❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ P✐❛✉í
❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❞❛ ◆❛t✉r❡③❛
Pós✲●r❛❞✉❛çã♦ ❡♠ ▼❛t❡♠át✐❝❛
▼❡str❛❞♦ Pr♦❢✐ss✐♦♥❛❧ ❡♠ ▼❛t❡♠át✐❝❛ ✲ P❘❖❋▼❆❚
❯❙❖ ❉❊ ▼❖❉❊▲❆●❊▼ ▼❆❚❊▼➪❚■❈❆ ◆❖
❈➪▲❈❯▲❖ ❉❖ ❱❖▲❯▼❊ ❊ ❉❆ ➪❘❊❆ ❉❆
❙❯P❊❘❋❮❈■❊ ❉❊ ❯▼❆ ▼❆➬➹
❏❛♥✐❡❧ ▼❛rt✐♥s ◆❡✈❡s
❏❛♥✐❡❧ ▼❛rt✐♥s ◆❡✈❡s
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦✿
❯❙❖ ❉❊ ▼❖❉❊▲❆●❊▼ ▼❆❚❊▼➪❚■❈❆ ◆❖ ❈➪▲❈❯▲❖ ❉❖
❱❖▲❯▼❊ ❊ ❉❆ ➪❘❊❆ ❉❆ ❙❯P❊❘❋❮❈■❊ ❉❊ ❯▼❆ ▼❆➬➹
❉✐ss❡rt❛çã♦ s✉❜♠❡t✐❞❛ à ❈♦♦r❞❡♥❛çã♦ ❆❝❛❞ê♠✐❝❛ ■♥st✐t✉❝✐♦♥❛❧ ❞♦ Pr♦❣r❛♠❛ ❞❡ ▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠ ▼❛t❡♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧ ♥❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ P✐❛✉í✱ ♦❢❡r❡❝✐❞♦ ❡♠ ❛ss♦❝✐❛çã♦ ❝♦♠ ❛ ❙♦❝✐❡❞❛❞❡ ❇r❛s✐❧❡✐r❛ ❞❡ ▼❛t❡♠át✐❝❛✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ♦❜t❡♥çã♦ ❞❡ ♠❡str❡ ❡♠ ▼❛t❡♠át✐❝❛✳
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ▼s❝✳ ▼❛♥♦❡❧ ❱✐❡✐r❛ ❞❡ ▼❛t♦s ◆❡t♦
❆❣r❛❞❡❝✐♠❡♥t♦s
❆ ♠✐♥❤❛ ❢❛♠í❧✐❛✱ q✉❡ ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s ♠❡ ❛♣♦✐❛r❛♠ ❡ q✉❡ ❛♦ ❧♦♥❣♦ ❞❡ t♦❞❛ ♠✐♥❤❛ ❢♦r♠❛çã♦✱ s❡♠♣r❡ ♠❡ ✐♥❝❡♥t✐✈❛r❛♠ ♥♦s ♠♦♠❡♥t♦s ❞❡ ❢r❛q✉❡③❛ ❡ s❡r✈✐r❛♠ ❞❡ ❛❧❡♥t♦ ♥♦s ♠♦♠❡♥t♦s ❞✐❢í❝❡✐s✳
❆♦s ♠❡✉s ❛♠✐❣♦s ❞❡ t✉r♠❛ ❡s♣❡❝✐❛❧♠❡♥t❡ ❱❛❧t❡r❝✐♦✱ ▼❛r❝♦s ◆❡r② ❡ ❩❛✐❣❧❛✱ s❡♠ ❛ ❛❥✉❞❛ ❞❡❧❡s✱ ♦ ❝❛♠✐♥❤♦ ✜❝❛r✐❛ ♠✉✐t♦ ♠❛✐s ❞✐❢í❝✐❧✳
❆ t♦❞♦s ♦s ♠❡✉s ❛♠✐❣♦s ❡ ❝♦❧❡❣❛s q✉❡ ❡st✐✈❡r❛♠ s❡♠♣r❡ ❛♦ ♠❡✉ ❧❛❞♦ ❡ ❢❡③ ❝♦♠ q✉❡ ♦s ❞✐❛s ♣❛ss❛ss❡♠ ❞❡ ❢♦r♠❛ ♠❛✐s ❢❡❧✐③✳
❆♦ Pr♦❢❡ss♦r ▼❛♥♦❡❧ ❱✐❡✐r❛ ❞❡ ▼❛t♦s ◆❡t♦✱ ♠❡✉ ♦r✐❡♥t❛❞♦r✳ ❈❡rt❛♠❡♥t❡ ❡st❡ tr❛❜❛❧❤♦ só ❢♦✐ ❝♦♥❝❧✉í❞♦ ❝♦♠ s❡✉ ❣r❛♥❞❡ ❛✉①í❧✐♦ ❡ ✐♥❝❡♥t✐✈♦✳ ❆ ✈♦❝ê✱ ♠✐♥❤❛ ❡t❡r♥❛ ❣r❛t✐❞ã♦✳
❊ ❛ t♦❞❛s ❛s ♣❡ss♦❛s q✉❡ ❞❡ ❝❡rt❛ ❢♦r♠❛ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ q✉❡ ❡st❡ tr❛❜❛❧❤♦ ❢♦ss❡ ❝♦♥✲ ❝❧✉í❞♦✳
✏❖ ❜♦♠ ❡❞✉❝❛❞♦r ❞❡✈❡ ❡st✐♠✉❧❛r ❛ ❞✐✈❡r✲ s✐❞❛❞❡✱ t♦r❝❡♥❞♦ ♣❛r❛ q✉❡ s❡✉s ❛❧✉♥♦s t❡✲ ♥❤❛♠ s✉❛s ♣ró♣r✐❛s ✐❞❡✐❛s✳ ❊✱ ♠❛✐s ❞♦ q✉❡ ✐ss♦✱ t❡♥❤❛♠ ❛ ❝♦r❛❣❡♠ ❞❡ ❞❡❢❡♥❞ê✲❧❛s✱ ❞❡✲ ✈✐❞❛♠❡♥t❡ ❢✉♥❞❛♠❡♥t❛❞❛s✱ ❡♠ q✉❛❧q✉❡r s✐t✉❛çã♦✳ ❊✱ s♦❜r❡t✉❞♦✱ t❡♥❤❛♠ ❛ ❝♦r❛❣❡♠ ❡ ❛ s❡❣✉r❛♥ç❛ ❞❡ s❡ ❛❞♠✐t✐r❡♠ ❡rr❛❞♦s ❡ ♠✉❞❛r❡♠ s✉❛ ♦♣✐♥✐ã♦✳✧✳
❘❡s✉♠♦
◆❡st❡ tr❛❜❛❧❤♦ tr❛t❛♠♦s ❞♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ❡ ❞❛ s✉❛ ár❡❛ s✉♣❡r✜❝✐❛❧✱ ♣❛r❛ ✐ss♦ ✉s❛♠♦s ❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ❡ s✉❛s ❡t❛♣❛s✳ ❆♣r❡s❡♥t❛r❡♠♦s ❝♦♠♦ ❡str❛té❣✐❛s ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡ t❛✐s ❝á❧❝✉❧♦s ♦ Pr✐♥❝í♣✐♦ ❞❡ ❈❛✈❛❧✐❡r✐✱ ♦ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s✱ ♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ❡ ♦ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧✳ ❙❡♥❞♦ q✉❡ ❡st❛s ♦❜❡❞❡❝❡♠ ❛ ✉♠❛ s❡q✉ê♥❝✐❛ ❣r❛❞✉❛❧ ❡♠ t❡r♠♦s ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡ ❝♦♥❝❡✐t✉❛❧ ❡ ❞❡✈❡♠ ♣r♦♣♦r❝✐♦♥❛r ❛♦s ❛❧✉♥♦s ❞♦ ❊♥s✐♥♦ ▼é❞✐♦ ❛✉♠❡♥t❛r ❛ s✉❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✳
❆❜str❛❝t
■♥ t❤✐s ♣❛♣❡r ✇❡ tr❡❛t t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ✈♦❧✉♠❡ ♦❢ t❤❡ ❛♣♣❧❡ ❛♥❞ ✐ts s✉r❢❛❝❡ ❛r❡❛✱ ❢♦r t❤✐s ✇❡ ✉s❡ t♦ ▼❛t❤❡♠❛t✐❝❛❧ ▼♦❞❡❧✐♥❣ ❛♥❞ ✐ts st❛❣❡s✳ Pr❡s❡♥t ❛s str❛t❡❣✐❡s ❢♦r ♣❡r❢♦r♠✐♥❣ s✉❝❤ ❝❛❧❝✉❧❛t✐♦♥s t❤❡ Pr✐♥❝✐♣❧❡ ♦❢ ❈❛✈❛❧✐❡r✐✱ ❚❤❡♦r❡♠ ♦❢ P❛♣♣✉s✱ t❤❡ ❉✐✛❡r❡♥t✐❛❧ ❛♥❞ ■♥t❡❣r❛❧ ❈❛❧❝✉❧✉s✳ ❆♥❞ t❤❡s❡ ❢♦❧❧♦✇ ❛ ❣r❛❞✉❛❧ s❡q✉❡♥❝❡ ✐♥ t❡r♠s ♦❢ ❝♦♥❝❡♣t✉❛❧ ❝♦♠♣❧❡①✐t② ❛♥❞ ♠✉st ♣r♦✈✐❞❡ ❤✐❣❤ s❝❤♦♦❧ st✉❞❡♥ts ✐♥❝r❡❛s❡ t❤❡✐r ❛❜✐❧✐t② t♦ s♦❧✈❡ ♣r♦❜❧❡♠s✳
❙✉♠ár✐♦
✶ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ✶✶
✶✳✶ ❈♦♥t❡①t♦ ❤✐stór✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✷ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ♥❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✶✳✸ ❊t❛♣❛s ❞❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸
✷ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✶✺ ✷✳✶ ❖ Pr✐♥❝í♣✐♦ ❞❡ ❈❛✈❛❧✐❡r✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✷ ❉❡t❡r♠✐♥❛çã♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ❡s❢❡r❛ ✉t✐❧✐③❛♥❞♦ ♦ ♣r✐♥❝í♣✐♦ ❞❡ ❈❛✈❛❧✐❡r✐ ✳ ✳ ✳ ✶✼ ✷✳✸ ❉❡t❡r♠✐♥❛çã♦ ❞❛ ár❡❛ s✉♣❡r✜❝✐❛❧ ❞❛ ❡s❢❡r❛ ✉t✐❧✐③❛❞♦ ♦ ✈♦❧✉♠❡ ❞❛ ❡s❢❡r❛ ❡
❞♦ ❝♦♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✹ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s ❞❡ ❆❧❡①❛♥❞r✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✺ ❈❡♥tr♦s ❞❡ ●r❛✈✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✻ ❈❡♥tr♦ ❞❡ ●r❛✈✐❞❛❞❡ ❞❡ ✉♠❛ P♦❧✐❣♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✼ ❉❡♠♦♥str❛çã♦ ❞♦ Pr✐♠❡✐r♦ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✽ ❈❡♥tr♦ ❞❡ ●r❛✈✐❞❛❞❡ ❞❡ ✉♠ P♦❧í❣♦♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✾ ❆ ❘♦t❛çã♦ ❞❡ ✉♠ ❘❡tâ♥❣✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✶✵ ❉❡♠♦♥str❛çã♦ ❞♦ ❙❡❣✉♥❞♦ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✶✶ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✶✷ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✶✸ ❱♦❧✉♠❡ ❞❡ só❧✐❞♦ ♦❜t✐❞♦ ♣❡❧❛ r♦t❛çã♦✱ ❡♠ t♦r♥♦ ❞♦ ❡✐①♦ ❳✱ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❆ ✸✽ ✷✳✶✹ ➪r❡❛ ❞❡ s✉♣❡r❢í❝✐❡ ❞❡ ✉♠ só❧✐❞♦ ❞❡ r❡✈♦❧✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✹✷ ✸✳✶ ❯s❛♥❞♦ ♦ ✈♦❧✉♠❡ ❞❡ ✉♠❛ ❡s❢❡r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✷ ❯s❛♥❞♦ ❢❛t✐❛s ❞❛ ♠❛çã ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
❙✉♠ár✐♦ ✽ ✸✳✸ ❯s❛♥❞♦ ♦ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✸✳✹ ❯s❛♥❞♦ ✐♥t❡❣r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✹ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛ ár❡❛ s✉♣❡r✜❝✐❛❧ ❞❛ ♠❛çã ✺✶ ✹✳✶ ❯s❛♥❞♦ ❛ ár❡❛ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ✉♠❛ ❡s❢❡r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✷ ❯s❛♥❞♦ ❢❛t✐❛s ❞❛ ♠❛çã ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✸ ❯s❛♥❞♦ ♦ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✹ ❯s❛♥❞♦ ✐♥t❡❣r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✺ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✻✵
■♥tr♦❞✉çã♦
◆❡st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛♠♦s ✈ár✐♦s ♣r♦❝❡❞✐♠❡♥t♦s ♥❛ ❜✉s❝❛ ❞❛ ❝♦♥str✉çã♦ ❞♦ ❝♦♥❤❡✲ ❝✐♠❡♥t♦✱ s❡♥❞♦ ❡st❡s ❞❡s❡♥✈♦❧✈✐❞♦s ❛tr❛✈és ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ❛♣❧✐❝❛❞❛ ❛♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❡ ❞❛ ár❡❛ s✉♣❡r✜❝✐❛❧ ❞❛ ♠❛çã✳ ❚r❛t❛✲s❡ ❞❡ ✉♠❛ ♠❡t♦✲ ❞♦❧♦❣✐❛ q✉❡ ♣❡r♠✐t❡ ❛♦ ❛❧✉♥♦ ❞❡s♣❡rt❛r ♠❛✐♦r ✐♥t❡r❡ss❡ ♥♦s ❝♦♥t❡ú❞♦s ❡♥✈♦❧✈✐❞♦s t❡♥❞♦ ❝❧❛r❛♠❡♥t❡ ❛ ✐❞❡✐❛ ❞❡ q✉❡ ❛ r❡❛❧✐❞❛❞❡ ♣r❡s❡♥t❡ ♥❛ ✈✐❞❛ s♦❝✐❛❧ ❡stá s❡♥❞♦ r❡♣r❡s❡♥t❛❞❛ ❡ ✐♥t❡r♣r❡t❛❞❛ ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦✳
◆♦ ♣r✐♠❡✐r♦ ❝❛♣ít✉❧♦✱ ✜③❡♠♦s ✉♠❛ ❛♥á❧✐s❡ ❤✐stór✐❝❛ s♦❜r❡ ❛ ♣❡rs♣❡❝t✐✈❛ ❞❛ ▼♦❞❡❧❛✲ ❣❡♠ ▼❛t❡♠át✐❝❛ ❡ ♣♦st❡r✐♦r♠❡♥t❡ ❛❞✐❝✐♦♥❛♠♦s ❛ t❡♦r✐❛ ♠♦str❛♥❞♦ ❛ ❝♦♥tr✐❜✉✐çã♦ q✉❡ ❡❧❛ tr♦✉①❡✳ ❊st❡ ❝❛♣ít✉❧♦ ♣♦ss✉✐ ❛✐♥❞❛ ✉♠❛ r❡✢❡①ã♦ s♦❜r❡ ♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❡ ❛❧❣✉♥s ❛✉✲ t♦r❡s s♦❜r❡ ❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛✱ s❡♥❞♦ ❡❧❡s✿ ❆r✐st✐❞❡s ❈❛♠❛r❣♦ ❇❛rr❡t♦✱ ❯❜✐r❛t❛♥ ❉✬❆♠❜r♦s✐♦✱ ❘♦❞♥❡② ❈❛r❧♦s ❇❛ss❡♥❡③✐ ❡ ❉✐♦♥ís✐♦ ❇✉r❛❦✳
❖ s❡❣✉♥❞♦ ❝❛♣ít✉❧♦ é ❞❡❞✐❝❛❞♦ ❛ t♦❞❛ ❛ ❢✉♥❞❛♠❡♥t❛çã♦ t❡ór✐❝❛ q✉❡ s❡rá ✉t✐❧✐③❛❞❛✱ ♥❡❧❡ ❛♣r❡s❡♥t❛r❡♠♦s✿ ♦ Pr✐♥❝í♣✐♦ ❞❡ ❈❛✈❛❧✐❡r✐✱ ♦ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s✱ ♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ❡ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧✱ ❝♦♠ ✉♠❛ ❜r❡✈❡ ❛❜♦r❞❛❣❡♠ ❤✐stór✐❝❛ ❡ ❝♦♠ ❛❧❣✉♠❛s ❛♣❧✐❝❛çõ❡s ❞♦s ♠❡s♠♦s✳
◆♦ t❡r❝❡✐r♦ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛♠♦s q✉❛tr♦ ❡str❛té❣✐❛s ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã✳ Pr✐♠❡✐r♦ ❝❛❧❝✉❧❛♠♦s ♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✉t✐❧✐③❛♥❞♦ ♦ ✈♦❧✉♠❡ ❞❡ ✉♠❛ ❡s❢❡r❛ q✉❡ ❢♦✐ ❞❡♠♦♥str❛❞❛ ♣❡❧♦ Pr✐♥❝í♣✐♦ ❞❡ ❈❛✈❛❧✐❡r✐✳ ❆ s❡❣✉✐r ✉t✐❧✐③❛♠♦s ♦ ♠ét♦❞♦ ❞❡ ❢❛t✐❛♠❡♥t♦ ❞❛ ♠❛çã ♥♦ ❢♦r♠❛t♦ ❞❡ ❝✐❧✐♥❞r♦s ❝❛❧❝✉❧❛♥❞♦ ♦ ✈♦❧✉♠❡ ❞❡ss❡s ❝✐❧✐♥❞r♦s ❡ s♦♠❛♥❞♦✱ t❡♠✲s❡ ❛✐♥❞❛ ❛ ❛♣❧✐❝❛çã♦ ❞♦ ❙❡❣✉♥❞♦ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s ♣❛r❛ ❝❛❧❝✉❧❛r ❡ss❡ ✈♦❧✉♠❡✳ ❊ ♥♦ ✜♥❛❧ ✉s❛♠♦s ♦ ✈♦❧✉♠❡ ❞♦ só❧✐❞♦ ❡♠ r❡✈♦❧✉çã♦ s♦❜r❡ ♦ ❡✐①♦ ❞❛s ❛❜s❝✐ss❛s ♦♥❞❡ ❢♦r❛♠ ❡♠♣r❡❣❛❞❛s ❞✉❛s ❞❛s ♣r✐♥❝✐♣❛✐s ❢❡rr❛♠❡♥t❛s ❞♦ ❈á❧❝✉❧♦✱ ❛ ❞❡r✐✈❛❞❛ ❡ ❛ ✐♥t❡❣r❛❧✳ ◆♦ q✉❛rt♦ ❝❛♣ít✉❧♦ ♠♦str❛♠♦s ❝♦♠♦ s❡ ❞á ♦ ♣r♦❝❡ss♦ ♣❛r❛ ❝❛❧❝✉❧❛r ❛ ár❡❛ s✉♣❡r✜❝✐❛❧ ❞❡ ✉♠❛ ♠❛çã✳ P❛r❛ t❛♥t♦ ✉t✐❧✐③❛♠♦s ♦s s❡❣✉✐♥t❡s ♣r♦❝❡❞✐♠❡♥t♦s✿ ♦ ❝á❧❝✉❧♦ ❞❛ ár❡❛ s✉♣❡r✜❝✐❛❧ ❞❛ ❡s❢❡r❛❀ ♦ ❢❛t✐❛♠❡♥t♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❛ ♠❛çã ❡♠ ❢♦r♠❛t♦s ❝✐❧í♥❞r✐❝♦s ❝❛❧❝✉❧❛♥❞♦ ❛ ár❡❛ ❞❛
❙✉♠ár✐♦ ✶✵ s✉♣❡r❢í❝✐❡ ❞❡ss❡s ❝✐❧✐♥❞r♦s ❡ s♦♠❛♥❞♦❀ Pr✐♠❡✐r♦ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s❀ ❡ ❛ ❢ór♠✉❧❛ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❝❛❧❝✉❧❛r ❛ ár❡❛ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ✉♠ só❧✐❞♦ ❞❡ r❡✈♦❧✉çã♦ ✉s❛♥❞♦ ❛♣❡♥❛s ✐♥t❡❣r❛❧ ❡ ❞❡r✐✈❛❞❛✳
■♠♣♦rt❛♥t❡ s❛❧✐❡♥t❛r q✉❡ ♦s ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s ✉t✐❧✐③❛❞♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❡ ❞❛ ár❡❛ ❞❡ ✉♠❛ ♠❛çã ❡stã♦ ❝♦❧♦❝❛❞♦s ❡♠ ✉♠❛ s❡q✉ê♥❝✐❛ q✉❡ ♦❜❡❞❡❝❡ ❛ ✉♠ ♥í✈❡❧ ❣r❛❞❛t✐✈♦ ❞❡ ❞✐✜❝✉❧❞❛❞❡ ❡ ❝♦♠♣❧❡①✐❞❛❞❡ ❝♦♥❝❡✐t✉❛❧✳ ◆♦ ❡♥t❛♥t♦✱ ✐st♦ ♥ã♦ s✐❣♥✐✜❝❛ ♥❡❝❡ss❛r✐❛♠❡♥t❡ q✉❡ ♦ r❡s✉❧t❛❞♦ ♦❜t✐❞♦ ♣❛r❛ ❛ ❛♣r♦①✐♠❛çã♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã s❡❥❛ tã♦ ♠❛✐s ♣r❡❝✐s♦ q✉❛♥t♦ ♠❛✐♦r ❢♦r ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦ ♠♦❞❡❧♦ ✉t✐❧✐③❛❞❛✳
❈❛♣ít✉❧♦ ✶
▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛
✶✳✶ ❈♦♥t❡①t♦ ❤✐stór✐❝♦
❆ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ s❡♠♣r❡ ❡st❡✈❡ ♣r❡s❡♥t❡ ♥❛ ✈✐❞❛ ❞♦ s❡r ❤✉♠❛♥♦✳ ❉❡s❞❡ ✺✳✵✵✵ ❛✳❈✳ ❢♦✐ ♥♦tá✈❡❧ q✉❡ ♦ ❤♦♠❡♠ ❜✉s❝♦✉ s♦❧✉❝✐♦♥❛r ♣r♦❜❧❡♠❛s ❞❡ s❡✉ ❝♦t✐❞✐❛♥♦ ✉s❛♥❞♦ ❛ ▼❛t❡♠át✐❝❛ ❡ ♦ r❛❝✐♦❝í♥✐♦ ❧ó❣✐❝♦✳ ❊ss❛ ♣r♦❡③❛ ❤✉♠❛♥❛ ❞❡✉ ♦r✐❣❡♠ ❛♦ s✉r❣✐♠❡♥t♦ ❞❛ r♦❞❛✳ ❆ss✐♠✱ ♣♦❞❡♠♦s ♣❡♥s❛r ♠❛t❡♠❛t✐❝❛♠❡♥t❡ ♣❛r❛ ❡♥t❡♥❞❡r ♦ q✉❡ ❧❡✈♦✉ ♦ ❤♦♠❡♠ ❛ ✐♥✈❡♥t❛r ❛ r♦❞❛ ♣❛r❛ ❢❛❝✐❧✐t❛r s✉❛s t❛r❡❢❛s ❞✐ár✐❛s✳
❆ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ♥❛ ❊❞✉❝❛çã♦✱ ❡♠❜♦r❛ ❝♦♥s♦❧✐❞❛❞❛ ❡♠ ♥í✈❡❧ ✐♥t❡r♥❛❝✐♦♥❛❧ ❞❡s❞❡ ♠❡❛❞♦s ❞♦ sé❝✉❧♦ ❳❳✱ s❡ ❢♦rt❛❧❡❝❡✉ ♥♦ ❇r❛s✐❧ ❛ ♣❛rt✐r ❞♦s ❛♥♦s ❞❡ ✶✾✾✵✳ ➱ ❞✐❢í❝✐❧ s❛❜❡r q✉❡♠ ❢♦r❛♠ t♦❞♦s ♦s ♣r❡❝✉rs♦r❡s ❜r❛s✐❧❡✐r♦s ♥♦ ✉s♦ ❞❛ ▼♦❞❡❧❛❣❡♠ ♦✉ ♥❛ ❝♦♥str✉çã♦ ❞❡ ♠ét♦❞♦s ❡♠ s✉❛s ♣r❛t✐❝❛s ❞❡ s❛❧❛ ❞❡ ❛✉❧❛✳ ▼❡s♠♦ ❛ss✐♠✱ três ♥♦♠❡s s❡ ❞❡st❛❝❛♠ ❡ sã♦ ❝♦♥s✐❞❡r❛❞♦s ❢✉♥❞❛♠❡♥t❛✐s ♣❛r❛ ♦ ✐♠♣✉❧s♦ ❡ ❛ ❝♦♥s♦❧✐❞❛çã♦ ❞❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ♥♦ ❡♥s✐♥♦ ❜r❛s✐❧❡✐r♦✿ ❆r✐st✐❞❡s ❈❛♠❛r❣♦ ❇❛rr❡t♦ ❝♦♥s✐❞❡r❛❞♦ ♣♦r ♠✉✐t♦s ❝♦♠♦ ♦ ♣r✐♥❝✐♣❛❧ ♣r❡❝✉rs♦r ❡♠ r❡❛❧✐③❛r ❡①♣❡r✐ê♥❝✐❛s ❡♠ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ♥❛ ❡❞✉❝❛çã♦✱ r❡♣r❡s❡♥t❛ ♦ ❇r❛s✐❧ ❡♠ ❝♦♥❣r❡ss♦s ✐♥t❡r♥❛❝✐♦♥❛✐s ❡ ♣✉❜❧✐❝❛ ❛rt✐❣♦s r❡❧❛❝✐♦♥❛❞♦s ❝♦♠ ❛ ▼♦❞❡❧❛❣❡♠❀ ❯❜✐r❛t❛♥ ❉✬ ❆♠❜r♦s✐♦ q✉❡ é ♦ r❡♣r❡s❡♥t❛♥t❡ ❜r❛s✐❧❡✐r♦ ♥❛ ❈♦♠✉♥✐❞❛❞❡ ■♥t❡r♥❛❝✐♦♥❛❧ ❞❡ ❊❞✉❝❛çã♦ ▼❛t❡♠át✐❝❛❀ ❡ ❘♦❞♥❡② ❈❛r❧♦s ❇❛ss❛♥❡③✐ q✉❡ s❡ t♦r♥♦✉ ♦ ♣r✐♥❝✐♣❛❧ ❞✐ss❡♠✐♥❛❞♦r ❞❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛✱ ♣♦✐s✱ ❛♦ ❛❞♦tá✲❧❛ ❡♠ s✉❛s ♣rát✐❝❛s ❞❡ s❛❧❛ ❞❡ ❛✉❧❛ ❝♦♥q✉✐st♦✉ ✉♠ ♥ú♠❡r♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❡ ❛❞❡♣t♦s ♣♦r t♦❞♦ ♦ ❇r❛s✐❧✳
❆s ♣❡sq✉✐s❛s ❡ ❝♦♥tr✐❜✉✐çõ❡s ❛❧❝❛♥ç❛❞❛s ♣♦r ❡ss❡s três ♥❛ ár❡❛ ❞❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠á✲ t✐❝❛ ♣r♦❞✉③✐r❛♠ ❡①♣r❡ss✐✈♦ ✐♠♣✉❧s♦ ♥❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ♥❛ ❊❞✉❝❛çã♦ ❇r❛s✐❧❡✐r❛✳ ❆♦ ♠❡s♠♦ t❡♠♣♦ ❡♠ q✉❡ ♦❜t✐♥❤❛♠ s✉❝❡ss♦ ❡♠ s✉❛s ❛♥á❧✐s❡s ❡ ♣❡sq✉✐s❛s ❝♦♠ ❛ ▼♦❞❡❧❛✲
❈❛♣ít✉❧♦ ✶✳ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ✶✷ ❣❡♠✱ ❡❧❡s t❛♠❜é♠ ✐♥st✐❣❛✈❛♠ ♠✉✐t♦s ♣r♦❢❡ss♦r❡s ♥❡ss❡ â♠❜✐t♦✱ ✐♥❞✉③✐♥❞♦✲♦s ❛ ❧❛♥ç❛r❡♠ ♥♦✈❛s ❛t✐✈✐❞❛❞❡s ❡ ❛té ♠❡s♠♦ ♣❡sq✉✐s❛s✳ ➱ ✐♠♣♦rt❛♥t❡ ❛❝r❡s❝❡♥t❛r q✉❡ ❡❧❡s ❛t✉❛r❛♠ ❛♣❡✲ ♥❛s ❡♠ ♥í✈❡❧ ❞❡ ❣r❛❞✉❛çã♦ ❡ ♣ós ✲ ❣r❛❞✉❛çã♦✳ ❆♦ t❡♠♣♦ q✉❡ t✐♥❤❛♠ ót✐♠❛s ✐❞❡✐❛s ♣❛r❛ ❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛ ❡♠ r❡❣✐õ❡s ♣❡r✐❢ér✐❝❛s ❞♦ ❇r❛s✐❧ ♥ã♦ t✐♥❤❛♠ ❡ss❛ ✈✐✈ê♥❝✐❛ ❞❡ ❢❛t♦✳
✶✳✷ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ♥❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛
❖ ✐♥t❡r❡ss❡ ❡♠ ✉t✐❧✐③❛r ❛ ▼♦❞❡❧❛❣❡♠ ❝♦♠♦ ❡str❛té❣✐❛ ❞❡ ❡♥s✐♥♦ ❞❡ ▼❛t❡♠át✐❝❛ ❝♦♠ ❛❧✉♥♦s ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦ r❡♣♦✉s❛ ♥❛ ❜✉s❝❛ ❞❛ ♠❡❧❤♦r✐❛ ❞❛ q✉❛❧✐❞❛❞❡ ❞❡ ❡♥s✐♥♦ ❞❡st❛ ❞✐s❝✐♣❧✐♥❛✳ ❯♠❛ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ♠❛r❝❛♥t❡s ❞❡st❛ ❢❛s❡ ❞❛ ✈✐❞❛ ❡st✉❞❛♥t✐❧ ❞♦s ❛❧✉♥♦s é ♦ ✐♥í❝✐♦ ❞❛ ❛❜str❛çã♦ ❞❡ ❝♦♥❝❡✐t♦s ♠❛t❡♠át✐❝♦s ❛♣r❡♥❞✐❞♦s ❡♠ sér✐❡s ❛♥t❡r✐♦r❡s ❡ q✉❡✱ ♠✉✐t❛s ✈❡③❡s✱ ♥ã♦ ❢♦r❛♠ ❜❡♠ ❛ss✐♠✐❧❛❞♦s✱ ❡✱ ♣♦rt❛♥t♦✱ ♣♦❞❡♠ s❡ t♦r♥❛r ❞✐st❛♥t❡s ❡ ✐rr❡❛✐s✳
◆❡st❡ ❝♦♥t❡①t♦✱ ❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ é ✉♠❛ ❝♦♥tr✐❜✉✐çã♦ ♣❛r❛ ❛♠❡♥✐③❛r ♦s ♣r♦✲ ❜❧❡♠❛s r❡s✉❧t❛♥t❡s ❞❡st❛ tr❛♥s✐çã♦✳ ❆♣r❡s❡♥t❛♥❞♦ ✉♠❛ ▼❛t❡♠át✐❝❛ ♠❛✐s r❡❛❧✱ ✐♥s❡r✐❞❛ ♥♦ ❝♦t✐❞✐❛♥♦ ❞♦s ❛❧✉♥♦s✳ ❈♦♠ ✐ss♦ ♦ ♣r♦❢❡ss♦r tr❛r✐❛ ♣❛r❛ ❞❡♥tr♦ ❞❡ s❛❧❛ ❛ r❡❛❧✐❞❛❞❡ ❞♦ ❛❧✉♥♦✱ ✉♠❛ ✈❡③ q✉❡ ❛ ▼❛t❡♠át✐❝❛ só ❢❛rá s❡♥t✐❞♦ ♣❛r❛ ♦s ❡❞✉❝❛♥❞♦s q✉❛♥❞♦ ❡❧❛ s❡ t♦r♥❛r s✐❣♥✐✜❝❛t✐✈❛ ❡ ♣r❛③❡r♦s❛✳ ❊ss❛s ❞✐✈❡rs❛s s✐t✉❛çõ❡s✲♣r♦❜❧❡♠❛s ❢❛rã♦ ❝♦♠ q✉❡ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ✐♥t❡r♣r❡t❛çã♦ ❞♦s ❛❧✉♥♦s ♠❡❧❤♦r❡ ❝♦♠ ❛ ♣rát✐❝❛✱ ❡ ❛ss✐♠✱ ♦s ♠❡s♠♦s ❛ss✉♠❛♠ ✉♠❛ ♣♦s✐çã♦ ❝rít✐❝❛ ❛♦ t❡♥t❛r r❡s♦❧✈❡r t❛✐s ♣r♦❜❧❡♠❛s✱ ♦✉ s❡❥❛✱ ❝♦♥s✐❣❛♠ ❛♥❛❧✐s❛r ❜❡♠ ❝❛❞❛ ❝❛s♦✱ ✐♥❝❧✉s✐✈❡ ❛♣♦♥t❛♥❞♦ ♠❛✐s ❞❡ ✉♠ ❝❛♠✐♥❤♦ ♣❛r❛ ❛ s♦❧✉çã♦✳
❆ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛✱ ❛❧é♠ ❞❡ s❡r ✉♠❛ t❡♥❞ê♥❝✐❛ q✉❡ ♣r♦♣♦r❝✐♦♥❛ ✉♠❛ ❛rt✐❝✉❧❛✲ çã♦ ❡♥tr❡ ♦s ❝♦♥❝❡✐t♦s ♠❛t❡♠át✐❝♦s ❡ ❛ r❡❛❧✐❞❛❞❡✱ ♣♦❞❡ s❡r ✈✐st❛ t❛♠❜é♠ ♥✉♠❛ ♣❡rs♣❡❝t✐✈❛ q✉❡ ✈❛❧♦r✐③❛ ♦ ♣❡♥s❛♠❡♥t♦ ❝rít✐❝♦ ❡ r❡✢❡①✐✈♦ ❞♦ ❛❧✉♥♦✳
❆ss✐♠✱ ✈❛♠♦s ♥♦s r❡❢❡r✐r às t❡♥❞ê♥❝✐❛s ❞✐❞át✐❝♦✲♣❡❞❛❣ó❣✐❝❛s ❡♠ ●❡♦♠❡tr✐❛ ♣❛r❛ ❡♥t❡♥❞ê✲ ❧❛s ❝♦♠♦ ✉♠ ♠♦❞♦ ❞❡ ♣r♦❞✉③✐r ❝♦♥❤❡❝✐♠❡♥t♦s ❣❡♦♠étr✐❝♦s ❛ ♣❛rt✐r ❞♦s s❛❜❡r❡s ❡ ❞♦s ✐♥t❡r❡ss❡s ❞♦s ❛❧✉♥♦s✱ ✐st♦ é✱ ❢❛③❡r ❝♦♠ q✉❡ ♦ ❡♥s✐♥♦ ❞❛ ❣❡♦♠❡tr✐❛ q✉❡ ♣♦ss❛ ♣r♦❞✉③✐r s✐❣♥✐✜❝❛❞♦s r❡❛✐s ♣❛r❛ ♦ ❛❧✉♥♦✳ Pr♦❞✉③✐r s✐❣♥✐✜❝❛❞♦ ♣❛r❛ ❝♦♥❝❡✐t♦s ❣❡♦♠étr✐❝♦s s✉❜t❡♥❞❡ r❡❧❛❝✐♦♥á✲❧♦s ❛ ♦✉tr♦s ❝♦♥t❡①t♦s ✐♥t❡r♥♦s ♦✉ ❡①t❡r♥♦s à ▼❛t❡♠át✐❝❛✳
❈❛♣ít✉❧♦ ✶✳ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ✶✸ ▼❡s♠♦ ♥ã♦ ❡①✐st✐♥❞♦ ✉♠ ❝♦♥❝❡✐t♦ ú♥✐❝♦ ♣❛r❛ ❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛✱ ❡❧❛ ♣♦❞❡ s❡r r❡s✉♠✐❞❛ ❝♦♠♦ ❛ ❝r✐❛çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦ ✭✉♠ ♣❛❞rã♦✱ ❡♠ ❣❡r❛❧ ✉♠❛ ❢ór♠✉❧❛✮ ♣❛r❛ r❡♣r❡s❡♥t❛r ♦✉ ❝♦♠♣r❡❡♥❞❡r ❞❡ ✉♠ ❢❡♥ô♠❡♥♦ ♥❛t✉r❛❧✳ ❖♥❞❡ ❡st❡ ❢❡♥ô♠❡♥♦ ♣♦❞❡ s❡r ❞❡ q✉❛❧q✉❡r ár❡❛ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ ❙❡♥❞♦ ❛ss✐♠✱ ❡❧❛ ♣♦ss✉✐✉ ✈ár✐❛s ❛♣❧✐❝❛çõ❡s✱ ❡ ♥❡st❡ tr❛❜❛❧❤♦ ✈❡r❡♠♦s ✉♠❛ ❞❡ss❛s ❛♣❧✐❝❛çõ❡s ❞❡ ❢♦r♠❛ ♠❛✐s ❞❡t❛❧❤❛❞❛✿ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❡ ❞❛ ár❡❛ ❞❛ ♠❛çã✳ ❉❛í✱ ✈❛♠♦s✱ ❛ ♣❛rt✐r ❞❡ ✉♠ ❡①❡♠♣❧♦ ♣❛rt✐❝✉❧❛r✱ tr❛❜❛❧❤❛r ❛s ❞✐❢❡r❡♥t❡s ❢♦r♠❛s ♣❛r❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ❡♠ r❡❧❛çã♦ ❛ ❡st❡ ♠❡s♠♦ ♣r♦❜❧❡♠❛✳
✶✳✸ ❊t❛♣❛s ❞❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛
❆s ❡t❛♣❛s ❞❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ s❡❣✉♥❞♦ ❉✐♦♥ís✐♦ ❇✉r❛❦ ❬✶✷❪❀
■✮ ❊s❝♦❧❤❛ ❞♦ t❡♠❛✿ ❖ tr❛❜❛❧❤♦ ❝♦♠ ❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ♣❛rt❡ ❞❡ t❡♠❛s ♣r♦✲ ♣♦st♦s ♣❡❧❛ ❝❧❛ss❡ ♦✉ ♣❡❧♦ ♣r♦❢❡ss♦r✳ ◆❡ss❛ ♣❡rs♣❡❝t✐✈❛✱ ♦ ❡♥s✐♥♦ ❞❛ ▼❛t❡♠át✐❝❛ t♦r♥❛✲s❡ ❞✐♥â♠✐❝♦✱ ♠❛✐s ✈✐✈♦✱ ❡✱ ❡♠ ❝♦♥s❡q✉ê♥❝✐❛✱ ♠❛✐s s✐❣♥✐✜❝❛t✐✈♦s ♣❛r❛ ♦ ❛❧✉♥♦✳ ❈♦♥tr✐❜✉✐ ♣❛r❛ t♦r♥❛r ♠❛✐s ✐♥t❡♥s❛ ❡ ♠❛✐s ❡✜❝❛③ ❛ ❝♦♥str✉çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♣♦r ♣❛rt❡ ❞❡ ❝❛❞❛ ❛❧✉♥♦✳
➱ s❡♥s❛t♦ q✉❡ ❛ s✐t✉❛çã♦ ♣r♦❜❧❡♠❛ ❡s❝♦❧❤✐❞❛ ♣♦ss❛ s❡r ❧✐♠✐t❛❞❛ ♣♦r ✉♠ ❝♦♥t❡ú❞♦ ❡s♣❡❝í✜❝♦ q✉❡ s❡ q✉❡r ♠♦❞❡❧❛r✳
■■✮ P❡sq✉✐s❛ ❡①♣❧♦r❛tór✐❛✿ ◆❛ ▼♦❞❡❧❛❣❡♠✱ ♦ ❝♦♥t❡ú❞♦ ♠❛t❡♠át✐❝♦ ❛ s❡r tr❛❜❛❧❤❛❞♦ é ❞❡t❡r♠✐♥❛❞♦ ♣❡❧♦s ♣r♦❜❧❡♠❛s ❧❡✈❛♥t❛❞♦s ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞❛ ♣❡sq✉✐s❛ ❞❡ ❝❛♠♣♦✱ ❞❡♥♦♠✐♥❛❞❛ ♣❡sq✉✐s❛ ❡①♣❧♦r❛tór✐❛✱ q✉❡ ♦❝♦rr❡ ❞❡♥tr♦ ❞♦ ❝❛♠♣♦ ♠❛t❡♠át✐❝♦✳ ❆q✉✐ ♦s ❝♦♥t❡ú❞♦s tr❛❜❛❧❤❛❞♦s ❣❛♥❤❛♠ ✐♠♣♦rtâ♥❝✐❛ ❡ s✐❣♥✐✜❝❛❞♦s✳ ❆ ❝♦❧❡t❛ ❞♦s ❞❛❞♦s ❡ ♦❜t❡♥çã♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ❡♥❝♦♥tr❛❞♦s ❡♠ ❥♦r♥❛✐s✱ r❡✈✐st❛s✱ ✐♥t❡r♥❡t✳
■■■✮ ▲❡✈❛♥t❛♠❡♥t♦ ❞♦s ♣r♦❜❧❡♠❛s✿ ◆❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ♦s ♣r♦❜❧❡♠❛s ❛♣r❡s❡♥t❛♠✲ s❡ ❞❡ ❢♦r♠❛s ❞✐❢❡r❡♥t❡s ❡♠ r❡❧❛çã♦ à ♠❛✐♦r✐❛ ❞♦s ❧✐✈r♦s t❡①t♦s✳ ❙ã♦ ❛❜❡rt♦s ❡ ❡❧❛✲ ❜♦r❛❞♦s ❛ ♣❛rt✐r ❞❛ s✐t✉❛çã♦✲♣r♦❜❧❡♠❛✱ ♣♦rt❛♥t♦✱ sã♦ ❝♦♥t❡①t✉❛❧✐③❛❞♦s✳ ❉❡✈❡♠✲s❡ ❧❡✈❛r ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛s ♥❡❝❡ss✐❞❛❞❡s ❞♦s ❛❧✉♥♦s❀
❈❛♣ít✉❧♦ ✶✳ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ✶✹ ♥♦ ❝♦♥t❡①t♦ ❞♦ t❡♠❛ ❡s❝♦❧❤✐❞♦✱ ♣♦❞❡♠ s❡r ❞❡s❡♥✈♦❧✈✐❞♦s ♦✉tr♦s ♣r♦❝❡ss♦s ♠❛t❡♠á✲ t✐❝♦s ♣r♦✈❡♥✐❡♥t❡s ❞♦s ❞❛❞♦s ❝♦❧❡t❛❞♦s ❡ ❞❛s ❤✐♣ót❡s❡s ❧❡✈❛♥t❛❞❛s ♣❡❧♦ ♣r♦❢❡ss♦r ♦✉ ♣❡❧♦s ❛❧✉♥♦s✱ ♣♦r ✐ss♦ ❛s s✐t✉❛çõ❡s ♣r♦❜❧❡♠❛ ❛♥t❡s ❞❡ s❡r❡♠ ♣r♦♣♦st❛s ❞❡✈❡♠ s❡r ❛✈❛❧✐❛❞❛s ❛ ✜♠ ❞❡ ❞✐r❡❝✐♦♥❛r ♦ ♠♦❞❡❧♦ ♠❛✐s ❛❞❡q✉❛❞❛♠❡♥t❡✱ ❡✈✐t❛♥❞♦ ✉♠ tr❛❜❛❧❤♦ ❞❡♠♦r❛❞♦ ♦✉ ❢♦r❛ ❞❛ ❞✐s❝✐♣❧✐♥❛✳
❱✮ ❆♥á❧✐s❡ ❝rít✐❝❛ ❞❛s s♦❧✉çõ❡s ♣r♦♣♦st❛s✿ ➱ ❛ ❡t❛♣❛ ♠❛r❝❛❞❛ ♣❡❧❛ ❝r✐t✐❝✐❞❛❞❡✳ ❆q✉✐ ❛ ▼❛t❡♠át✐❝❛ ♥♦✈❛♠❡♥t❡ s❡ ✉♥❡ à ♣rát✐❝❛ ❞❡ ♠❛♥❡✐r❛ ❝♦♥t❡①t✉❛❧✐③❛❞❛✳
❈❛♣ít✉❧♦ ✷
Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦
✈♦❧✉♠❡ ❞❛ ♠❛çã
❖ t❡♠❛ ❛q✉✐ ♣r♦♣♦st♦ é ♦ ❝á❧❝✉❧♦ ❞❡ ✉♠❛ ❛♣r♦①✐♠❛çã♦ ♣❛r❛ ♦ ✈♦❧✉♠❡ ❡ ♣❛r❛ ❛ ár❡❛ ❞❡ ✉♠❛ ♠❛çã✳ P❛r❛ t❛❧✱ ❢❛r❡♠♦s ✉s♦ ❞❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ♣❛r❛ ❛❜♦r❞❛r ♦ ♣r♦❜❧❡♠❛ s♦❜ três ❝♦♥t❡①t♦s✳ ❱❛❧❡ r❡ss❛❧t❛r q✉❡ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞♦ t❡♠❛ ♥ã♦ ❡stá ♥♦ ♣r♦❜❧❡♠❛ ❡♠ s✐✱ ❤❛❥❛ ✈✐st❛ q✉❡ ♦ r❡s✉❧t❛❞♦ ♣♦❞❡ s❡r ♦❜t✐❞♦ ♣♦r ♠❡✐♦ ❞❡ ♣r♦❝❡ss♦ ♠❡❝â♥✐❝♦✿ ❇❛st❛ ♠❡r❣✉✲ ❧❤❛♠♦s ✉♠❛ ♠❛çã ❡♠ ✉♠ r❡❝✐♣✐❡♥t❡ ❝♦♠♣❧❡t❛♠❡♥t❡ ❝❤❡✐♦ ❞❡ á❣✉❛ ❡ ♠❡❞✐♠♦s ♦ ✈♦❧✉♠❡ ❞♦ ❧✐q✉✐❞♦ ❡①tr❛✈❛s❛❞♦ ❞♦ r❡❝✐♣✐❡♥t❡✱ ♠❛s ❡①♣❧♦r❛r ❛s ❞✐❢❡r❡♥t❡s ❛❜♦r❞❛❣❡♥s ♣❡r♠✐t✐❞❛s ♣❡❧❛ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ❞❡ ♠♦❞♦ ❛ ♣r♦♣♦r❝✐♦♥❛r ❛ r❡✢❡①ã♦ ❡ ❛ ♣❡sq✉✐s❛ ❡①♣❧♦r❛tór✐❛ ❡ ❝♦♥tr✐❜✉✐r ♣❛r❛ q✉❡ ♦s ❝♦♥❝❡✐t♦s ❣❛♥❤❡♠ s✐❣♥✐✜❝❛❞♦s ❡ ✐♥t❡r❛çã♦ ❝♦♠ ❛ r❡❛❧✐❞❛❞❡✱ ❛s✲ s✐♠✱ ♣❡r♠✐t✐rá ♦ s✉r❣✐♠❡♥t♦ ❞❡ ✉♠ ❝♦♥t❡①t♦ ❝r✐❛t✐✈♦ ❡ ♠♦t✐✈❛✲t❡ ♣❛r❛ ❛ ❝♦♥s♦❧✐❞❛çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳
❋❛r❡♠♦s ❛ ❛❜♦r❞❛❣❡♠ s♦❜ três ❛s♣❡❝t♦s✿ ❖ Pr✐♥❝í♣✐♦ ❞❡ ❈❛✈❛❧✐❡r✐✱ ♦ ❚❡♦r❡♠❛ ❞❡ P❛♣✲ ♣✉s ❡ ❛ ❛♣❧✐❝❛çã♦ ❞❡ ❞❡r✐✈❛❞❛s ❡ ✐♥t❡❣r❛✐s✳ P❛r❛ ❝❛❞❛ ✉♠✱ ✐♥tr♦❞✉③✐♠♦s ✉♠❛ ❛❜♦r❞❛❣❡♠ ❤✐stór✐❝❛ ❞❡ ♠♦❞♦ ❛ ❞❛r r❡❧❡✈â♥❝✐❛ ❛♦s ♣r♦❝❡❞✐♠❡♥t♦s✳
✷✳✶ ❖ Pr✐♥❝í♣✐♦ ❞❡ ❈❛✈❛❧✐❡r✐
❊st❡ ❡st✉❞♦ ❢♦✐ ❜❛s❡❛❞♦ ❡♠ ❛rt✐❣♦s ❞❡ ❧✐✈r♦s ❡ ✐♥t❡r♥❡t q✉❡✱ ❣❡r❛❧♠❡♥t❡✱ ✈ê♠ ♥✉♠❛ ❢♦r♠❛ ❜ás✐❝❛✳ ❆q✉✐ ❞❡st❛❝❛♠♦s ❛ ❝♦♥tr✐❜✉✐çã♦ ❞❡ ❇♦♥❛✈❡♥t✉r❛ ❈❛✈❛❧✐❡r✐ ✭▼✐❧ã♦✱ ✶✺✾✽ ✲ ❇♦❧♦✲ ♥❤❛✱ ✶✻✹✼✮✱ ✉♠ s❛❝❡r❞♦t❡ ❥❡s✉ít❛ ❡ ♠❛t❡♠át✐❝♦ ✐t❛❧✐❛♥♦✱ ❞✐s❝í♣✉❧♦ ❞❡ ●❛❧✐❧❡✉✱ q✉❡ ✉t✐❧✐③❛r❛ s❡✉ ♠ét♦❞♦ ❞♦s ✐♥❞✐✈✐sí✈❡✐s ❝♦♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦s ❝á❧❝✉❧♦s ❡ ❢❛③❡♥❞♦ ✉s♦ ❞❡ ✐❧✉str❛✲
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✶✻ çõ❡s✳
❈❛✈❛❧✐❡r✐ ♣✉❜❧✐❝♦✉ ❡♠ ✶✻✸✷✱ ♦ ❧✐✈r♦ ❉✐r❡❝t♦r✐✉♠ ❯♥✐✈❡rs❛❧❡ ❯r❛♥♦♠❡tr✐❝✉♠ ✭❉✐r❡tó✲ r✐♦ ❯♥✐✈❡rs❛❧ ❞❡ ❯r❛♥♦♠❡tr✐❛✮✳ ❖ t❡r♠♦ ✉r❛♥♦♠étr✐❝♦ ❡stá r❡❧❛❝✐♦♥❛❞♦ à ♠❡❞✐çã♦ ❞❡ ❞✐stâ♥❝✐❛s ❝❡❧❡st❡s✳ ❊♥tr❡t❛♥t♦✱ ❈❛✈❛❧✐❡r✐ ❛❞♦t♦✉ ❡ss❡ ♥♦♠❡ ♣r♦✈❛✈❡❧♠❡♥t❡ ❛♣❡♥❛s ❝♦♠ ♦ s✐❣♥✐✜❝❛❞♦ ❞❡ ♠❡❞✐çõ❡s✳ ❊st❡ tr❛❜❛❧❤♦ ❢♦✐ r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ✐♥tr♦❞✉çã♦ ♥❛ ■tá❧✐❛ ❞♦ ❧♦❣❛r✐t♠♦ ❡ ❞❛s ❢✉♥çõ❡s tr✐❣♦♥♦♠étr✐❝❛s ♣❛r❛ ♦ ❡♠♣r❡❣♦ ❡♠ ❝á❧❝✉❧♦s ❛str♦♥ô♠✐❝♦s✳
❊♠ ✶✻✸✺✱ ♣✉❜❧✐❝♦✉ s✉❛ ♦❜r❛ ♠❛✐s ❝♦♥❤❡❝✐❞❛✱ ●❡♦♠❡tr✐❛ ✐♥❞✐✈✐s✐❜✐❧✐❜✉s ❝♦♥t✐♥✉♦r✉♠ ♥♦✈❛ ✭◆♦✈❛ ●❡♦♠❡tr✐❛ ❞♦s ■♥❞✐✈✐sí✈❡✐s ❈♦♥tí♥✉♦s✮✱ ❡♠ q✉❡ ❞❡s❡♥✈♦❧✈❡✉ ❛ ✐❞❡✐❛ ❞❡ ❑❡♣❧❡r s♦❜r❡ q✉❛♥t✐❞❛❞❡s ✐♥✜♥✐t❛♠❡♥t❡ ♣❡q✉❡♥❛s✿ ✉♠❛ r❡❣✐ã♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♣♦❞❡ s❡r ♣❡♥s❛❞❛ ❝♦♠♦ s❡♥❞♦ ❢♦r♠❛❞❛ ♣♦r s❡❣♠❡♥t♦s ♦✉ ✧✐♥❞✐✈✐sí✈❡✐s✧✱ ❡ q✉❡ ✉♠ só❧✐❞♦ ♣♦❞❡ s❡r ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ❝♦♠♣♦st♦ ❞❡ r❡❣✐õ❡s q✉❡ tê♠ ✈♦❧✉♠❡s ✐♥❞✐✈✐sí✈❡✐s✳ ❖ r❛❝✐♦❝í♥✐♦ ✉t✐❧✐③❛❞♦ é ♦ ♠❡s♠♦ ♣❡♥s❛❞♦ ♣♦r ❆rq✉✐♠❡❞❡s✱ ♠❛s ❛ ❞✐❢❡r❡♥ç❛ ❡stá ♥❛ ♠❛♥❡✐r❛ ❝♦♠♦ ♦s ❞♦✐s ❞❡♠♦♥str❛r❛♠ t❛❧ ♣❡♥s❛♠❡♥t♦✳ ❊st❛ ✐❞❡✐❛ ❢❡❝✉♥❞❛✱ ♠❛❧❣r❛❞♦ ❛ ✐♥❡①❛t✐❞ã♦ q✉❡ ❡❧❛ ❡①♣r✐♠❡✱ ♣❡r♠✐t❡ ♥♦✈❛s ❛✈❛❧✐❛çõ❡s ❞❡ s✉♣❡r❢í❝✐❡s ❡ ❞❡ ✈♦❧✉♠❡s ❡ ❛ ❞❡t❡r♠✐♥❛çã♦ ❣❡♦♠étr✐❝❛ ❞❡ ❝❡♥tr♦s ❞❡ ❣r❛✈✐❞❛❞❡ ❞❛s ✜❣✉r❛s ♣❧❛♥❛s ❡ ❞♦s só❧✐❞♦s✳ ❆ ♣❛rt✐r ❞❡ s✉❛s ❝♦♥s✐❞❡r❛çõ❡s ❡❧❡ ❞❡s❡♥✈♦❧✈❡✉ ✉♠ ♠ét♦❞♦ q✉❡ ❢♦✐ ✉t✐❧✐③❛❞♦ ❞✉r❛♥t❡ ❝✐♥q✉❡♥t❛ ❛♥♦s ❡ q✉❡ ❢♦✐ s✉❜st✐t✉í❞♦ ♣❡❧♦ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧✳ ❆ t❡♦r✐❛ ❞❡ ❈❛✈❛❧✐❡r✐ ♣❡r♠✐t✐✉✲❧❤❡ ❞❡t❡r♠✐♥❛r r❛♣✐❞❛♠❡♥t❡ ár❡❛s ❡ ✈♦❧✉♠❡s ❞❡ ✜❣✉r❛s ❣❡♦♠étr✐❝❛s✳
❙❡✉ ♠ét♦❞♦ s♦❜r❡ ♦s ✐♥❞✐✈✐sí✈❡✐s ❢♦✐ ♠✉✐t♦ ❝r✐t✐❝❛❞♦ ♥❛ é♣♦❝❛✱ ♣♦✐s ♥ã♦ ❛♣r❡s❡♥t❛✈❛ ♦ r✐❣♦r ♠❛t❡♠át✐❝♦ ❞❡s❡❥❛❞♦✳ ❈❛✈❛❧✐❡r✐ ❡♥tã♦✱ ❡♠ ✶✻✹✼✱ ♣✉❜❧✐❝♦✉ ❛ ♦❜r❛ ❊①❡r❝✐t❛t✐♦♥❡s ❣❡♦♠❡tr✐❝❛❡ s❡① ✭❙❡✐s ❊①❡r❝í❝✐♦s ●❡♦♠étr✐❝♦s✮✱ ♥❛ q✉❛❧ ❛♣r❡s❡♥t♦✉ ❞❡ ♠❛♥❡✐r❛ ♠❛✐s ❝❧❛r❛ s✉❛ t❡♦r✐❛✳ ❚❛❧ ❧✐✈r♦ tr❛♥s❢♦r♠♦✉✲s❡ ❡♠ ❢♦♥t❡ ✐♠♣♦rt❛♥t❡ ♣❛r❛ ♦s ♠❛t❡♠át✐❝♦s ❞♦ sé❝✉❧♦ ❳❱■■✳
◆♦ ❡♥t❛♥t♦✱ é ✉♠ ♣♦✉❝♦ ❞✐❢í❝✐❧ ❞❡s❝♦❜r✐r ♦ q✉❡ ❡❧❡ ❡♥t❡♥❞✐❛ ♣♦r ✧✐♥❞✐✈✐sí✈❡❧✧✳ ❚✉❞♦ ✐♥❞✐❝❛ q✉❡ ✉♠ ✐♥❞✐✈✐sí✈❡❧ ❞❡ ✉♠❛ ♣♦rçã♦ ♣❧❛♥❛ ❞❛❞❛ é ✉♠❛ ❝♦r❞❛ ❞❡ss❛ ♣♦rçã♦ ❡ ♦ ✐♥❞✐✲ ✈✐sí✈❡❧ ❞❡ ✉♠ só❧✐❞♦ é ✉♠❛ s❡❝çã♦ ❞❡ss❡ só❧✐❞♦✳ ❈♦♥s✐❞❡r❛✲s❡ q✉❡ ✉♠❛ ♣♦rçã♦ ♣❧❛♥❛ s❡❥❛ ❢♦r♠❛❞❛ ♣♦r ✐♥✜♥✐t❛s ❝♦r❞❛s ♣❛r❛❧❡❧❛s✳ ❊♥tã♦✱ ❛r❣✉♠❡♥t❛✈❛ ❈❛✈❛❧✐❡r✐✱ ❢❛③❡♥❞♦ ❞❡s❧✐③❛r ❝❛❞❛ ✉♠ ❞♦s ❡❧❡♠❡♥t♦s ❞♦ ❝♦♥❥✉♥t♦ ❞❛s ❝♦r❞❛s ♣❛r❛❧❡❧❛s ❞❡ ✉♠❛ ♣♦rçã♦ ♣❧❛♥❛ ❞❛❞❛ ❛♦ ❧♦♥❣♦ ❞❡ s❡✉ ♣ró♣r✐♦ ❡✐①♦✱ ❞❡ ♠♦❞♦ q✉❡ ❛s ❡①tr❡♠✐❞❛❞❡s ❞❛s ❝♦r❞❛s ❛✐♥❞❛ ❞❡s❝r❡✈❛♠ ✉♠ ❝♦♥t♦r♥♦ ❝♦♥tí♥✉♦✱ ❛ ár❡❛ ❞❛ ♥♦✈❛ ♣♦rçã♦ ♣❧❛♥❛ é ✐❣✉❛❧ à ♦r✐❣✐♥❛❧✱ ✉♠❛ ✈❡③ q✉❡ ❛♠❜❛s sã♦ ❢♦r♠❛❞❛s ♣❡❧❛s ♠❡s♠❛s ❝♦r❞❛s✳
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✶✼ ❡ ♣❛r❛❧❡❧❛s q✉❡ ❢♦r♥❡❝❡rá ✉♠ ♥♦✈♦ só❧✐❞♦ ❝♦♠ ♠❡s♠♦ ✈♦❧✉♠❡✳ ❯♠❛ ✐❧✉str❛çã♦ ❞❡st❡ r❡s✉❧t❛❞♦ ♣♦❞❡ s❡r ❞❡♠♦♥str❛❞❛ ✉t✐❧✐③❛♥❞♦ ❞✉❛s ♣✐❧❤❛s ❞❡ ♠♦❡❞❛s ❞❡ ♠❡s♠♦ ❢♦r♠❛t♦✿ ❛ ♣r✐♠❡✐r❛ ♣✐❧❤❛ ❢❛③❡♥❞♦ ✉♠ ❝✐❧✐♥❞r♦ r❡t♦ ❡ ❛ s❡❣✉♥❞❛ ❝♦♠ s✉❛s ❧❛t❡r❛✐s ❞❡❢♦r♠❛❞❛s✿
❋✐❣✉r❛ ✷✳✶✿ ❙ó❧✐❞♦s ❝♦♠ ♠♦❡❞❛s
❖❜✈✐❛♠❡♥t❡ q✉❡ ♦s ✈♦❧✉♠❡s s❡rã♦ ♦s ♠❡s♠♦s✱ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞❛ ❣❡♦♠❡tr✐❛ ♦❜t✐❞❛ ♣❡❧❛ ❞❡❢♦r♠❛çã♦ ♥❛ s❡❣✉♥❞❛ ♣✐❧❤❛ ❞❡ ♠♦❡❞❛s✱ ✉♠❛ ✈❡③ q✉❡ sã♦ ✉t✐❧✐③❛❞❛s ♠♦❡❞❛s ❞♦ ♠❡s♠♦ ❢♦r♠❛t♦ ❡ q✉❛♥t✐❞❛❞❡s ✐❣✉❛✐s ♣❛r❛ ❝❛❞❛ ♣✐❧❤❛✳
❊ss❡s r❡s✉❧t❛❞♦s✱ ❧✐❣❡✐r❛♠❡♥t❡ ❣❡♥❡r❛❧✐③❛❞♦s✱ ❢♦r♥❡❝❡♠ ♦s ❝❤❛♠❛❞♦s Pr✐♥❝í♣✐♦s ❞❡ ❈❛✲ ✈❛❧✐❡r✐✱ q✉❡ ♣♦❞❡♠ s❡r ❡♥✉♥❝✐❛❞♦s ❝♦♠♦✿
✶✳ ❙❡ ❞✉❛s ♣♦rçõ❡s ♣❧❛♥❛s sã♦ t❛✐s q✉❡ t♦❞❛ r❡t❛ s❡❝❛♥t❡ ❛ ❡❧❛s ❡ ♣❛r❛❧❡❧❛ ❛ ✉♠❛ r❡t❛ ❞❛❞❛ ❞❡t❡r♠✐♥❛ ♥❛s ♣♦rçõ❡s s❡❣♠❡♥t♦s ❞❡ r❡t❛ ❝✉❥❛ r❛③ã♦ é ❝♦♥st❛♥t❡✱ ❡♥tã♦✱ ❛ r❛③ã♦ ❡♥tr❡ ❛s ár❡❛s ❞❡ss❛s ♣♦rçõ❡s é ❛ ♠❡s♠❛ ❝♦♥st❛♥t❡✳ ❊ ✐ss♦ ♥♦s ❧❡✈❛ ❛ ❞✐③❡r q✉❡ ❛s ár❡❛s ❞❛s ❞✉❛s ♣♦rçõ❡s sã♦ ✐❣✉❛✐s✳
✷✳ ❙❡ ❞♦✐s só❧✐❞♦s sã♦ t❛✐s q✉❡ t♦❞♦ ♣❧❛♥♦ s❡❝❛♥t❡ ❛ ❡❧❡s ❡ ♣❛r❛❧❡❧♦ ❛ ✉♠ ♣❧❛♥♦ ❞❛❞♦ ❞❡t❡r♠✐♥❛✲♥♦s só❧✐❞❛s s❡❝çõ❡s ❝✉❥❛ r❛③ã♦ é ❝♦♥st❛♥t❡✱ ❡♥tã♦ ❛ r❛③ã♦ ❡♥tr❡ ♦s ✈♦❧✉♠❡s ❞❡ss❡s só❧✐❞♦s é ❛ ♠❡s♠❛ ❝♦♥st❛♥t❡✳ ❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✿ ❞♦✐s só❧✐❞♦s ❝♦♠ ❛ ♠❡s♠❛ ❛❧t✉r❛ tê♠ ♦ ♠❡s♠♦ s❡ s❡❝❝✐♦♥❛❞♦s ♣♦r ✉♠ ♣❧❛♥♦ ♣❛r❛❧❡❧♦ ❛♦ ♣❧❛♥♦ ♦♥❞❡ ❡stã♦ ❛ss❡♥t❛❞♦s✱ ❣❡r❛♠ ár❡❛s ✐❣✉❛✐s✳
✷✳✷ ❉❡t❡r♠✐♥❛çã♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ❡s❢❡r❛ ✉t✐❧✐③❛♥❞♦ ♦ ♣r✐♥✲
❝í♣✐♦ ❞❡ ❈❛✈❛❧✐❡r✐
❈♦♥s✐❞❡r❡ ♥❛ ✜❣✉r❛ ❞❡ ✉♠❛ ❡s❢❡r❛ ❞❡ r❛✐♦r❡ ✉♠❛ ❛♥t✐❝❧❡♣s✐❞r❛ ✭só❧✐❞♦ ❣❡♦♠étr✐❝♦ ❣❡r❛❞♦
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✶✽ ❜❛s❡s ❝♦✐♥❝✐❞❡♠ ❝♦♠ ❛s ❜❛s❡s ❞♦ ❝✐❧✐♥❞r♦✮✱ ❛ss❡♥t❛❞♦s ♥✉♠ ♠❡s♠♦ ♣❧❛♥♦α✳ ❙❡❝❝✐♦♥❛♥❞♦
❛♠❜♦s só❧✐❞♦s ❝♦♠ ✉♠ ♣❧❛♥♦β♣❛r❛❧❡❧♦ ❛♦ ♣❧❛♥♦α❛ ✉♠❛ ❛❧t✉r❛h❞♦s ✈ért✐❝❡s ❞♦s ❝♦♥❡s✿
❋✐❣✉r❛ ✷✳✷✿ ❊s❢❡r❛ ❡ ❛♥t✐❝❧❡♣s✐❞r❛
❊ss❡ ♣❧❛♥♦ β s❡❝❝✐♦♥❛ ❡s❢❡r❛ ❣❡r❛♥❞♦ ✉♠ ❝ír❝✉❧♦ ❞❡ r❛✐♦ s ❡ ❛ ❛♥t✐❝❧❡♣s✐❞r❛ ❣❡r❛♥❞♦
✉♠❛ ❝♦r♦❛ ❝✐r❝✉❧❛r✳
❯t✐❧✐③❛♥❞♦ ❞❛ ❣❡♦♠❡tr✐❛ ❡❧❡♠❡♥t❛r✱ ✈❛♠♦s ♠♦str❛r q✉❡ ❛♠❜❛s ❛s s❡❝çõ❡s tê♠ ár❡❛ ✐❣✉❛❧ ❛π(r✷−h✷)✳
❉❛ ❡s❢❡r❛✱ ♣♦❞❡♠♦s ❞❡st❛❝❛r ♦ tr✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦ ❛❜❛✐①♦ ❡ ✉t✐❧✐③❛r ♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s ♣❛r❛ ❡s❝r❡✈❡r ♦ r❛✐♦s ❡♠ ❢✉♥çã♦ ❞❡ r❡ h✳
❋✐❣✉r❛ ✷✳✸✿ ❚r✐â♥❣✉❧♦ ❘❡tâ♥❣✉❧♦ ❞❡ ❝❛t❡t♦s ✧h✧❡ ✧s✧❡ ❤✐♣♦t❡♥✉s❛ ✧r✧
r✷ = h✷+s✷
s✷ = r✷−h✷ ✭✷✳✶✮
❊ ❛ ár❡❛ ❞❛ s❡❝çã♦ ❝✐r❝✉❧❛r s❡rá ❞❛❞❛ ♣♦r✿
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✶✾ ❙✉❜st✐t✉✐♥❞♦ ✭✷✳✸✮ ❡♠ ✭✷✳✹✮✱ ♦❜t❡♠♦s✿
A=π·(r✷−h✷)
❆❣♦r❛ ❢❛❧t❛ ♠♦str❛r q✉❡ ❛ ár❡❛ ❞❛ ❝♦r♦❛ ❝✐r❝✉❧❛r é ✐❣✉❛❧ à ár❡❛ ❞❛ s❡❝çã♦ ❝✐r❝✉❧❛r✳ ❉❛ ❛♥t✐❝❧❡♣s✐❞r❛ ❞❡st❛❝❛♠♦s ♦ tr✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦✿ P♦r s❡♠❡❧❤❛♥ç❛ ❞❡ tr✐â♥❣✉❧♦s t❡♠♦s q✉❡✿
❋✐❣✉r❛ ✷✳✹✿ ❚r✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦ ❡ tr✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦ ✐sós❝❡❧❡s
r
h =
r t
h = t ✭✷✳✸✮
❆ ár❡❛ ❞❛ ❝♦r♦❛ s❡rá ❞❛❞❛ ♣❡❧❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❛ ár❡❛ ❞♦ ❝ír❝✉❧♦ ❞❡ r❛✐♦r ❡ ❞♦ ❝ír❝✉❧♦
❞❡ r❛✐♦t✿
Ac = πr✷−πt✷ ✭✷✳✹✮
❙✉❜st✐t✉✐♥❞♦ ✭✷✳✺✮ ❡♠ ✭✷✳✻✮✱ ♦❜t❡♠♦s✿
A = π(r✷−h✷)
Pr♦✈❛♠♦s q✉❡ ❛s ár❡❛s ❞❛s s❡❝çõ❡s ❣❡r❛❞❛s ♣❡❧♦ ♣❧❛♥♦β♥♦s só❧✐❞♦s sã♦ ✐❣✉❛✐s✳ ❙❡❣✉❡✲
s❡✱ ❡♥tã♦✱ q✉❡ ♣❡❧♦ Pr✐♥❝í♣✐♦ ❞❡ ❈❛✈❛❧✐❡r✐✱ q✉❡ ♦s ❞♦✐s só❧✐❞♦s tê♠ ✈♦❧✉♠❡s ✐❣✉❛✐s✳ ▲♦❣♦ ♦ ✈♦❧✉♠❡ ❱ ❞❛ ❡s❢❡r❛ é ✐❣✉❛❧ ❛♦ ✈♦❧✉♠❡ ❱ ❞❛ ❛♥t✐❝❧❡♣s✐❞r❛✿
Vesfera =Vcilindro−✷·Vcone
❈♦♠♦ ♥♦ ❝✐❧✐♥❞r♦ ❡q✉✐❧át❡r♦ ❛ ❛❧t✉r❛h é ✐❣✉❛❧ ❛ ✷r✱ t❡♠♦s✿
Vcone = πr✷·✷r−
✷ ✸πr✷·r
Vcone =
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✷✵
✷✳✸ ❉❡t❡r♠✐♥❛çã♦ ❞❛ ár❡❛ s✉♣❡r✜❝✐❛❧ ❞❛ ❡s❢❡r❛ ✉t✐❧✐③❛❞♦
♦ ✈♦❧✉♠❡ ❞❛ ❡s❢❡r❛ ❡ ❞♦ ❝♦♥❡
❙✉♣♦♥❤❛ ❛ ❡s❢❡r❛ ❞❡ r❛✐♦ R✱ ❞✐✈✐❞✐❞❛ ❡♠ ✉♠ ♥ú♠❡r♦ ♥ ♠✉✐t♦ ❣r❛♥❞❡ ❞❡ r❡❣✐õ❡s✱ t♦❞❛s
❝♦♠ ár❡❛ ❡ ♣❡rí♠❡tr♦ ♠✉✐t♦ ♣❡q✉❡♥♦✳ ❈♦♠♦ s❡ ❛ ❡s❢❡r❛ ❡st✐✈❡ss❡ ❝♦❜❡rt❛ ♣♦r ✉♠❛ r❡❞❡ ❞❡ ♠❛❧❤❛ ♠✉✐t❛ ✜♥❛✳ ❈❛❞❛ ✉♠❛ ❞❡ss❛s r❡❣✐õ❡s✱ q✉❡ é ✧q✉❛s❡✧♣❧❛♥❛ s❡ n ❢♦r ♠✉✐t♦ ❣r❛♥❞❡✱
s❡rá ❜❛s❡ ❞❡ ✉♠ ❝♦♥❡ ❝♦♠ ✈ért✐❝❡ ♥♦ ❝❡♥tr♦ ❞❛ ❡s❢❡r❛✳ ❆ss✐♠✱ ❛ ❡s❢❡r❛ ✜❝❛rá ❞✐✈✐❞✐❞❛ ❡♠ ♥ ❝♦♥❡s✱ t♦❞♦s ❝♦♠ ❛❧t✉r❛ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✐❣✉❛❧ ❛R ✭t❛♥t♦ ♠❛✐s ❛♣r♦①✐♠❛❞❛♠❡♥t❡
q✉❛♥t♦ ♠❡♥♦r ❢♦r à ❜❛s❡ ❞♦ ❝♦♥❡✮✳
❋✐❣✉r❛ ✷✳✺✿ ❊s❢❡r❛ ❝♦♠ ✈ár✐♦s ❝♦♥❡s ♥❡❧❛ ✐♥s❝r✐t♦s
❙❡A é ❛ ár❡❛ ❞❛ ❡s❢❡r❛ ❡ A✶✱A✷✱ ✳ ✳ ✳ ✱An✱ sã♦ ❛s ár❡❛s ❞❛s ❞✐✈❡rs❛s r❡❣✐õ❡s✱ t❡♠♦s✿
✹
✸πR✸ =∼ ✶
✸A✶R+ ✶
✸A✷R+✳ ✳ ✳+ ✶ ✸AnR
✹
✸πR✸ =∼ ✶
✸(A✶+A✷+✳ ✳ ✳+An)R
✹
✸πR✸ =∼ ✶ ✸AR
A =∼ ✹πR✷
▲♦❣♦ ❛ ár❡❛ ❞❛ s✉♣❡r❢í❝✐❡ ❡s❢ér✐❝❛ ❡ ✐❣✉❛❧ ❛A=∼ ✹πR✷✳
✷✳✹ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s ❞❡ ❆❧❡①❛♥❞r✐❛
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✷✶ ❣r❡❣❛✳ ❱✐✈❡✉ ❡♠ ❆❧❡①❛♥❞r✐❛✱ ❞✉r❛♥t❡ ♦ r❡✐♥❛❞♦ ❞❡ ❉✐♦❝❧❡❝✐❛♥♦ ✭✷✽✹ ❞✳❈✳✲✸✵✺ ❞✳❈✳✮ ❡ ✜❝♦✉ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ s❡❣✉✐❞♦r ❞❛s ✐❞❡✐❛s ▼❛t❡♠át✐❝❛s ❞❡ ❊✉❞♦①♦ ❡ ❆rq✉✐♠❡❞❡s✳ ❊♥tr❡ s❡✉s ❧✐✈r♦s ♦ ♠❛✐s ❢❛♠♦s♦ ❢♦✐ ❙②♥❛❣♦❣❡ ✭✸✷✵ ❞✳ ❈✳✮ ♦✉ ❈♦❧❡çã♦ ▼❛t❡♠át✐❝❛✱ ✉♠ tr❛t❛❞♦ ❡♠ ❣r❡❣♦ ❝♦♠♣♦st♦ ❡♠ ♦✐t♦ ❧✐✈r♦s✱ ✐♠♣♦rt❛♥t❡ ♣♦r ✈ár✐♦s ❢❛t♦r❡s✱ ❝♦♥t✐♥❤❛ ✐♥❢♦r♠❛çõ❡s ✐♥é❞✐t❛s ♣❛r❛ é♣♦❝❛ ❡ ❤♦❥❡ é ✉♠❛ r✐❝❛ ❢♦♥t❡ ❤✐stór✐❝❛ ❞❛ ▼❛t❡♠át✐❝❛ ❣r❡❣❛ ❡ ❛♣r❡s❡♥t❛♥❞♦ ♣r♦✈❛s ♥♦✈❛s ❡ ❧❡♠❛s s✉♣❧❡♠❡♥t❛r❡s ♣❛r❛ ❛s ♦❜r❛s ❞❡ ❊✉❝❧✐❞❡s✱ ❆rq✉✐♠❡❞❡s✱ ❆♣♦❧ô♥✐♦ ❡ Pt♦❧♦♠❡✉✳
❉❛ ❝♦❧❡çã♦ ♦ ♣r✐♠❡✐r♦ ❡ ♣❛rt❡ ❞♦ s❡❣✉♥❞♦ ❡①tr❛✈✐❛r❛♠✲s❡✱ ♠❛s ♥♦s ❞❡♠❛✐s sã♦ ❡♥❝♦♥tr❛✲ ❞♦s r❡❧❛t♦s ❡ ♥♦✈❛s ♣r♦✈❛s ❡ t❡♠❛s s✉♣❧❡♠❡♥t❛r❡s ♣❛r❛ ✈ár✐❛s ♣r♦♣♦s✐çõ❡s ❞❡ ❆rq✉✐♠❡❞❡s✱ ❊✉❝❧✐❞❡s✱ ❆♣♦❧ô♥✐♦ ❡ Pt♦❧♦♠❡✉✱ ❡♥tr❡ ♦✉tr♦s✱ s♦❜r❡ s✉♣❡r❢í❝✐❡s ❞❡ r❡✈♦❧✉çã♦✱ ♣❧❛♥♦s✱ só✲ ❧✐❞♦s ❡ ❧✐♥❡❛r❡s✳ ❙✉❛ ♣r✐♥❝✐♣❛❧ ♦❜r❛ é ❛ ❈♦❧❡çã♦ ▼❛t❡♠át✐❝❛✱ ✉♠❛ ♠✐st✉r❛ ❞❡ ❣✉✐❛ ❞❛ ❣❡♦♠❡tr✐❛ ❞❛ é♣♦❝❛✱ ❛❝♦♠♣❛♥❤❛❞❛ ❞❡ ❝♦♠❡♥tár✐♦s✱ ❝♦♠ ♥✉♠❡r♦s❛s ♣r♦♣♦s✐çõ❡s ♦r✐❣✐♥❛✐s✱ ❛♣r✐♠♦r❛♠❡♥t♦s✱ ❡①t❡♥sõ❡s ❡ ♥♦t❛s ❤✐stór✐❝❛s✳ ◆♦ ❧✐✈r♦ ❱■■✱ ❛♣❛r❡❝❡ ✉♠❛ ❛♥t❡❝✐♣❛çã♦ ❞♦ t❡♦r❡♠❛ ❞♦ ❝❡♥tr♦✐❞❡ ❞❡ P✳ ●✉❧❞✐♥ ✭✶✺✼✼✕✶✻✹✷✮✳
P❛♣♣✉s ❞❡s❝♦❜r✐✉ ✈ár✐♦s t❡♦r❡♠❛s ♣r❡❝✉rs♦r❡s ❞❛ ●❡♦♠❡tr✐❛ Pr♦❥❡t✐✈❛✱ ♣❡sq✉✐s♦✉ ♦ ❝❤❛♠❛❞♦ Pr♦❜❧❡♠❛ ❞❡ ❉✐❞♦ ♦✉ ■s♦♣❡r✐♠étr✐❝♦ ❡✱ ❝✉r✐♦s❛♠❡♥t❡✱ ❞❡♠♦♥str♦✉ q✉❡✱ ❞❡♥tr❡ ❛s ❢♦r♠❛s q✉❡ ❛s ❛❜❡❧❤❛s ♣♦❞❡r✐❛♠ t❡r ❡♠♣r❡❣❛❞♦ ♣❛r❛ ❢❛③❡r s❡✉s ❢❛✈♦s✱ ❛ ❛❞♦t❛❞❛ é ❛ q✉❡ ♠❛✐s ❡❝♦♥♦♠✐③❛ ❝❡r❛✳ ❙✉❛s ❝♦♥❝❧✉sõ❡s ❢♦r❛♠ ♦ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛ ♣❛r❛ ❛ ✐♥✈❡♥çã♦ ❞❛ ❣❡♦♠❡tr✐❛ ❛♥❛❧ít✐❝❛ ♣♦r ❉❡s❝❛rt❡s✱ tr❡③❡ sé❝✉❧♦s ❛♣ós✳ ❏✉♥t♦ ❝♦♠ ❉✐♦❢❛♥t♦✱ ❢♦r❛♠ ♦s ❞♦✐s ♣r✐♥❝✐♣❛✐s ♠❛t❡♠át✐❝♦s ❞❛ ❝❤❛♠❛❞❛ ■❞❛❞❡ ❞❡ Pr❛t❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❆❧❡①❛♥❞r✐❛ ✭✷✺✵✕✸✺✵✮✳
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✷✷
✷✳✺ ❈❡♥tr♦s ❞❡ ●r❛✈✐❞❛❞❡
❚♦❞♦s ♥ós t❡♠♦s ✉♠❛ ♥♦çã♦ ✐♥t✉✐t✐✈❛ ❞♦ q✉❡ s❡❥❛ ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ✭♦✉ ❜❛r✐❝❡♥tr♦✮ ❞❡ ✉♠❛ ✜❣✉r❛ ♣❧❛♥❛✳ ❊ss❡ ♣♦♥t♦ é t❛❧ q✉❡ s❡ ✜①❛r♠♦s ♥❡❧❡ ✉♠ ✜♦✱ ❛ ✜❣✉r❛ ♣❡♥❞✉r❛❞❛ ♣♦r ❡❧❡ ✜❝❛rá ❡♠ ❡q✉✐❧í❜r✐♦ ✐♥❞✐❢❡r❡♥t❡✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ s❡ ❛ ✜❣✉r❛ ❡st✐✈❡r ❡♠ ✉♠ ♣❧❛♥♦ ❤♦r✐③♦♥t❛❧✱ ❞❡♣♦✐s ❞❡ ♣❡♥❞✉r❛❞❛ ♣❡r♠❛♥❡❝❡rá ❤♦r✐③♦♥t❛❧✳
❋✐❣✉r❛ ✷✳✻✿ ❋✐❣✉r❛ ♣❧❛♥❛
P♦❞❡♠♦s ❡♥❝♦♥tr❛r ♦ ❜❛r✐❝❡♥tr♦ ❞❡ ✉♠❛ ✜❣✉r❛ ❋ ♣♦r ✉♠ ♣r♦❝❡ss♦ ♣rát✐❝♦ q✉❡ é ♦ s❡❣✉✐♥t❡✳ Pr✐♠❡✐r♦ ♣❡♥❞✉r❛♠♦s ❛ ✜❣✉r❛ ♣♦r ✉♠ ♣♦♥t♦P✶ ❞❡ s❡✉ ❜♦r❞♦ ❡ tr❛ç❛♠♦s s♦❜r❡ ❋
❛ r❡t❛ ✈❡rt✐❝❛❧ q✉❡ ❝♦♥té♠ ❡ss❡ ♣♦♥t♦✱ ♦✉ s❡❥❛✱ ❛ r❡t❛ q✉❡ ❝♦♥té♠ ♦ ✜♦✳ ❉❡♣♦✐s✱ ♣❡♥❞✉r❛♠♦s ❛ ✜❣✉r❛ ♣♦r ♦✉tr♦ ♣♦♥t♦P✷ ❞❡ s❡✉ ❜♦r❞♦ ❡ tr❛ç❛♠♦s t❛♠❜é♠ s♦❜r❡ ❋ ❛ r❡t❛ ✈❡rt✐❝❛❧ q✉❡
❝♦♥té♠ P✷✳ ❆ ✐♥t❡rs❡çã♦ ❞❛s ❞✉❛s r❡t❛s é ♦ ❜❛r✐❝❡♥tr♦ ❞❡ ❋✳
❋✐❣✉r❛ ✷✳✼✿ ● é ♦ ❜❛r✐❝❡♥tr♦ ❞❛ ✜❣✉r❛ ❋
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✷✸ ❝♦♠ ❛ ✜❣✉r❛ ✷✳✽✳ ❊♥tr❡t❛♥t♦✱ ♥♦ ♣r✐♠❡✐r♦ ❛ ✜❣✉r❛ ❝♦♥s✐st❡ ♥♦ ❝♦♥❥✉♥t♦ ❞♦s ♣♦♥t♦s ✐♥t❡r✐✲ ♦r❡s à ❧✐♥❤❛ ❞❡s❡♥❤❛❞❛ ❡ ♥♦ s❡❣✉♥❞♦ ❛ ✜❣✉r❛ ❝♦♥s✐st❡ ❛♣❡♥❛s ♥♦s ♣♦♥t♦s ❞❛ ♣ró♣r✐❛ ❧✐♥❤❛✳ P❛r❛ ❞❛r ✉♠❛ ✐❞❡✐❛ ♠❛✐s ❝♦♥❝r❡t❛ ❛♦ q✉❡ ❞✐ss❡♠♦s✱ ✐♠❛❣✐♥❡ q✉❡ ♥♦ ♣r✐♠❡✐r♦ ❝❛s♦ ❛ ✜❣✉r❛ ❢♦✐ r❡❝♦rt❛❞❛ ❞❡ ✉♠❛ ❝❤❛♣❛ ❞❡ ♠❛❞❡✐r❛ ❡ ♥♦ s❡❣✉♥❞♦ ❝❛s♦✱ ❛ ✜❣✉r❛ ❢♦✐ ❢❡✐t❛ ❛♣❡♥❛s ❝♦♠ ❛r❛♠❡✳ ❖s ❝❡♥tr♦s ❞❡ ❣r❛✈✐❞❛❞❡ ❞❡ss❛s ✜❣✉r❛s sã♦G✶ ❡G✷✳
❋✐❣✉r❛ ✷✳✽✿ ❋✐❣✉r❛s ♣❧❛♥❛s
❱❛♠♦s tr❛t❛r ❛❣♦r❛ ❞❡ ♠♦str❛r ❝♦♠♦ s❡ ❞❡t❡r♠✐♥❛ ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❡ ✜❣✉r❛s s✐♠♣❧❡s✳ ▼❛s✱ ♣❛r❛ ✐ss♦✱ ❞❡✈❡♠♦s ❡st❛❜❡❧❡❝❡r ❝♦♠♦ ❛①✐♦♠❛s ❛s ♣r♦♣♦s✐çõ❡s s❡❣✉✐♥t❡s✿
✶✳ ❖ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❡ ✉♠ s❡❣♠❡♥t♦ é s❡✉ ♣♦♥t♦ ♠é❞✐♦✳
✷✳ ❙❡ ✉♠❛ ✜❣✉r❛ ♣♦ss✉✐ ✉♠ ❡✐①♦ ❞❡ s✐♠❡tr✐❛ ❡♥tã♦ ♦ s❡✉ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ♣❡rt❡♥❝❡ ❛ ❡ss❡ ❡✐①♦✳
❈♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛✱ s❡ ✉♠❛ ✜❣✉r❛ ♣♦ss✉✐ ✉♠ ❝❡♥tr♦ ❞❡ s✐♠❡tr✐❛ ✭✐♥t❡rs❡çã♦ ❞❡ ❞♦✐s ❡✐①♦s s✐♠❡tr✐❛✮✱ ❡♥tã♦ ❡ss❡ ♣♦♥t♦ é ♦ s❡✉ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡✳
✷✳✻ ❈❡♥tr♦ ❞❡ ●r❛✈✐❞❛❞❡ ❞❡ ✉♠❛ P♦❧✐❣♦♥❛❧
❈♦♥s✐❞❡r❡♠♦s ✉♠❛ ❧✐♥❤❛ ♣♦❧✐❣♦♥❛❧ ❢♦r♠❛❞❛ ♣♦r s❡❣♠❡♥t♦s ❝♦♥s❡❝✉t✐✈♦s l✶✱l✷✱ ✳ ✳ ✳ ✱ln ❞❡
❝♦♠♣r✐♠❡♥t♦s a✶✱a✷✱ ✳ ✳ ✳ ✱an r❡s♣❡❝t✐✈❛♠❡♥t❡✳ P❛r❛ ❥✉st✐✜❝❛r ❛ ❞❡✜♥✐çã♦ q✉❡ ❞❛r❡♠♦s✱
✈❛♠♦s ✐♠❛❣✐♥❛r q✉❡ ♦s ❧❛❞♦s ❞❡ss❛ ♣♦❧✐❣♦♥❛❧ s❡❥❛♠ ✈❛r❡t❛s ❢❡✐t❛s ❞♦ ♠❡s♠♦ ♠❛t❡r✐❛❧ ❡ ❝♦♠ ♠❡s♠❛ s❡çã♦ r❡t❛ ✭s❡çã♦ ♣❡r♣❡♥❞✐❝✉❧❛r ❛ ❝❛❞❛ ✈❛r❡t❛✮✳ ❉❡st❛ ❢♦r♠❛✱ ❛ ♠❛ss❛ ❞❡ ❝❛❞❛ ✈❛r❡t❛ é ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ s❡✉ ❝♦♠♣r✐♠❡♥t♦✱ ♦✉ s❡❥❛✱mk = c·ak ♣❛r❛ ✶ 6 k6 n✳ ❈♦♠♦
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✷✹ ❉❡✜♥✐çã♦✿ ❙❡ ✉♠❛ ♣♦❧✐❣♦♥❛❧ P é ❢♦r♠❛❞❛ ♣♦r s❡❣♠❡♥t♦s ❝♦♥s❡❝✉t✐✈♦s l✶✱l✷✱ ✳ ✳ ✳ ✱ln
❞❡ ❝♦♠♣r✐♠❡♥t♦sa✶✱a✷✱ ✳ ✳ ✳ ✱an✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❡ s❡♥❞♦(xk✱yk) ♦ ♣♦♥t♦ ♠é❞✐♦ ❞♦ s❡❣✲
♠❡♥t♦ lk✱ ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❡ P é ♦ ♣♦♥t♦ G= (x✱y) ♦♥❞❡✿
x = a✶x✶+a✷x✷+✳✳✳+anxn a✶+a✷+✳✳✳+an
❡ y= a✶y✶+a✷y✷+✳✳✳+anyn a✶+a✷+✳✳✳+an
P❛r❛ ✜①❛r ❛s ✐❞❡✐❛s✱ ✈❛♠♦s ♠♦str❛r ✉♠ ❡①❡♠♣❧♦ ♦♥❞❡ ❝❛❧❝✉❧❛r❡♠♦s ❛ ♣♦s✐çã♦ ❞♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞♦ ❜♦r❞♦ ❞♦ tr✐â♥❣✉❧♦✳
❊①❡♠♣❧♦✿ ❉❡t❡r♠✐♥❛r ❛ ♣♦s✐çã♦ ❞♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞♦ ❜♦r❞♦ ❞❡ ✉♠ tr✐â♥❣✉❧♦ ❝✉❥♦s ❧❛❞♦s ♠❡❞❡♠ ✸✵ ❝♠✱ ✸✵ ❝♠ ❡ ✸✻ ❝♠✳
❙❖▲❯➬➹❖✿ ❙❡❥❛ ❆❇❈ ♦ tr✐â♥❣✉❧♦ ❡♠ q✉❡stã♦ ❝♦♠ ❆❇ ❂ ❆❈ ❂ ✸✵ ❡ ❇❈ ❂ ✸✻✳ ❱❛♠♦s ❛♣♦✐á✲❧❛ ❡♠ ✉♠❛ r❡t❛ ❳ q✉❡ ❝♦♥té♠ ❇❈✳
❋✐❣✉r❛ ✷✳✾✿ ❚r✐â♥❣✉❧♦ ✐sós❝❡❧❡s
❈♦♠♦ tr✐â♥❣✉❧♦ é ✐sós❝❡❧❡s ❡♥tã♦ ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ♣r♦❝✉r❛❞♦ ❡stá ❡♠ s❡✉ ❡✐①♦ ❞❡ s✐♠❡tr✐❛✱ ♦✉ s❡❥❛✱ ❡❧❡ ♣❡rt❡♥❝❡ à ❛❧t✉r❛ r❡❧❛t✐✈❛ ❛♦ ❧❛❞♦ ❇❈✳ ▲♦❣♦✱ ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛ s✉❛ ♣♦s✐çã♦✱ ❜❛st❛ ❞❡t❡r♠✐♥❛r ❛ q✉❡ ❞✐stâ♥❝✐❛ ❡❧❡ ❡stá ❞❛ r❡t❛ ❳✳ ❆ ❛❧t✉r❛ r❡❧❛t✐✈❛ à ❇❈ ❞✐✈✐❞❡ ♦ tr✐â♥❣✉❧♦ ❞❛❞♦ ❡♠ ❞♦✐s tr✐â♥❣✉❧♦s r❡tâ♥❣✉❧♦s ❝♦♠ ❤✐♣♦t❡♥✉s❛ ✐❣✉❛❧ ❛ ✸✵ ❡ ✉♠ ❝❛t❡t♦ ✐❣✉❛❧ ❛ ✶✽✳ P❡❧♦ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s✱ ❝♦♥❝❧✉í♠♦s q✉❡ ❞✐stâ♥❝✐❛ ❞❡ ❆ à r❡t❛ ❳ ♠❡❞❡ ✷✹ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛s ❞✐stâ♥❝✐❛s ❞♦s ♣♦♥t♦s ♠é❞✐♦s ❞❡ ❆❇ ❡ ❆❈ à r❡t❛ ❳ ✈❛❧❡♠ ✶✷✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ♥♦ss❛ ❞❡✜♥✐çã♦✱ ❛ ❞✐stâ♥❝✐❛ ❞♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❡ss❡ tr✐â♥❣✉❧♦ ❆❇❈ à r❡t❛ ❳ é✿
y= ✸✵·✶✷+✸✵·✶✷+✸✻·✵
✸✵+✸✵+✸✻ =✼✱ ✺
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✷✺ ✐❣✉❛❧ ❛ ✷✹✸ =✽✳ ❊♥tr❡t❛♥t♦ ♥♦ss♦s ❝á❧❝✉❧♦s ♠♦str❛r❛♠ q✉❡ ❡ss❛ ❞✐stâ♥❝✐❛ é ✼✱✺✳ ❖♥❞❡ ❡stá
♦ ❡rr♦❄
◆❛ r❡❛❧✐❞❛❞❡✱ ♥ã♦ ❤á ❡rr♦ ♥❡♥❤✉♠✳ ◆❡st❡ ❡①❡♠♣❧♦✱ ♦ tr✐â♥❣✉❧♦ é ❛♣❡♥❛s ❛ r❡✉♥✐ã♦ ❞♦s três ❧❛❞♦s✱ ♦✉ s❡❥❛✱ ❛q✉✐ ❛ ♣❛❧❛✈r❛ tr✐â♥❣✉❧♦ r❡❢❡r❡✲s❡ ❛ ✉♠❛ ❧✐♥❤❛ ♣♦❧✐❣♦♥❛❧ ❢❡❝❤❛❞❛ ❢♦r♠❛❞❛ ♣♦r três s❡❣♠❡♥t♦s ❡ ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❡ss❛ ✜❣✉r❛ ❡stá ♠❡s♠♦ ❛ ✼✱✺ ❝♠ ❞❡ ❞✐stâ♥❝✐❛ ❞♦ ❧❛❞♦ ❇❈✳ ❖ q✉❡ ♦❝♦rr❡ é q✉❡ ♦ ❜❛r✐❝❡♥tr♦ ❞♦ tr✐â♥❣✉❧♦ q✉❡ ❝♦♥❤❡❝❡♠♦s ✐♥t❡rs❡çã♦ ❞❡ s✉❛s ♠❡❞✐❛♥❛s é ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❡ s✉❛ s✉♣❡r❢í❝✐❡✳
✷✳✼ ❉❡♠♦♥str❛çã♦ ❞♦ Pr✐♠❡✐r♦ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s
❚r❛t❛r❡♠♦s ❛❣♦r❛ ❡♠ ❞❡✜♥✐r ❡ ❞❡♠♦♥str❛r ♦ Pr✐♠❡✐r♦ ❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s q✉❡ s❡ tr❛t❛r ❡♠ ❝❛❧❝✉❧❛r ❛ ár❡❛ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ só❧✐❞♦ ❞❡ r❡✈♦❧✉çã♦ ✉t✐❧✐③❛♥❞♦ ❝♦♥t❡ú❞♦s ❞♦ ❡♥s✐♥♦ ♠é❞✐♦✳
❚❡♦r❡♠❛ ✶✳ ❙❡ ✉♠❛ ❧✐♥❤❛ ♣❧❛♥❛ ❣✐r❛ ❡♠ t♦r♥♦ ❞❡ ✉♠ ❡✐①♦ ❞❡ s❡✉ ♣❧❛♥♦✱ ❡♥tã♦ ❛ ár❡❛ ❞❛ s✉♣❡r❢í❝✐❡ ❣❡r❛❞❛ é ✐❣✉❛❧ ❛♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ss❛ ❧✐♥❤❛ ♠✉❧t✐♣❧✐❝❛❞♦ ♣❡❧♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ❞❡s❝r✐t❛ ♣❡❧♦ s❡✉ ❜❛r✐❝❡♥tr♦✳
❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ s❡ ✉♠❛ ❧✐♥❤❛ ♣❧❛♥❛ t❡♠ ❝♦♠♣r✐♠❡♥t♦ L ❡ s❡ x é ❛ ❞✐stâ♥❝✐❛ ❞♦
❜❛r✐❝❡♥tr♦ ❞❡ss❛ ❧✐♥❤❛ ❛ ✉♠ ❡✐①♦ ❊✱ ♦ ✶◦❚❡♦r❡♠❛ ❞❡ P❛♣♣✉s ❛✜r♠❛ q✉❡ ❛ ár❡❛ ❞❛ s✉♣❡r❢í❝✐❡
❞❡ r❡✈♦❧✉çã♦ q✉❡ ❣❡r❛❞❛ ♣❡❧❛ r♦t❛çã♦ ❞❛ ❧✐♥❤❛ ❡♠ t♦r♥♦ ❞❡ ❊ ✈❛❧❡ ✷πxL✳ ❆✐♥❞❛ ✱ ❡st❛♠♦s
✉s❛♥❞♦ ❛q✉✐ ❛ ♣❛❧❛✈r❛ ❜❛r✐❝❡♥tr♦ s✐❣♥✐✜❝❛♥❞♦ ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡✳
❋✐❣✉r❛ ✷✳✶✵✿ ▲✐♥❤❛ ♣❧❛♥❛ ▲✱ ❢♦♥t❡ ❬✸❪
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✷✻ ❈♦♥s✐❞❡r❡♠♦s ❡♥tã♦ ❝♦♠♦ ♥❛ ✜❣✉r❛ ❛ s❡❣✉✐r✱ ✉♠❛ ♣♦❧✐❣♦♥❛❧ ♣❧❛♥❛ ❝✉❥♦s ❧❛❞♦s tê♠ ❝♦♠♣r✐♠❡♥t♦s a✶✱a✷✱ ✳ ✳ ✳ ✱an ❡ ❝✉❥♦s ♣♦♥t♦s ♠é❞✐♦s ❞✐st❛♠ x✶✱x✷✱ ✳ ✳ ✳ ✱xn ❞❡ ❊✱ r❡s♣❡❝t✐✲
✈❛♠❡♥t❡✳ ❙❡❥❛ ❛✐♥❞❛L=a✶ +a✷+✳ ✳ ✳+an ✳
❋✐❣✉r❛ ✷✳✶✶✿ ▲✐♥❤❛ ♣♦❧✐❣♦♥❛❧✱ ❢♦♥t❡ ❬✸❪
❆ r♦t❛çã♦ ❞❡ ❝❛❞❛ s❡❣♠❡♥t♦ ❡♠ t♦r♥♦ ❞❡ ❊✱ ❣❡r❛ ❛ s✉♣❡r❢í❝✐❡ ❧❛t❡r❛❧ ❞❡ ✉♠ tr♦♥❝♦ ❞❡ ❝♦♥❡ ❡✱ ♣♦rt❛♥t♦✱ ❛ ár❡❛ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ r❡✈♦❧✉çã♦ ❣❡r❛❞❛ ♣❡❧❛ ♣♦❧✐❣♦♥❛❧ é ❛ s♦♠❛ ❞❛s ár❡❛s ❞❡ t♦❞♦s ♦s tr♦♥❝♦s✳ ❚❡♠♦s ❡♥tã♦ ♣❛r❛ ❛ ár❡❛ ❞❛ s✉♣❡r❢í❝✐❡ ❣❡r❛❞❛ ♣❡❧❛ ♣♦❧✐❣♦♥❛❧✿
A = ✷πx✶a✶+✷πx✷a✷+✳ ✳ ✳+✷πxnan
A = ✷π(x✶a✶+x✷a✷+✳ ✳ ✳+xnan)
❊♥tr❡t❛♥t♦✱ s❡x é ❛ ❞✐stâ♥❝✐❛ ❞♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❛ ♣♦❧✐❣♦♥❛❧ ❛♦ ❡✐①♦ ❊ ❡♥tã♦✿
x = x✶a✶+x✷a✷+✳ ✳ ✳+xnan a✶+a✷+✳ ✳ ✳+an
xL = x✶a✶+x✷a✷+✳ ✳ ✳+xnan
P♦rt❛♥t♦✱ ❛ ár❡❛ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ r❡✈♦❧✉çã♦ ❣❡r❛❞❛ ♣❡❧❛ r♦t❛çã♦ ❞❛ ♣♦❧✐❣♦♥❛❧ ❡♠ t♦r♥♦ ❞♦ ❡✐①♦ é✿
A=✷πxL
✷✳✽ ❈❡♥tr♦ ❞❡ ●r❛✈✐❞❛❞❡ ❞❡ ✉♠ P♦❧í❣♦♥♦
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✷✼ ❊♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✱ ✈❛♠♦s ❡♥t❡♥❞❡r ♣♦rq✉❡ ♦ ♣♦♥t♦ ❞❡ ✐♥t❡rs❡çã♦ ❞❛s ♠❡❞✐❛♥❛s ❞❡ ✉♠ tr✐â♥❣✉❧♦ é ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❡ s✉❛ s✉♣❡r❢í❝✐❡✳
■♠❛❣✐♥❡ ✉♠ tr✐â♥❣✉❧♦ ❆❇❈ r❡❝♦rt❛❞♦ ❞❡ ✉♠❛ ❝❤❛♣❛ ❞❡ ♠❛❞❡✐r❛ ❡ ♣❡♥❞✉r❛❞♦ ♣❡❧♦ ✈ért✐❝❡ ❆✳ P♦rq✉❡ ❛ r❡t❛ ✈❡rt✐❝❛❧ q✉❡ ♣❛ss❛ ♣♦r ❆✱ ♣❛ss❛ t❛♠❜é♠ ♥♦ ♣♦♥t♦ ♠é❞✐♦ ❞❡ ❇❈❄
❋✐❣✉r❛ ✷✳✶✷✿ ❚r✐â♥❣✉❧♦ ❆❇❈
P❛r❛ r❡s♣♦♥❞❡r✱ ✐♠❛❣✐♥❡ ♦ tr✐â♥❣✉❧♦ ❆❇❈ ❝♦rt❛❞♦ ♣♦r r❡t❛s ♣❛r❛❧❡❧❛s ❛ ❇❈ ❡♠ ❢❛t✐❛s ♠✉✐t♦ ✜♥❛s✳ ❈❛❞❛ ❢❛t✐❛ é ✏q✉❛s❡✑ ✉♠ s❡❣♠❡♥t♦ ❡✱ ♣♦rt❛♥t♦ só ✜❝❛ ❡q✉✐❧✐❜r❛❞❛ s❡ ♣❡♥❞✉r❛❞❛ ♣❡❧♦ s❡✉ ♣♦♥t♦ ♠é❞✐♦✳ ▲♦❣♦✱ ❛ r❡t❛ ✈❡rt✐❝❛❧ q✉❡ ❝♦♥té♠ ❆ ♣❛ss❛ ♣❡❧♦s ♣♦♥t♦s ♠é❞✐♦s ❞❡ t♦❞❛s ❛s ❢❛t✐❛s ❡✱ ❡♠ ♣❛rt✐❝✉❧❛r✱ ♣❡❧♦ ♣♦♥t♦ ♠é❞✐♦ ❞❡ ❇❈✳ ❖r❛✱ s❡ ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ✉♠ tr✐â♥❣✉❧♦ ♣❡rt❡♥❝❡ ❛ ✉♠❛ ♠❡❞✐❛♥❛✱ ❡♥tã♦ ✭r❡♣❡t✐♥❞♦✲s❡ ❛ ❡①♣❡r✐ê♥❝✐❛✮ ❡❧❡ é ♦ ♣♦♥t♦ ❞❡ ✐♥t❡rs❡çã♦ ❞❛s ♠❡❞✐❛♥❛s ❞❡ ✉♠ tr✐â♥❣✉❧♦ é ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❡ s✉❛ s✉♣❡r❢í❝✐❡✳
P❛r❛ ❞❡t❡r♠✐♥❛r ❛ ♣♦s✐çã♦ ❞♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ✉♠ ♣♦❧í❣♦♥♦✱ ✈❛♠♦s ✐♠❛❣✐♥á✲❧♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❞✐✈✐❞✐❞♦ ❡♠ tr✐â♥❣✉❧♦s T✶✱T✷✱ ✳ ✳ ✳ ✱Tn ❝♦♠ ár❡❛s A✶✱A✷✱ ✳ ✳ ✳ ✱An
r❡s♣❡❝t✐✈❛♠❡♥t❡ ✭✜❣✉r❛ ✷✳✶✸✮✳ ❈♦♥s✐❞❡r❡♠♦s ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ♥♦ ♣❧❛♥♦ ❞♦ ♣♦✲ ❧í❣♦♥♦ ❡ s❡❥❛(xk✱yk) ♦ ❜❛r✐❝❡♥tr♦ ❞♦ tr✐â♥❣✉❧♦ Tk ❆♣❡❧❛♥❞♦ ♥♦✈❛♠❡♥t❡ ♣❛r❛ ♦ r❛❝✐♦❝í♥✐♦
❢ís✐❝♦ ❞❡ ❝♦♥s✐❞❡r❛r ❛ ✜❣✉r❛ r❡❝♦rt❛❞❛ ❡♠ ✉♠❛ ❝❤❛♣❛ ✉♥✐❢♦r♠❡ ❞❡ ❡s♣❡ss✉r❛ ❝♦♥st❛♥t❡✱ t❡♠♦s q✉❡ ❛ ♠❛ss❛ ❞❡ ❝❛❞❛ tr✐â♥❣✉❧♦ é ♣r♦♣♦r❝✐♦♥❛❧ à s✉❛ ár❡❛✱ ♦✉ s❡❥❛✱ ❛ ♠❛ss❛ mk ❞♦
tr✐â♥❣✉❧♦ Tk é ✐❣✉❛❧ ❛ c·Tk ♣❛r❛ ❝❡rt❛ ❝♦♥st❛♥t❡ ❝ ✭q✉❡ ❞❡♣❡♥❞❡ ❞♦ ♠❛t❡r✐❛❧✮✳ P♦❞❡♠♦s
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞✐♠❡♥t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈♦❧✉♠❡ ❞❛ ♠❛çã ✷✽ ❜❛r✐❝❡♥tr♦✳
❋✐❣✉r❛ ✷✳✶✸✿ P♦❧í❣♦♥♦ ❧♦❝❛❧✐③❛❞♦ ♥♦ ♣❧❛♥♦ ❝❛rt❡s✐❛♥♦
❊ss❛s ❝♦♥s✐❞❡r❛çõ❡s ♣❡r♠✐t❡♠ ❛❝❡✐t❛r ❛ ❞❡✜♥✐çã♦ s❡❣✉✐♥t❡✳
❉❡✜♥✐çã♦✿ ❙❡ ✉♠ ♣♦❧í❣♦♥♦ P ❡stá ❞✐✈✐❞✐❞♦ ❡♠ ✜❣✉r❛sT✶✱T✷✱ ✳ ✳ ✳ ✱Tn✱ ❞❡ ár❡❛sA✶✱A✷✱ ✳ ✳ ✳ ✱An✱
r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❡ s❡♥❞♦(xk✱yk) ♦ ❜❛r✐❝❡♥tr♦ ❞❛ ✜❣✉r❛Tk ✱ ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❛ s✉✲
♣❡r❢í❝✐❡ ❞❡P é ♦ ♣♦♥t♦ G= (x✱y)✱ t❛❧ q✉❡✿
x= A✶x✶+A✷x✷+✳✳✳+Anxn A✶+A✷+✳✳✳+An ❡
y= A✶y✶+A✷y✷+✳✳✳+Anyn A✶+A✷+✳✳✳+An
P❛r❛ ✜①❛r ❡ss❛ ✐❞❡✐❛✱ ✈❛♠♦s✱ ♥♦ ❡①❡♠♣❧♦ ❛ s❡❣✉✐r✱ ❞❡t❡r♠✐♥❛r ❛ ♣♦s✐çã♦ ❞♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ✉♠ tr❛♣é③✐♦✳
❊①❡♠♣❧♦✿ ❉❡t❡r♠✐♥❡ ❛ ♣♦s✐çã♦ ❞♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ tr❛♣é③✐♦ ❆❇❈❉ ♦♥❞❡A=D=✾✵◦✱
AB=✶✵✱ CD=✹ ❡ AD=✻✳
❙❖▲❯➬➹❖✿ ❈♦♥s✐❞❡r❡♠♦s ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s✱ A = (✵✱ ✵)✱ B= (✶✵✱ ✵)✱ C= (✹✱ ✻) ❡ D= (✵✱ ✻)✱ ❝♦♠♦ ♥❛ ✜❣✉r❛ ❛ s❡❣✉✐r✳
