ s✐t✉❛❞❛ ♥♦ ❜❛✐rr♦ ❙ã♦ ❇❡♥❡❞✐t♦✱ ❘✉❛ ❙ã♦ ❏♦ã♦✱ s✴♥✳ ❊st❛ ❡s❝♦❧❛ ❢♦✐ ✐♥❛✉❣✉r❛❞❛ ♥♦ ❞✐❛ ✵✷ ❞❡ ❛❜r✐❧ ❞❡ ✶✾✼✹✱ ♥❛ ❣❡stã♦ ❞♦ ♣r❡❢❡✐t♦ ◆❛♣♦❧❡ã♦ ●✉✐♠❛rã❡s✳ ❋♦r♠❛❞❛ ❛♣❡♥❛s ♣♦r q✉❛tr♦ s❛❧❛s ❡ ♣♦ss✉✐♥❞♦ ♣♦✉❝♦s ❢✉♥❝✐♦♥ár✐♦s✱ ❛ ❡s❝♦❧❛ ❡r❛ ♣❡q✉❡♥❛✱ ♣♦ré♠ ❡♠ ✶✾✼✼ ❛ ❡s❝♦❧❛ ♣❛ss♦✉ ❛ ♣❡rt❡♥❝❡r ❛♦ ❡st❛❞♦✱ ♣❛ss❛♥❞♦ ❛ss✐♠ ♣♦r ✉♠❛ ❣r❛♥❞❡ r❡❢♦r♠❛ q✉❡ r❡s✉❧t♦✉ ♥❛ ❝♦♥str✉çã♦ ❞❡ ♠❛✐s ❝✐♥❝♦ s❛❧❛s✱ ✉♠ ♣át✐♦ ❛♠♣❧♦✱ ✉♠❛ s❛❧❛ ♣❛r❛ ♣r♦❢❡ss♦r❡s ❡ ♠❛✐s ❜❛♥❤❡✐r♦s✳
◆♦ ❞❡❝♦rr❡r ❞♦s ❛♥♦s ♦ ♣ré❞✐♦ ❝r❡s❝❡✉ ❛✐♥❞❛ ♠❛✐s ❝♦♠ ❛ ✐♠♣❧❛♥t❛çã♦ ❞❛ ♣ré✲❡s❝♦❧❛ ♥♦ s✐st❡♠❛ ❡❞✉❝❛❝✐♦♥❛❧ ❞♦ ❡st❛❞♦✱ ❣❛♥❤♦✉ ❞♦✐s ❣❛❧♣õ❡s ❡q✉✐♣❛❞♦s ❞❡ ❜❛♥❤❡✐r♦s ♠❛s❝✉❧✐♥♦s ❡ ❢❡♠✐♥✐♥♦s✱ ❝❛♥t✐♥❛❀ ❡s♣❛ç♦ ❡st❡ q✉❡ ❝♦♥❢♦r♠❡ ❛✉t♦r✐③❛çã♦ ❞♦ ❈♦♥s❡❧❤♦ ❊st❛❞✉❛❧ ❞❡ ❊❞✉❝❛çã♦ r❡❝❡❜❡✉ ♦ ♥♦♠❡ ❞❡ ✧❏❛r❞✐♠ ❞❡ ■♥❢â♥❝✐❛ ▼♦r❛♥❣✉✐♥❤♦✧✱ ❢✉♥❝✐♦♥❛♥❞♦ ❞♦ ✶♦
❛♦ ✸♦ ♣❡rí♦❞♦ ♥♦s t✉r♥♦s ♠❛t✉t✐♥♦ ❡ ✈❡s♣❡rt✐♥♦ ❛té ❤♦❥❡❀ só q✉❡ ❛♦s ♣♦✉❝♦s ❡stá s❡♥❞♦
❡❧✐♠✐♥❛❞♦✱ ♣♦✐s ♥ã♦ é ♠❛✐s ❞❛ ❛❧ç❛❞❛ ❞♦ ❊st❛❞♦ ❡st❛ ♠♦❞❛❧✐❞❛❞❡ ❞❡ ❡♥s✐♥♦✱ t❛♥t♦ q✉❡ ✉♠ ❞♦s ❣❛❧♣õ❡s ❢♦✐ tr❛♥s❢♦r♠❛❞♦ ❡♠ r❡❢❡✐tór✐♦ ❛❣♦r❛ ♥♦ ❛♥♦ ❞❡ ✷✵✵✵✳
❆ ❡s❝♦❧❛ ♣♦ss✉✐ ✉♠ ❡s♣❛ç♦ ❢ís✐❝♦ ♠✉✐t♦ ❜♦♠✱ ♣♦✐s ♣♦ss✉✐ só ❞❡ ár❡❛ ❝♦❜❡rt❛ ♠❛✐s ❞❡ ♠✐❧ ♠❡tr♦s q✉❛❞r❛❞♦s✱ s❡♥❞♦ ❛ss✐♠ ❞✐str✐❜✉í❞♦s✿ ✶✶ s❛❧❛s ❞❡ ❛✉❧❛✱ ✵✶ s❛❧❛ ❞❡ ♣r♦❢❡ss♦r❡s✱ ✵✶ s❛❧❛ ❞❡ ✈í❞❡♦✱ ✵✶ s❛❧❛ ❞❡ ❧❡✐t✉r❛✱ ✵✺ ❜❛♥❤❡✐r♦s✱ ✵✶ ❞✐r❡t♦r✐❛✱ ✵✶ r❡❢❡✐tór✐♦ ♦✉ ❝❛♥t✐♥❛✱ ✵✶ ♣át✐♦✱ ✵✶ t❡rr❛ç♦ ♦♥❞❡ ❢✉♥❝✐♦♥❛ ❛ s❡❝r❡t❛r✐❛ ❡ ❛ r❡❝❡♣çã♦✱ ✵✶ q✉❛❞r❛ ❞❡ ❡s♣♦rt❡s✳
◆♦ ❛♥♦ ✷✵✶✹ ❡ss❛ ❡s❝♦❧❛ ♣❛ss♦✉ s❡r ❞❡ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❞♦ ▼✉♥✐❝í♣✐♦ ❞❡ ❚✐♠♦♥✱ ❡♠ q✉❡ ♦ q✉❛❞r♦ ❞❡ ❢✉♥❝✐♦♥ár✐♦s é ❞❛ r❡❞❡ ♠✉♥✐❝✐♣❛❧✳ ❘❡❝❡♥t❡♠❡♥t❡ ♣❛ss♦✉ ♣♦r ✉♠❛ r❡❢♦r♠❛ ♥❛ q✉❛❧ ❢♦✐ ❝❧✐♠❛t✐③❛❞❛ ♣❛r❛ ♠❡❧❤♦r ❛t❡♥❞❡r ♦s ❛❧✉♥♦s✳ ❆ ❡s❝♦❧❛ ♣♦ss✉✐ ❤♦❥❡ ✉♠ t♦t❛❧ ❞❡ ✺✼✷ ❛❧✉♥♦s✱ ❞✐str✐❜✉í❞♦s ♥♦s t✉r♥♦s ♠❛♥❤ã✱ t❛r❞❡ ❡ ♥♦✐t❡ ❝♦♠ ❛s ♠♦❞❛❧✐❞❛❞❡s ❞❡ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧ ❘❡❣✉❧❛r ❡ ❊❏❆✳
✸✳✸ ❉✐♥â♠✐❝❛ ❞♦ ❏♦❣♦
❏✉st✐✜❝❛t✐✈❛ ✷✼
❛ ♣♦♥t✉❛çã♦ ♥ã♦ ❞❡✈❡ s❡r ❛ ♠❡s♠❛✱ ♥❛ ❛♣❧✐❝❛çã♦ ❢♦✐ ❞❛❞♦ ♣♦♥t✉❛çã♦ ✵✶ ✭✉♠✮✳ ◆ã♦ ❞❡✈❡ ❤❛✈❡r ❧✐♠✐t❡ ❞♦ ♥ú♠❡r♦ ❞❡ ✈❡③❡s q✉❡ ✉♠ ♠❡s♠♦ ❛❧✉♥♦ s✉❜st✐t✉✐ ♦ ❝♦❧❡❣❛ ❞❡ ❣r✉♣♦✱ ♣♦ré♠ ❡♠ ❝❛❞❛ r♦❞❛❞❛ só ❞❡✈❡ ❤❛✈❡r ✉♠❛ s✉❜st✐t✉✐çã♦ ❡♠ ❝❛❞❛ ❣r✉♣♦✳ ❙❡ ♦ ❛❧✉♥♦ r❡s♣♦♥❞❡r ❡rr❛❞♦✱ ♣♦♥t✉❛çã♦ ✵✵ ✭③❡r♦✮✳ ❙❡ ❛❧❣✉♠ ✐♥t❡❣r❛♥t❡ ❞♦s ❣r✉♣♦s ❢❛❧❛r ❛ r❡s♣♦st❛ ♣❛r❛ ♦ ❛❧✉♥♦ ❡s❝♦❧❤✐❞♦ ♣❛r❛ r❡s♣♦♥❞❡r ♦ ♣r♦❜❧❡♠❛✱ ♦ ❣r✉♣♦ ✜❝❛ ❝♦♠ ♣♦♥t✉❛çã♦ ✵✵ ✭③❡r♦✮✳ ❱❡♥❝❡ ♦ ❥♦❣♦ ❛ ❡q✉✐♣❡ q✉❡ t✐✈❡r ❛ ♠❛✐♦r ♣♦♥t✉❛çã♦ ♥♦ ✜♥❛❧ ❞❛ ❞✐s♣✉t❛✳ ❈❛s♦ ❞❡s❡❥❡✱ s❡r✐❛ ✉♠❛ ❜♦❛ ✐❞❡✐❛ ♣r❡s❡♥t❡❛r ♦s ✈❡♥❝❡❞♦r❡s✱ ♣❛r❛ ❞❛r ✉♠❛ ♠♦t✐✈❛çã♦ ❛ ♠❛✐s✱ ♠❡s♠♦ q✉❡ s❡❥❛ ❝♦♠ ❝♦✐s❛s ❜❡♠ s✐♠♣❧❡s✳
✸✳✹ ❏✉st✐✜❝❛t✐✈❛
◗✉❛♥❞♦ ♦ ♣r♦❢❡ss♦r ♣r❡♣❛r❛ ❛❧❣♦ ❝♦♠♦ ♦ ❥♦❣♦ ❛❝✐♠❛ ♠❡♥❝✐♦♥❛❞♦✱ ❛❧é♠ ❞❡ r❡♣❛ss❛r ❞❡ ❢♦r♠❛ ♠❛✐s ❢á❝✐❧ ♦ ❝♦♥t❡ú❞♦ ❞✐❞át✐❝♦ ♦♥❞❡ ❝♦♥s❡❣✉❡ ✉♠❛ ♠❛✐♦r ❛t❡♥çã♦ ❞♦ ❛❧✉♥♦✱ ♦ ♣r♦❢❡ss♦r ❝♦♥s❡❣✉❡ ✉♠❛ ♠❛✐♦r ❛❞♠✐r❛çã♦ ❞♦ ❛❧✉♥♦✱ ❡❧❡s r❡s♣❡✐t❛♠ ♠❛✐s ❛ ♠❡t♦❞♦❧♦❣✐❛ ❞♦ ♣r♦❢❡ss♦r✱ ♠❡s♠♦ q✉❡ ❡❧❡ ✈♦❧t❡ às ❛✉❧❛s tr❛❞✐❝✐♦♥❛✐s✳ ❆❧❣♦ ❞❡st❡ t✐♣♦ ♣♦❞❡ s❡r ❝r✉❝✐❛❧ ♣❛r❛ ♦ ❛♣r❡♥❞✐③❛❞♦ ❞♦ ❛❧✉♥♦ ❡ ❡❧❡s ✈ã♦ q✉❡r❡r s❡♠♣r❡ ❛❧❣♦ ♣❛r❡❝✐❞♦✳
❊♠ ✉♠❛ t✉r♠❛ ❝♦♠ ♠❛✐s ❞❡ ✸✵ ❛❧✉♥♦s✱ ❝❛s♦ ♥ã♦ s❡❥❛ ❛❞♦t❛❞❛s ♠❡t♦❞♦❧♦❣✐❛s ❛❧t❡r✲ ♥❛t✐✈❛s✱ ♦ ❝♦♥tr♦❧❡ ❞♦s ❛❧✉♥♦s ✜❝❛ ♣r❛t✐❝❛♠❡♥t❡ ✐♠♣♦ssí✈❡❧✱ ❛✐♥❞❛ ♠❛✐s s❡ s❡ tr❛t❛r ❞❡ ✉♠❛ ❡s❝♦❧❛ ♣ú❜❧✐❝❛✱ ♦♥❞❡ ♥ã♦ sã♦ tã♦ ❝♦❜r❛❞♦s ❝♦♠♦ ❛❧✉♥♦s ❡♠ ❡s❝♦❧❛s ♣❛rt✐❝✉❧❛r❡s ♦✉ ❡s❝♦❧❛s ♣ú❜❧✐❝❛s ❝♦♠ ✉♠❛ ❜♦❛ ❛❞♠✐♥✐str❛çã♦✳
✸✳✺ ❈♦♥❝❧✉sçã♦
◆❛ ❡①♣❡r✐ê♥❝✐❛ ❡①♣❧❛♥❛❞❛ ❛❝✐♠❛✱ ❢♦r❛♠ ❢♦r♠❛❞♦ ❞♦✐s ❣r✉♣♦s✿ ✉♠ ❢♦r♠❛❞♦ ♣❡❧♦s ♠❡♥✐♥♦s ❡ ♦✉tr♦ ♣❡❧❛s ♠❡♥✐♥❛s✳ ❖ t❡♠♣♦ ♣❛r❛ ❝❛❞❛ r❡s♣♦st❛ ❡r❛ ❞❡ ✵✷ ✭❞♦✐s✮ ♠✐♥✉t♦s ❡ ❛ ♣♦♥t✉❛çã♦ ❢♦✐ ❝♦♠♦ ❛ ❞❡s❝r✐t❛ ❛♥t❡r✐♦r♠❡♥t❡✳ ❆♦ ✜♥❛❧ ❞❡ ✾✵ ✭♥♦✈❡♥t❛✮ ♠✐♥✉t♦s ❞❡ ❞✐s♣✉t❛✱ ♦s ♠❡♥✐♥♦s ❞❛ s❛❧❛ s❛ír❛♠ ✈✐t♦r✐♦s♦s✱ ❝♦♠ ❝❡rt❛ ✈❛♥t❛❣❡♠ ❡♠ r❡❧❛çã♦ às ♠❡♥✐♥❛s✳ ❋♦✐ ♥♦tá✈❡❧ ❛ t✐♠✐❞❡③ ❞❡ ❛❧❣✉♠❛s ♠❡♥✐♥❛s ❡♠ ✐r ❛té ❛ ❢r❡♥t❡ r❡s♣♦♥❞❡r ❛s q✉❡stõ❡s✱ ❡♥q✉❛♥t♦ q✉❡ ♦s ♠❡♥✐♥♦s ♥ã♦ t✐✈❡r❛♠ ❛ ♠❡♥♦r ❞✐✜❝✉❧❞❛❞❡✳ ❉❡♣♦✐s ❞❡ ❡♥❝❡rr❛❞♦s ♦s tr❛❜❛❧❤♦s✱ ♦s ❛❧✉♥♦s ❢♦r❛♠ ❧✐❜❡r❛❞♦s ♣❛r❛ ♦ ❧❛♥❝❤❡✳
✹ ❆ ❚r✐❣♦♥♦♠❡tr✐❛
✹✳✶ ■♥tr♦❞✉çã♦
❆ ♣❛❧❛✈r❛ ❚r✐❣♦♥♦♠❡tr✐❛ é ❢♦r♠❛❞❛ ♣♦r três r❛❞✐❝❛✐s ❣r❡❣♦s ✭tr✐→ três✱ ❣♦♥♦s → â♥❣✉❧♦s✱ ♠❡tr♦♥ →♠❡❞✐r✮✱ ❞❛í s❡✉ s✐❣♥✐✜❝❛❞♦✿ ♠❡❞✐❞❛s ❞♦s tr✐â♥❣✉❧♦s✳ ❆ tr✐❣♦♥♦♠❡✲ tr✐❛ é ♦ r❛♠♦ ❞❛ ▼❛t❡♠át✐❝❛ q✉❡ ❡st✉❞❛ ❛ r❡❧❛çã♦ ❡♥tr❡ ♦s â♥❣✉❧♦s ✐♥t❡r♥♦s ❡ ♦s ❧❛❞♦s ❞❡ ✉♠ tr✐â♥❣✉❧♦✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❡st✉❞❛r❡♠♦s ❛ ❚r✐❣♦♥♦♠❡tr✐❛ ♥♦ tr✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦ ❡ s✉❛s ❛♣❧✐❝❛çõ❡s✱ ❥á q✉❡ ♦ t♦❞♦ ♦ tr❛❜❛❧❤♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❡♠ ✉♠❛ t✉r♠❛ ❞❡ ✾♦ ❛♥♦ ❞♦
❡♥s✐♥♦ ❜ás✐❝♦✳ ❆♥t❡s ❞❡ ❝♦♠❡ç❛r♠♦s ♥♦ss♦ tr❛❜❛❧❤♦ ❡♠ s❡✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ ❝♦♥❤❡❝❡r ✉♠ ♣♦✉❝♦ ❞❛ ❤✐stór✐❛ ❞❛ tr✐❣♦♥♦♠❡tr✐❛✳
✹✳✷ ❈♦♥t❡①t♦ ❍✐stór✐❝♦
❆ tr✐❣♦♥♦♠❡tr✐❛ ♥ã♦ é ♦❜r❛ ❞❡ ✉♠ só ❤♦♠❡♠ ♦✉ ♥❛çã♦✳ ❆ s✉❛ ❤✐stór✐❛ t❡♠ ♠✐✲ ❧❤❛r❡s ❞❡ ❛♥♦s ❡ ❢❛③ ♣❛rt❡ ❞❡ t♦❞❛s ❛s ❣r❛♥❞❡s ❝✐✈✐❧✐③❛çõ❡s✳ ❉❡✈❡ s❡r ♥♦t❛❞♦ q✉❡✱ ❞❡s❞❡ ♦s t❡♠♣♦s ❞❡ ❍✐♣❛r❝♦ ❛té ♦s t❡♠♣♦s ♠♦❞❡r♥♦s✱ ♥ã♦ ❤❛✈✐❛ t❛❧ ❝♦✐s❛ ❝♦♠♦ ✧r❛✲ ③ã♦✧tr✐❣♦♥♦♠étr✐❝❛✳ ❆♦ ✐♥✈és ❞✐ss♦✱ ♦s ❣r❡❣♦s ❡ ❞❡♣♦✐s ♦s ❤✐♥❞✉s ❡ ♦s ♠✉ç✉❧♠❛♥♦s ✉s❛✲ r❛♠ ❧✐♥❤❛s tr✐❣♦♥♦♠étr✐❝❛s✳ ❊ss❛s ❧✐♥❤❛s ♣r✐♠❡✐r♦ t♦♠❛r❛♠ ❛ ❢♦r♠❛ ❞❡ ❝♦r❞❛s ❡ ♠❛✐s t❛r❞❡ ♠❡✐❛s ❝♦r❞❛s✱ ♦✉ s❡♥♦s✳ ❊ss❛s ❝♦r❞❛s ❡ ❧✐♥❤❛s ❞❡ s❡♥♦s ❡♥tã♦ s❡r✐❛♠ ❛ss♦❝✐❛❞❛s ❛ ✈❛❧♦r❡s ♥✉♠ér✐❝♦s✱ ♣♦ss✐✈❡❧♠❡♥t❡ ❛♣r♦①✐♠❛çõ❡s ❡ ❧✐st❛❞♦s ❡♠ t❛❜❡❧❛s tr✐❣♦♥♦♠étr✐❝❛s✳
❆ ♦r✐❣❡♠ ❞❛ tr✐❣♦♥♦♠❡tr✐❛ é ✐♥❝❡rt❛✳ ❊♥tr❡t❛♥t♦✱ ♣♦❞❡✲s❡ ❞✐③❡r q✉❡ ♦ ✐♥í❝✐♦ ❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ tr✐❣♦♥♦♠❡tr✐❛ s❡ ❞❡✉ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞❡✈✐❞♦ ❛♦s ♣r♦❜❧❡♠❛s ❣❡r❛❞♦s ♣❡❧❛ ❆str♦♥♦♠✐❛✱ ❆❣r✐♠❡♥s✉r❛ ❡ ◆❛✈❡❣❛çõ❡s✱ ♣♦r ✈♦❧t❛ ❞♦ sé❝✉❧♦ ■❱ ♦✉ ❱ ❛✳❈✳✱ ❝♦♠ ♦s ❡❣í♣❝✐♦s ❡ ❜❛❜✐❧ô♥✐♦s✳ ➱ ♣♦ssí✈❡❧ ❡♥❝♦♥tr❛r ♣r♦❜❧❡♠❛s ❡♥✈♦❧✈❡♥❞♦ ❛ ❝♦t❛♥❣❡♥t❡ ♥♦ P❛✲ ♣✐r♦ ❘❤✐♥❞ ❡ t❛♠❜é♠ ✉♠❛ ♥♦tá✈❡❧ tá❜✉❛ ❞❡ s❡❝❛♥t❡s ♥❛ tá❜✉❧❛ ❝✉♥❡✐❢♦r♠❡ ❜❛❜✐❧ô♥✐❝❛ P❧✐♠♣t♦♥ ✸✷✷✳ ◆ã♦ s❡ s❛❜❡ ❛♦ ❝❡rt♦ s❡ ♦ ❝♦♥❝❡✐t♦ ❞❛ ♠❡❞✐❞❛ ❞❡ â♥❣✉❧♦ s✉r❣✐✉ ❝♦♠ ♦s ❣r❡❣♦s ♦✉ s❡ ❡❧❡s✱ ♣♦r ❝♦♥t❛t♦ ❝♦♠ ❛ ❝✐✈✐❧✐③❛çã♦ ❜❛❜✐❧ô♥✐❝❛✱ ❛❞♦t❛r❛♠ s✉❛s ❢r❛çõ❡s s❡①❛✲ ❣❡s✐♠❛✐s✳ ▼❛s ♦s ❣r❡❣♦s ✜③❡r❛♠ ✉♠ ❡st✉❞♦ s✐st❡♠át✐❝♦ ❞❛s r❡❧❛çõ❡s ❡♥tr❡ â♥❣✉❧♦s ✲ ♦✉ ❛r❝♦s ✲ ♥✉♠❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ❡ ♦s ❝♦♠♣r✐♠❡♥t♦s ❞❡ s✉❛s ❝♦r❞❛s✳ ◆❛s ♦❜r❛s ❞❡ ❊✉❝❧✐❞❡s ❥á ❡①✐st✐❛♠ t❡♦r❡♠❛s ❡q✉✐✈❛❧❡♥t❡s ❛ ❧❡✐s ♦✉ ❢ór♠✉❧❛s tr✐❣♦♥♦♠étr✐❝❛s✳ ❊♠ ❖s ❡❧❡♠❡♥t♦s✱ ✉♠❛ ❞❛s ♦❜r❛s ♠❛✐s ❝♦♥❤❡❝✐❞❛s ❞❛ ❤✐stór✐❛ ❞❛ ♠❛t❡♠át✐❝❛✱ é ♣♦ssí✈❡❧ ❡♥❝♦♥tr❛r ❛s ❧❡✐s
✸✵ ❆ ❚r✐❣♦♥♦♠❡tr✐❛
❞♦ ❝♦ss❡♥♦ ♣❛r❛ â♥❣✉❧♦s ♦❜t✉s♦s ❡ ❛❣✉❞♦s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♥❛s Pr♦♣♦s✐çõ❡s ■■✳✶✷ ❡ ■■✳✶✸✱ ♣♦ré♠ ❡♥✉♥❝✐❛❞❛s ❡♠ ❧✐♥❣✉❛❣❡♠ ❣❡♦♠étr✐❝❛✳ P♦ré♠✱ ❢♦✐ ♦ ❛strô♥♦♠♦ ❍✐♣❛r❝♦ ❞❡ ◆✐❝é✐❛ ✭✶✾✵ ❛✳❈✳ ✲ ✶✷✺ ❛✳❈✳✮ q✉❡♠ ❣❛♥❤♦✉ ♦ ❞✐r❡✐t♦ ❞❡ s❡r ❝❤❛♠❛❞♦ ♦ ♣❛✐ ❞❛ ❚r✐❣♦♥♦♠❡✲ tr✐❛ ♣♦✐s✱ ♥❛ s❡❣✉♥❞❛ ♠❡t❛❞❡ ❞♦ sé❝✉❧♦ ■■ ❛✳❈✳✱ ❢❡③ ✉♠ tr❛t❛❞♦ ❡♠ ❞♦③❡ ❧✐✈r♦s ❡♠ q✉❡ s❡ ♦❝✉♣♦✉ ❞❛ ❝♦♥str✉çã♦ ❞♦ q✉❡ ❞❡✈❡ t❡r s✐❞♦ ❛ ♣r✐♠❡✐r❛ t❛❜❡❧❛ tr✐❣♦♥♦♠étr✐❝❛✱ ✐♥❝❧✉✐♥❞♦ ✉♠❛ tá❜✉❛ ❞❡ ❝♦r❞❛s✳ Pt♦❧♦♠❡✉ ✭✾✵ ❞✳❈✳ ✲ ✶✻✽ ❞✳❈✳✮✱ ♥❛ ♠❡s♠❛ é♣♦❝❛✱ ❛♣r❡s❡♥t♦✉ s✉❛ tá❜✉❛ ❞❡ ❝♦r❞❛s ❝♦♥t❡♥❞♦ ♦ ❝á❧❝✉❧♦ ❞♦ s❡♥♦ ❞♦s â♥❣✉❧♦s ❞❡ ✵♦ ❛ ✾✵♦✱ â♥❣✉❧♦s q✉❡ s❡r✐❛♠
✉t✐❧✐③❛❞♦s ♥♦s ❡st✉❞♦s ❛str♦♥ô♠✐❝♦s ❡♠ q✉❡ ❡❧❡ ❡st❛✈❛ ❡♥❣❛❥❛❞♦✳
❍✐♣❛r❝♦ ❢♦✐ ♦ ♣r✐♠❡✐r♦ ❛ ❝❛❧❝✉❧❛r ❛ ♠❡❞✐❞❛ ❞♦ ❙❡♥♦ ❞❡ ❛❧❣✉♥s â♥❣✉❧♦s✱ s❡♠ ✉s❛r ❡ss❛ ♥♦♠❡♥❝❧❛t✉r❛✱ ❥á ♣❛❧❛✈r❛ ❝♦ss❡♥♦ s✉r❣✐✉ s♦♠❡♥t❡ ♥♦ sé❝✉❧♦ ❳❱■■✱ ❝♦♠♦ s❡♥❞♦ ♦ s❡♥♦ ❞♦ ❝♦♠♣❧❡♠❡♥t♦ ❞❡ ✉♠ â♥❣✉❧♦✳ ❖s ❝♦♥❝❡✐t♦s ❞❡ s❡♥♦ ❡ ❝♦ss❡♥♦ ❢♦r❛♠ ♦r✐❣✐♥❛❞♦s ♣❡❧♦s ♣r♦❜❧❡♠❛s r❡❧❛t✐✈♦s à ❆str♦♥♦♠✐❛✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ❝♦♥❝❡✐t♦ ❞❡ t❛♥❣❡♥t❡✱ ❛♦ q✉❡ ♣❛r❡❝❡✱ s✉r❣✐✉ ❞❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❝❛❧❝✉❧❛r ❛❧t✉r❛s ❡ ❞✐stâ♥❝✐❛s✳ ❖✉tr♦ ♠❛t❡♠át✐❝♦ ❣r❡❣♦✱ ▼❡♥❡❧❛✉ ❞❡ ❆❧❡①❛♥❞r✐❛ ✭✼✵ ❞✳❈✳ ✲ ✶✸✵ ❞✳❈✳✮ ♣r♦❞✉③✐✉ ✉♠ tr❛t❛❞♦ s♦❜r❡ ❝♦r❞❛s ♥✉♠ ❝ír❝✉❧♦✱ ❡♠ s❡✐s ❧✐✈r♦s✱ ♣♦ré♠ ✈ár✐♦s ❞❡❧❡s s❡ ♣❡r❞❡r❛♠✳ ❋❡❧✐③♠❡♥t❡ ♦ s❡✉ tr❛t❛❞♦ ❙♣❤❛❡r✐❝❛ ✱ ❡♠ três ❧✐✈r♦s✱ s❡ ♣r❡s❡r✈♦✉ ♥✉♠❛ ✈❡rsã♦ ár❛❜❡ ❡ é ♦ tr❛❜❛❧❤♦ ♠❛✐s ❛♥t✐❣♦ ❝♦♥❤❡❝✐❞♦ s♦❜r❡ tr✐❣♦♥♦♠❡tr✐❛ ❡s❢ér✐❝❛✳ ▼❛✐s t❛r❞❡✱ ❈❧❛✉❞✐✉s Pt♦❧♦♠❡✉ ❡①♣❛♥❞✐✉ ❛s ❈♦r❞❛s ❡♠ ✉♠ ❈ír❝✉❧♦ ❞❡ ❍✐♣❛r❝♦ ♥♦ s❡✉ ❆❧♠❛❣❡st♦✱ ♦✉ ❛ ❙✐♥t❛①❡ ▼❛t❡♠át✐❝❛✳ ❖s tr❡③❡ ❧✐✈r♦s ❞♦ ❆❧♠❛❣❡st♦ sã♦ ♦s ♠❛✐s ✐♥✢✉❡♥t❡s ❡ s✐❣♥✐✜❝❛t✐✈♦s tr❛❜❛❧❤♦s s♦❜r❡ tr✐❣♦♥♦♠❡tr✐❛ ❞❡ t♦❞❛ ❛ ❛♥t✐❣✉✐❞❛❞❡✳ ❯♠ t❡♦r❡♠❛ ❝❡♥tr❛❧ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛s ❝♦r❞❛s ❞❡ Pt♦❧♦♠❡✉ é ❝♦♥❤❡❝✐❞♦ ❛✐♥❞❛ ❤♦❥❡ ❝♦♠♦ t❡♦r❡♠❛ ❞❡ Pt♦❧♦♠❡✉ ❡ ❞✐③ q✉❡ ❛ s♦♠❛ ❞♦s ♣r♦❞✉t♦s ❞♦s ❧❛❞♦s ♦♣♦st♦s ❞❡ ✉♠ q✉❛❞r✐❧át❡r♦ ❝í❝❧✐❝♦ é ✐❣✉❛❧ ❛♦ ♣r♦❞✉t♦ ❞❛s ❞✐❛❣♦♥❛✐s✳ ❯♠ ❝❛s♦ ❡s♣❡❝✐❛❧ ❞♦ t❡♦r❡♠❛ ❞❡ Pt♦❧♦♠❡✉ ❛♣❛r❡❝❡✉ ❝♦♠♦ ❛ ♣r♦♣♦s✐çã♦ ✾✸ ♥❛ ♦❜r❛ ❉❛t❛✱ ❞❡ ❊✉❝❧✐❞❡s✳
❖ ♣ró①✐♠♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ tr✐❣♦♥♦♠❡tr✐❛ ❢♦✐ r❡❛❧✐③❛❞♦ ♥❛ ❮♥❞✐❛✳ ❖ ♠❛t❡♠át✐❝♦✲ ❛strô♥♦♠♦ ❆r②❛❜❤❛t❛ ✭✹✼✻ ❞✳❝✳ ✲ ✺✺✵ ❞✳❝✳✮✱ ♥❛ s✉❛ ♦❜r❛ ❆r②❛❜❤❛t❛✲❙✐❞❞❤❛♥t❛✱ ♣r✐♠❡✐r♦ ❞❡✜♥✐✉ ♦ s❡♥♦ ❝♦♠♦ ❛ r❡❧❛çã♦ ♠♦❞❡r♥❛ ❡♥tr❡ ❛ ♠❡t❛❞❡ ❞❡ ✉♠ â♥❣✉❧♦ ❡ ❛ ♠❡t❛❞❡ ❞❡ ✉♠❛ ❝♦r❞❛ ❡ ❡♥tã♦ ❞❡✜♥✐✉ ♦ ❝♦ss❡♥♦✱ ✈❡rs❡♥♦ ❡ ♦ s❡♥♦ ✐♥✈❡rs♦✳ ❙❡✉s tr❛❜❛❧❤♦s t❛♠❜é♠ ❝♦♥tê♠ ❛s t❛❜❡❧❛s ❞❡ ✈❛❧♦r❡s ❞❡ s❡♥♦ ❡ ✈❡rs❡♥♦ ♠❛✐s ❛♥t✐❣❛s q✉❡ s♦❜r❡✈✐✈❡r❛♠ ❛té ♥ós✱ ❡♠ ✐♥t❡r✈❛❧♦s ❞❡ ✸✳✼✺◦ ❞❡ ✵◦ ❛té ✾✵◦✱ ❝♦♠ ✉♠❛ ♣r❡❝✐sã♦ ❞❡ ✹ ❝❛s❛s ❞❡❝✐♠❛✐s✳ ❊❧❡ ✉s♦✉ ❛s ♣❛❧❛✈r❛s ❥②❛ ♣❛r❛ s❡♥♦✱ ❦♦❥②❛ ♣❛r❛ ❝♦ss❡♥♦✱ ✉❦r❛♠❛❥②❛ ♣❛r❛ ✈❡rs❡♥♦ ❡ ♦t❦r❛♠ ❥②❛ ♣❛r❛ s❡♥♦ ✐♥✈❡rs♦✳ ❆s ♣❛❧❛✈r❛s ❥②❛ ❡ ❦♦❥②❛ ❡✈❡♥t✉❛❧♠❡♥t❡ s❡ tr❛♥s❢♦r♠❛r❛♠ ❡♠ s❡♥♦ ❡ ❝♦ss❡♥♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❞❡♣♦✐s ❞❡ tr❛❞✉çõ❡s ❡q✉✐✈♦❝❛❞❛s✳
❉❡✜♥✐çõ❡s Pr❡❧✐♠✐♥❛r❡s ✸✶
✐♥✈és ❞❡ ❝ír❝✉❧♦s✱ ❝♦♠ t❛❜❡❧❛s ♣❛r❛ ❛s s❡✐s ❢✉♥çõ❡s tr✐❣♦♥♦♠étr✐❝❛s✳
❉❡♣♦✐s ❞❡ss❡ ❣r❛♥❞❡ ♣r♦❝❡ss♦ ❞❡ ❞❡s❝♦❜r✐♠❡♥t♦ ❞♦ ✉s♦ ❞❡ tr✐❣♦♥♦♠❡tr✐❛✱ ❛ ♠❛✐♦r✐❛ ❞♦s ❣r❛♥❞❡s ♠❛t❡♠át✐❝♦s ✐♥✢✉❡♥❝✐♦✉✱ ❞❡ ❛❧❣✉♠❛ ❢♦r♠❛✱ ♥♦ s❡✉ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦✳ ❈♦♠♦ ❞✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ tr✐❣♦♥♦♠❡tr✐❛ ❝♦♠♦ ❛ t❡♠♦s ❞♦s ❞✐❛s ❛t✉❛✐s ♥ã♦ é r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ só ♣❡ss♦❛ ♦✉ ♣♦r ✉♠❛ s♦❝✐❡❞❛❞❡✳ ❚✉❞♦ ❛❝♦♥t❡❝❡✉ ❝♦♠♦ ✉♠ ♣r♦❝❡ss♦✱ ❝♦♠ ❝♦♥tr✐❜✉✐çã♦ ❞❡ ✈ár✐♦s ♣♦✈♦s ❞❡ t♦❞❛ ♣❛rt❡ ❞♦ ♠✉♥❞♦✳ ❈❛❞❛ ♣♦✈♦ ♣❛rt✐❝✐♣♦✉ ❞❡ ❛❧❣✉♠❛ ❢♦r♠❛✱ ❛❧❣✉♥s ❞❡❧❡s ♠❛✐s ♥❛ ♣❛rt❡ ❞❛ tr✐❣♦♥♦♠❡tr✐❛ ❡s❢ér✐❝❛ ❡✱ ❞❡✈✐❞♦ à ❛♥t✐❣✉✐❞❛❞❡ ❞❡ q✉❡ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❡ss❛ ár❡❛ ❞❛ ♠❛t❡♠át✐❝❛✱ é ✉♠ ♣♦✉❝♦ ❞✐❢í❝✐❧ s❛❜❡r ❛ ❡①❛t✐❞ã♦ ❞♦s ❡st✉❞♦s✳
✹✳✸ ❉❡✜♥✐çõ❡s Pr❡❧✐♠✐♥❛r❡s
❆♥t❡s ❞❡ ❝♦♠❡ç❛r♠♦s ♥♦ss♦ ❡st✉❞♦ s♦❜r❡ tr✐❣♦♥♦♠❡tr✐❛✱ ❢❛③ s❡ ♥❡❝❡ssár✐♦ ❛❞q✉✐r✐r ❛❧❣✉♥s ❝♦♥❤❡❝✐♠❡♥t♦s q✉❡ s❡r✈✐rã♦ ❞❡ ❜❛s❡ ♣❛r❛ ♥♦ss♦ tr❛❜❛❧❤♦✳ ◆♦ss♦s ❝♦♥❝❡✐t♦s ❡stã♦ r❡❧❛❝✐♦♥❛❞♦s ❛♦ ♣❧❛♥♦✱ ♥♦ss♦ ♦❜❥❡t♦ ❞❡ ❡st✉❞♦✳ Pr✐♠❡✐r❛♠❡♥t❡ ❞❡✈❡♠♦s ❝♦♥❝❡✐t✉❛r tr✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦✿ s❡✉s ❡❧❡♠❡♥t♦s✱ ♣r♦♣r✐❡❞❛❞❡s✱ r❡❧❛çõ❡s✱ ❡t❝✳
❯♠ tr✐â♥❣✉❧♦ é ✉♠ ♣♦❧í❣♦♥♦ ❞❡ três ❧❛❞♦s✱ ♥ã♦ ♣♦ss✉✐ ♥❡♥❤✉♠❛ ❞✐❛❣♦♥❛❧✱ ❛ s♦♠❛ ❞♦s s❡✉s â♥❣✉❧♦s ✐♥t❡r♥♦s é ✐❣✉❛❧ ❛ 180♦ ❡ ❛ s♦♠❛ ❞♦s â♥❣✉❧♦s ❡①t❡r♥♦s é 360♦ ✭360♦ t❛♠❜é♠ é s♦♠❛ ❞♦s â♥❣✉❧♦s ❞❡ q✉❛❧q✉❡r ♣♦❧í❣♦♥♦✮✳ ❊♠ ✉♠ tr✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦✱ ❝❛❞❛ ❧❛❞♦ é ♠❡♥♦r q✉❡ ❛ s♦♠❛ ❞♦s ♦✉tr♦s ❞♦✐s ❧❛❞♦s ✭❞❡s✐❣✉❛❧❞❛❞❡ tr✐❛♥❣✉❧❛r✮ ❡ ♦ ♠❛✐♦r ❧❛❞♦ s❡ ♦♣õ❡ ❛♦ ♠❛✐♦r â♥❣✉❧♦✳ ❯♠ tr✐â♥❣✉❧♦ ♣♦❞❡ s❡r ❝❛r❛❝t❡r✐③❛❞♦ ♣❡❧❛ ♠❡❞✐❞❛ ❞♦s s❡✉s ❧❛❞♦s ♦✉ ♣❡❧❛ ♠❡❞✐❞❛ ❞♦s s❡✉s â♥❣✉❧♦s✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ t❛❜❡❧❛ ❛❜❛✐①♦✿
❋✐❣✉r❛ ✹✳✶✿ ❈❧❛ss✐✜❝❛çã♦ ❞♦s ❚r✐â♥❣✉❧♦s
✸✷ ❆ ❚r✐❣♦♥♦♠❡tr✐❛
✉♠ tr✐â♥❣✉❧♦✳ ❙ã♦ ❡❧❡s✿ ❆❧t✉r❛✱ ❇✐ss❡tr✐③ ❡ ▼❡❞✐❛♥❛✳
❉❡✜♥✐çã♦ ✹✳✶✳ ❆ ♠❡❞✐❛♥❛ ❞❡ ✉♠ tr✐â♥❣✉❧♦ é ✉♠ s❡❣♠❡♥t♦ ❞❡ r❡t❛ q✉❡ ❧✐❣❛ ✉♠ ✈ért✐❝❡ ❝♦♠ ♦ ♣♦♥t♦ ♠é❞✐♦ ❞♦ ❧❛❞♦ ♦♣♦st♦✳
❉❡✜♥✐çã♦ ✹✳✷✳ ❆ ❇✐ss❡tr✐③ ❞❡ ✉♠ tr✐â♥❣✉❧♦ é ✉♠ s❡❣♠❡♥t♦ ❞❡ r❡t❛ q✉❡ ❧✐❣❛ ✉♠ ✈ért✐❝❡ ❝♦♠ ♦ ❧❛❞♦ ♦♣♦st♦ ❞❡ ✉♠ tr✐â♥❣✉❧♦✱ ❞✐✈✐❞✐♥❞♦ ♦ â♥❣✉❧♦ ❞♦ ✈ért✐❝❡ ❛♦ ♠❡✐♦✳
❉❡✜♥✐çã♦ ✹✳✸✳ ❆ ❆❧t✉r❛ ❞❡ ✉♠ tr✐â♥❣✉❧♦ é ✉♠ s❡❣♠❡♥t♦ ❞❡ r❡t❛ q✉❡ ❧✐❣❛ ✉♠ ✈ért✐❝❡ ❝♦♠ ♦ ❧❛❞♦ ♦♣♦st♦ ♦✉ s❡✉ ♣r♦❧♦♥❣❛♠❡♥t♦✱ ❢♦r♠❛♥❞♦ ❝♦♠ ❡st❡ ✉♠ â♥❣✉❧♦ r❡t♦✳
❊♠ ✉♠ tr✐â♥❣✉❧♦ ✐sós❝❡❧❡s✱ ❛ ♠❡❞✐❛♥❛✱ ❜✐ss❡tr✐③ ❡ ❛❧t✉r❛ r❡❧❛t✐✈❛ ❛ ❜❛s❡ ❞♦ tr✐â♥❣✉❧♦ ❝♦✐♥❝✐❞❡♠✳ ❊♠ ✉♠ tr✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦✱ ❝❛❞❛ ❝❛t❡t♦ t❛♠❜é♠ é ❛❧t✉r❛ r❡❧❛t✐✈❛ ❛♦ ♦✉tr♦ ❝❛t❡t♦✳ ◆♦ tr✐â♥❣✉❧♦ ❡q✉✐❧át❡r♦✱ ❜✐ss❡tr✐③✱ ❛❧t✉r❛ ❡ ❜✐ss❡tr✐③ ❞❡ ❝❛❞❛ ✈ért✐❝❡ ❝♦✐♥❝✐❞❡♠✳ ❉❡✜♥✐çã♦ ✹✳✹✳ ❉♦✐s tr✐â♥❣✉❧♦s sã♦ s❡♠❡❧❤❛♥t❡s q✉❛♥❞♦ s❡✉s â♥❣✉❧♦s ✐♥t❡r♥♦s ❝♦rr❡s✲ ♣♦♥❞❡♥t❡s sã♦ ❝♦♥❣r✉❡♥t❡s ❡ s❡✉s ❧❛❞♦s ❝♦rr❡s♣♦♥❞❡♥t❡s sã♦ ♣r♦♣♦r❝✐♦♥❛✐s✳
❋❛③✲s❡ ♥❡❝❡ssár✐♦ t❛♠❜é♠ r❡❧❡♠❜r❛r ❝♦♠♦ ♦♣❡r❛♠♦s ❢r❛çõ❡s✳
❉❡✜♥✐çã♦ ✹✳✺✳ ❙❡❥❛♠ a, b, c ❡ d ♥ú♠❡r♦s r❡❛✐s✱ ❛ ❞✐✈✐sã♦ ❡♥tr❡ ❛s r❛③õ❡s a s♦❜r❡ b ❡ c s♦❜r❡d é ✐❣✉❛❧ ❛♦ ♣r♦❞✉t♦ ❡♥tr❡ ❛s r❛③õ❡s a s♦❜r❡b ❡ d s♦❜r❡c✱ ♦✉ s❡❥❛✱ ♣❛r❛ ❞✐✈✐❞✐r
❞✉❛s ❢r❛çõ❡s ❞❡✈❡♠♦s r❡♣❡t✐r ❛ ♣r✐♠❡✐r❛ ❢r❛çã♦ ❡ ♠✉❧t✐♣❧✐❝á✲❧❛ ♣❡❧♦ ✐♥✈❡rs♦ ❞❛ s❡❣✉♥❞❛✳
a b c d = a b × d c
❉❡✜♥✐çã♦ ✹✳✻✳ P❛r❛ ❡❢❡t✉❛r ❛ ♠✉❧t✐♣❧✐❝❛çã♦ ❞❡ ❢r❛çõ❡s✱ ❜❛st❛ ♠✉❧t✐♣❧✐❝❛r ♥✉♠❡r❛❞♦r❡s ❡ ❞❡♥♦♠✐♥❛❞♦r❡s✱ s❡♣❛r❛❞❛♠❡♥t❡✳
a
b ×
c
d =
a×c
b×d
❉❡✜♥✐çã♦ ✹✳✼✳ P❛r❛ s♦♠❛r♠♦s ❞✉❛s ❢r❛çõ❡s✱ ❢❛③ s❡ ♥❡❝❡ssár✐♦s q✉❡ ❡❧❛s t❡♥❤❛♠ ♦ ♠❡s♠♦ ❞❡♥♦♠✐♥❛❞♦r✳ ❙❡ ❥á ♦ t✐✈❡r❡♠✱ ❝♦♥s❡r✈❛♠♦s ♦ ❞❡♥♦♠✐♥❛❞♦r ❡ s♦♠❛♠♦s ❛♣❡♥❛s ♦s ♥✉♠❡r❛❞♦r❡s✳ ❈❛s♦ ❝♦♥trár✐♦✱ ❞❡✈❡♠♦s ❡♥❝♦♥tr❛r ❢r❛çõ❡s ❡q✉✐✈❛❧❡♥t❡s ❛ ❛♥t❡r✐♦r❡s q✉❡ t❡♥❤❛♠ ♦ ♠❡s♠♦ ❞❡♥♦♠✐♥❛❞♦r ❡ só ❡♥tã♦ ❡❢❡t✉❛♠♦s ❛ s♦♠❛✳
a
c +
b
c =
a+b
c
❚❡♦r❡♠❛ ✶✳ ✭❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✮
❋✉♥çõ❡s ❚r✐❣♦♥♦♠étr✐❝❛ ♥♦ ❚r✐â♥❣✉❧♦ ❘❡tâ♥❣✉❧♦ ✸✸
❋✐❣✉r❛ ✹✳✷✿ ❚r✐â♥❣✉❧♦ ❘❡tâ♥❣✉❧♦
a2
=b2
+c2
✹✳✹ ❋✉♥çõ❡s ❚r✐❣♦♥♦♠étr✐❝❛ ♥♦ ❚r✐â♥❣✉❧♦ ❘❡tâ♥❣✉❧♦
❊♠ ✉♠ tr✐â♥❣✉❧♦✱ ♦ ♠❛✐♦r ❧❛❞♦ é ❝❤❛♠❛❞♦ ❞❡ ❤✐♣♦t❡♥✉s❛ ❡ ♦s ♦✉tr♦s ❞♦✐s ❧❛❞♦s sã♦ ❝❤❛♠❛❞♦s ❞❡ ❝❛t❡t♦s✳ ◗✉❛♥❞♦ ♦ ❝❛t❡t♦ ♥ã♦ é ❧❛❞♦ ❞❡ ✉♠ ❞♦s s❡✉s â♥❣✉❧♦s ✐♥t❡r♥♦s✱ ❞✐③❡♠♦s q✉❡ ❡ss❡ ❝❛t❡t♦ é ♦♣♦st♦ ❛♦ â♥❣✉❧♦ ❡♠ q✉❡stã♦✱ ❝❛s♦ ❝♦♥trár✐♦ ❡❧❡ é ❞✐t♦ ❛❞❥❛✲ ❝❡♥t❡ ❛♦ â♥❣✉❧♦✳ ❆ ❤✐♣♦t❡♥✉s❛✱ ♣♦r s❡r ♦ ♠❛✐♦r ❧❛❞♦✱ é s❡♠♣r❡ ♦♣♦st❛ ❛♦ â♥❣✉❧♦ r❡t♦✳ ❙❡❥❛ θ ✉♠ â♥❣✉❧♦ ❛❣✉❞♦✱ ❛ r❛③ã♦ ❡♥tr❡ ♦ ❧❛❞♦ ♦♣♦st♦ ❛♦ â♥❣✉❧♦θ ❡ ❛ ❤✐♣♦t❡♥✉s❛ é ✉♠
♥ú♠❡r♦ ❡♥tr❡ 0 ❡ 1✱ ❥á q✉❡ ❛ ❤✐♣♦t❡♥✉s❛ é s❡♠♣r❡ ♠❛✐♦r q✉❡ ❛ ♠❡❞✐❞❛s ❞♦s ❝❛t❡t♦s✳ ❊♠ ❞♦✐s tr✐â♥❣✉❧♦s s❡♠❡❧❤❛♥t❡s✱ ❛ r❛③ã♦ ❝✐t❛❞❛ é s❡♠♣r❡ ❛ ♠❡s♠❛✳ ❙❛❜❡♥❞♦ ❞✐ss♦✱ ♣♦❞❡♠♦s ❞❡✜♥✐r ✉♠❛ ❢✉♥çã♦ tr✐❣♦♥♦♠étr✐❝❛ ❙❡♥♦ ✭Sen✮✱ q✉❡ ❞❡♣❡♥❞❡ ❞✐r❡t❛♠❡♥t❡ ❞♦
â♥❣✉❧♦ θ ❡ q✉❡ ♣♦ss✉✐ ♦ ♠❡s♠♦ ✈❛❧♦r ♣❛r❛ tr✐â♥❣✉❧♦s r❡tâ♥❣✉❧♦s s❡♠❡❧❤❛♥t❡s✳
❉❡✜♥✐çã♦ ✹✳✽✳ ❙❡❥❛ ✉♠ tr✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦ ABC ❝✉❥♦s ❧❛❞♦s ♠❡❞❡♠ a, b ❡ c❀ ❝♦♠
â♥❣✉❧♦ r❡t♦ ❡♠ ➶ ❡ ❤✐♣♦t❡♥✉s❛ ❞❡ ❝♦♠♣r✐♠❡♥t♦ a✳ ❙❡❥❛ θ ✉♠ â♥❣✉❧♦ ❛❣✉❞♦ ♥❡st❡
tr✐â♥❣✉❧♦✱ ♦♣♦st♦ ❛♦ ❝❛t❡t♦ ❞❡ ❝♦♠♣r✐♠❡♥t♦ b ❡ ❝❛t❡t♦ ❛❞❥❛❝❡♥t❡ ❞❡ ❝♦♠♣r✐♠❡♥t♦ c✳
❉❡✜♥✐♠♦s ❛ ❢✉♥çã♦ s❡♥♦ ❝♦♠♦✿ s❡♥♦ ❞❡ θ é ✐❣✉❛❧ ❛ r❛③ã♦ ❡♥tr❡ ❛s ♠❡❞✐❞❛s ❞♦ ❝❛t❡t♦
♦♣♦st♦ ❡ ❛ ❤✐♣♦t❡♥✉s❛✳
❚♦♠❛♥❞♦ ❝♦♠♦ r❡❢❡rê♥❝✐❛ ♦ s❡❣✉✐♥t❡ tr✐â♥❣✉❧♦✿
❋✐❣✉r❛ ✹✳✸✿ ❚r✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦ ❝♦♠ ➶♥❣✉❧♦ ❛❣✉❞♦ θ
