❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❖ ❚❘■➶◆●❯▲❖ ▼■◆❊■❘❖ ▼❊❙❚❘❆❉❖ P❘❖❋■❙❙■❖◆❆▲ ❊▼ ▼❆❚❊▼➪❚■❈❆
❆ ▼❆❚❊▼➪❚■❈❆ ❋■◆❆◆❈❊■❘❆
❊ ❖ ❊◆❙■◆❖ ▼➱❉■❖
❊❞♠✐❧s♦♥ ◆❛❤❛ss ❋r❛♥❝♦
❊❞♠✐❧s♦♥ ◆❛❤❛ss ❋r❛♥❝♦
❆ ▼❆❚❊▼➪❚■❈❆ ❋■◆❆◆❊■❘❆ ❊ ❖ ❊◆❙■◆❖ ▼➱❉■❖
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ ❈✉rs♦ ❞❡ ▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠ ▼❛t❡♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧ ✲ P❘❖❋▼❆❚✱ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❚r✐✲ â♥❣✉❧♦ ▼✐♥❡✐r♦ ✲ ❯❋❚▼✱ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ▼❛✲ t❡♠át✐❝❛✱ ❝♦♠♦ ♣❛rt❡ ❞❛s ❛t✐✈✐❞❛❞❡s ♣❛r❛ ❛ ♦❜✲ t❡♥çã♦ ❞♦ ❚ít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ▼❛t❡♠át✐❝❛✱ s♦❜ ♦r✐❡♥t❛çã♦ ❞♦ Pr♦❢❡ss♦r ❉♦✉t♦r ◆❡❧s♦♥ ❋❡r♥❛♥❞♦ ■♥❢♦r③❛t♦✳
C a t a l o g a ç ã o n a f o n t e : B i b l i o t e c a d a U n i v e r s i d a d e F e d e r a l d o T r i â n g u l o M i n e i r o
Franco, Edmilson Nahass
F895m A matemática financeira e o ensino médio / Edmilson Nahass Franco. -- 2016.
136 f. : il., fig., graf., tab.
Dissertação (Mestrado Profissional em Matemática em Rede Nacional) -- Universidade Federal do Triângulo Mineiro, Uberaba, MG, 2016
Orientador: Prof. Dr. Nelson Fernando Inforzato
❉❡❞✐❝❛tór✐❛
❆❣r❛❞❡❝✐♠❡♥t♦s
❘❡s✉♠♦
◆❡st❡ tr❛❜❛❧❤♦ ♣r♦❝✉r❛♠♦s ❞❡s❡♥✈♦❧✈❡r ❝♦♥❝❡✐t♦s s✐♠♣❧❡s s♦❜r❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❡ ❘❡❣✐♠❡s ❞❡ ❏✉r♦s ❛❞♦t❛❞♦s ✉♥✐✈❡rs❛❧♠❡♥t❡✳ ❊st❛❜❡❧❡❝❡♠♦s ✉♠ ♣❛r❛❧❡❧♦ ❡♥tr❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❈♦♥tí♥✉❛ ❡ ❉❡s❝♦♥tí♥✉❛ ❡ ♦s ❘❡❣✐♠❡s ❞❡ ❏✉r♦s ❙✐♠♣❧❡s ❡ ❈♦♠♣♦st♦s✳ ▼♦str❛♠♦s q✉❡ ♦s ❈á❧❝✉❧♦s ❞❛s r❡♥✲ ❞❛s ❡ ❛♥✉✐❞❛❞❡s ❛❞♦t❛❞❛s ❤♦❥❡ ♥♦ ❇r❛s✐❧ sã♦ ❛♥❛t♦❝✐s♠♦ ❡ q✉❡ ♦s ✐♥t❡r❡ss❡s ❞❛s ■♥st✐t✉✐çõ❡s ❋✐♥❛♥❝❡✐r❛s sã♦ ❡st❛❜❡❧❡❝✐❞♦s ❡♠ ❢✉♥çã♦ ❞♦s ❘❡❣✐♠❡s ❞❡ ❏✉r♦s q✉❡ ❛s ❢❛✈♦r❡❝❡♠ ✉♥✐❧❛t❡r❛❧♠❡♥t❡✳ ❉❡s❡♥✈♦❧✈❡♠♦s ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ♣❛r❛ ❝á❧✲ ❝✉❧♦ ❞❡ ❘❡♥❞❛s ❡ ❆♥✉✐❞❛❞❡s ♣❡❧♦ ❘❡❣✐♠❡ ❞❡ ❏✉r♦s ❙✐♠♣❧❡s s❡♠ ❛ ♣r❡s❡♥ç❛ ❞♦ ❛♥❛t♦❝✐s♠♦✱ ♠♦str❛♥❞♦ q✉❡ ♦ t❡♠♣♦ ♥ã♦ é ❝✐♥❞í✈❡❧ ♣❛r❛ t❛❧ r❡❣✐♠❡✳ ❆♦ ✜♥❛❧✱ ♣r♦♣♦♠♦s ✉♠❛ s✉❣❡stã♦ ♣❛r❛ ✐♥tr♦❞✉çã♦ à ▼❛t❡♠át✐❝❛ ❋✐♥❛♥❝❡✐r❛ ♥♦ ❊♥s✐♥♦ ▼é❞✐♦✳
❆❜str❛❝t
■♥ t❤✐s ❞✐ss❡rt❛t✐♦♥ ✇❡ ❛✐♠ ❛t ❞❡✈❡❧♦♣✐♥❣ ❜❛s✐❝ ❝♦♥❝❡♣ts r❡❣❛r❞✐♥❣ ✉♥✐✈❡rs❛❧❧② ❛❞♦♣t❡❞ ❝❛♣✐t❛❧✐③❛t✐♦♥ s②st❡♠s ❛♥❞ ✐♥t❡r❡st s❝❤❡♠❡s✳ ❲❡ ❡st❛❜❧✐s❤ ❛ ♣❛r❛❧✲ ❧❡❧ ❜❡t✇❡❡♥ t❤❡ ❝♦♥t✐♥✉♦✉s ❛♥❞ t❤❡ ❞✐s❝♦♥t✐♥✉♦✉s ❛❝❝✉♠✉❧❛t✐♦♥ s②st❡♠s✱ ❛♥❞ s✐♠♣❧❡ ❛♥❞ ❝♦♠♣♦✉♥❞ ✐♥t❡r❡st s❝❤❡♠❡s✳ ❲❡ ✐♥t❡♥❞ t♦ ❞❡♠♦♥str❛t❡ t❤❛t t❤❡ ❝❛❧❝✉❧❛t✐♦♥s ♦❢ ✐♥❝♦♠❡ ❛♥❞ ❛♥♥✉✐t✐❡s ❝✉rr❡♥t❧② ❛❞♦♣t❡❞ ✐♥ ❇r❛③✐❧ ❛r❡ ♠❛❞❡ ❛s ❛♥❛t♦❝✐s♠ ❛♥❞ t❤❛t t❤❡ ✐♥t❡r❡sts ♦❢ t❤❡ ✜♥❛♥❝✐❛❧ ✐♥st✐t✉t✐♦♥s ❛r❡ ❞❡t❡r♠✐♥❡❞ ❛s ❛ r❡s✉❧t ♦❢ t❤❡ ✐♥t❡r❡st s❝❤❡♠❡s t❤❛t ❢❛✈♦r t❤❡♠ ✉♥✐❧❛t❡r❛❧❧②✳ ❲❡ ❤❛✈❡ ❞❡✲ ✈❡❧♦♣❡❞ ❛ ♣r♦❝❡❞✉r❡ ❢♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ ✐♥❝♦♠❡ ❛♥❞ ❛♥♥✉✐t✐❡s ❜② ♠❡❛♥s ♦❢ t❤❡ s✐♠♣❧❡ ✐♥t❡r❡st s❝❤❡♠❡ ❛♥❞ ❛✈♦✐❞✐♥❣ ❛♥❛t♦❝✐s♠✱ t❤✉s s❤♦✇✐♥❣ t❤❛t t✐♠❡ ✐s ♥♦t ✜ss✐♦♥❛❜❧❡ ❢♦r s✉❝❤ ❛ s❝❤❡♠❡✳ ■♥ t❤❡ ❡♥❞✱ ✇❡ s✉❣❣❡st ❛ ✇❛② ♦❢ ✐♥tr♦❞✉❝✐♥❣ ❋✐♥❛♥❝✐❛❧ ▼❛t❤❡♠❛t✐❝s ✐♥ ❤✐❣❤ s❝❤♦♦❧✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s ■
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❊①♣♦♥❡♥❝✐❛❧ ❞❡ ✉♠❛ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♥tí♥✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✷ ●rá✜❝♦ ❞❡ ✉♠❛ ❝❛♣✐t❛❧✐③❛çã♦ ❞❡s❝♦♥tí♥✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✸ ●rá✜❝♦ ❞❡ ✉♠❛ ❝❛♣✐t❛❧✐③❛çã♦ ❞❡s❝♦♥tí♥✉❛ s✐♠♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✹✳✹ ●rá✜❝♦ ❝♦♠♣❛r❛t✐✈♦ ❞❡ ✉♠❛ ❢✉♥çã♦ ❆✜♠ ❡ ✉♠❛ ❢✉♥çã♦ ❊①♣♦✲
♥❡♥❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✹✳✺ ●rá✜❝♦s ❞❛s ❢✉♥çõ❡s ❞❡ ❝♦♥✈❡♥çõ❡s ▲✐♥❡❛r ❡ ❊①♣♦♥❡♥❝✐❛❧✳ ✳ ✳ ✳ ✳ ✸✹ ✻✳✻ ❊✐①♦ ❞❡ t❡♠♣♦ ♠♦str❛♥❞♦ ✉♠❛ ❘❡♥❞❛ ❈♦♥st❛♥t❡ ■♠❡❞✐❛t❛✳ ✳ ✳ ✳ ✹✺ ✻✳✼ ❊✐①♦ ❞❡ t❡♠♣♦ ♠♦str❛♥❞♦ ✉♠❛ ❘❡♥❞❛ ❈♦♥st❛♥t❡ ❆♥t❡❝✐♣❛❞❛✳ ✳ ✹✻ ✻✳✽ ❊✐①♦ ❞❡ t❡♠♣♦ ♠♦str❛♥❞♦ ✉♠❛ ❘❡♥❞❛ ❈♦♥st❛♥t❡ ■♠❡❞✐❛t❛ ❉✐✲
❢❡r✐❞❛ ❞❡ ✉♠ t❡♠♣♦ ✏♠✑✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✻✳✾ ❊✐①♦ ❞❡ t❡♠♣♦ ♠♦str❛♥❞♦ ✉♠❛ ❘❡♥❞❛ ❈♦♥st❛♥t❡ ❆♥t❡❝✐♣❛❞❛
❉✐❢❡r✐❞❛ ❞❡ ✉♠ t❡♠♣♦ ✏♠✑✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✻✳✶✵ ❊✐①♦ ❞❡ t❡♠♣♦ ♠♦str❛♥❞♦ ✉♠❛ ❞❡s❝❛♣✐t❛❧✐③❛çã♦ ❡ ✉♠❛ ❝❛♣✐t❛✲
❧✐③❛çã♦ ❞❡ ✉♠❛ ♠❡s♠❛ q✉❛♥t✐❛ ♥♦ ❘❏❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✻✳✶✶ ❊✐①♦ ❞❡ t❡♠♣♦ ♠♦str❛♥❞♦ ✉♠❛ ❞❡s❝❛♣✐t❛❧✐③❛çã♦ ❡ ✉♠❛ ❝❛♣✐t❛❧✐✲
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✻✳✶✹ ❊✈♦❧✉çã♦ ❞❡ ✉♠ ❝❛♣✐t❛❧ C0 ❡ ❉❡s❝❛♣✐t❛❧✐③❛çã♦ ❞❡ ✉♠ ♠♦♥t❛♥t❡ Cn ♥♦ ❘❏❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✻✳✶✺ ❈❛♣✐t❛❧✐③❛çã♦ ❞❡ ✉♠ ❝❛♣✐t❛❧C0 ❡ ❉❡s❝❛♣✐t❛❧✐③❛çã♦ ❞❡ ✉♠ ♠♦♥✲
t❛♥t❡ Cn ♣❛r❛ ✉♠❛ ❞❛t❛ p ♥♦ ❘❏❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✻✳✶✻ ❊✐①♦ ❞❡ t❡♠♣♦ ♠♦str❛♥❞♦ ✉♠❛ ❞í✈✐❞❛ ❡ ❛ s✉❛ ♥❡❣♦❝✐❛çã♦✳ ✳ ✳ ✳ ✳ ✺✽ ✻✳✶✼ n ❛♥✉✐❛❞❡sX ❣❡r❛♥❞♦ ✉♠❛ r❡♥❞❛ C ♥♦ ❘❏❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✻✳✶✽ n ❛♥✉✐❞❛❞❡sX ❣❡r❛♥❞♦ ✉♠❛ r❡♥❞❛ C ♥♦ ❘❏❙✱ ❛♥t❡❝✐♣❛❞❛♠❡♥t❡✳ ✻✺ ✻✳✶✾ n ❛♥✉✐❞❛❞❡s X ❣❡r❛♥❞♦ ✉♠❛ r❡♥❞❛ C ♥♦ ❘❏❙✱ ❡♠ ❛♥✉✐❞❛❞❡s
✐♠❡❞✐❛t❛s ❞✐❢❡r✐❞❛s ❞❡ m ♣❡rí♦❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✻✳✷✵ n ❛♥✉✐❞❛❞❡s X ❣❡r❛♥❞♦ ✉♠❛ r❡♥❞❛ C ♥♦ ❘❏❙✱ ❡♠ ❛♥✉✐❞❛❞❡s
❛♥t❡❝✐♣❛❞❛s ❞✐❢❡r✐❞❛s ❞❡ m ♣❡rí♦❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✻✳✷✶ ✧♥✧❛♥✉✐❞❛❞❡s ✏❳✑ ❢♦r♠❛♥❞♦ ✉♠❛ ❘❡♥❞❛ ■♥❝✐❛❧ ✏❈✑ ♥♦ ❘❏❈ ✲
❘❡♥❞❛s ■♠❡❞✐❛t❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✻✳✷✷ ✏♥✑ ♣❛r❝❡❧❛s ✏❳✑ ♣❛❣❛♥❞♦ ✉♠❛ q✉❛♥t✐❛ ✏❈✑✱ ♥♦ ❘❏❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✻✳✷✸ n ❛♥✉✐❞❛❞❡sX ❣❡r❛♥❞♦ ✉♠❛ r❡♥❞❛ C✱ ♥♦ ❘❏❈✱ ❛tr❛✈és ❞❡ ✉♠❛
❘❡♥❞❛ ■♠❡❞✐❛t❛ ❉✐❢❡r✐❞❛ ❞❡ m ♣❡rí♦❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✼✳✷✹ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦ ❙✐st❡♠❛ ❋r❛♥❝ês ❡ ♦ ❙❆❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✷✺ ❙✐t✉❛çã♦ ❞❡ ✉♠ ✜♥❛♥❝✐❛♠❡♥t♦ ❞❡ ✉♠❛ ❞í✈✐❞❛ ❞❡ R$ 2 500,00
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ■■■
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❚❛❜❡❧❛ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ♦s ❞♦✐s t✐♣♦s ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❡ ♦s ❞♦✐s s✐st❡♠❛s ❞❡ ❥✉r♦s✿ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✹✳✷ ❚❛❜❡❧❛ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ❛s ❝♦♥✈❡çõ❡s ▲✐♥❡❛r ❡ ❊①♣♦♥❡♥❝✐❛❧✿ ✳ ✳ ✸✷ ✻✳✸ ❊✈♦❧✉çã♦ ❞❡ ✉♠ ❝❛♣✐t❛❧ C0 ♥♦ ❘❏❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✻✳✹ ❉❡s❝❛♣✐t❛❧✐③❛çã♦ ❞❡ ✉♠ ♠♦♥t❛♥t❡Cn ♥♦ ❘❏❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✻✳✺ ❊✈♦❧✉çã♦ ❞❡ ✉♠ ❝❛♣✐t❛❧ C0 ❡ ❉❡s❝❛♣✐t❛❧✐③❛çã♦ ❞❡ ✉♠ ♠♦♥t❛♥t❡
Cn ♥♦ ❘❏❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✻✳✻ ❆♠♦rt✐③❛çã♦ ❞❡ ✉♠❛ ❛♥✉✐❞❛❞❡ ✐♠❡❞✐❛t❛ ♥♦ ❘❏❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✻✳✼ ❆♠♦rt✐③❛çã♦ ❞❡ ✉♠❛ ❛♥✉✐❞❛❞❡ ❛♥t❡❝✐♣❛❞❛ ♥♦ ❘❏❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✻✳✽ ❆♠♦rt✐③❛çã♦ ❞❡ ✉♠❛ ❛♥✉✐❞❛❞❡ ❞✐❢❡r✐❞❛ ♥♦ ❘❏❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✻✳✾ ❆♠♦rt✐③❛çã♦ ❞❡ ✉♠❛ ❛♥✉✐❞❛❞❡ ✐♠❡❞✐❛t❛ ♥♦ ❘❏❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✻✳✶✵ ❆♠♦rt✐③❛çã♦ ❞❡ ✉♠❛ ❛♥✉✐❞❛❞❡ ❛♥t❡❝✐♣❛❞❛ ♥♦ ❘❏❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✻✳✶✶ ❆♠♦rt✐③❛çã♦ ❞❡ ✉♠❛ ❛♥✉✐❞❛❞❡ ❛♥t❡❝✐♣❛❞❛ ❞✐❢❡r✐❞❛ ❞❡ ✹ ♠❡s❡s
♥♦ ❘❏❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✼✳✶✷ ❆♠♦rt✐③❛çã♦ ❞❡ ✉♠❛ ❞í✈✐❞❛ C ♣❡❧♦ ❙✐st❡♠❛ Pr✐❝❡ ❡ ❙❆❈ ✳ ✳ ✳ ✳ ✽✽ ✼✳✶✸ ❱❛❧♦r ❞❛s ♣❛r❝❡❧❛s ♣❛r❛ ✉♠❛ ❞í✈✐❞❛ ❞❡ ❘✩ ✶✵ ✵✵✵✱✵✵ ❡♠ ❝✐♥❝♦
❙✉♠ár✐♦ ■❱
❙✉♠ár✐♦
■♥tr♦❞✉çã♦ ✶
✶ ✲ ❯♠ ♣♦✉❝♦ ❞❡ ❍✐stór✐❛ ✹
✶✳✶ ❆ ♦r✐❣❡♠ ❞♦ ❞✐♥❤❡✐r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✶✳✷ ❖s t✐♣♦s ❞❡ ❞✐♥❤❡✐r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✶✳✸ ❖ ❞✐♥❤❡✐r♦ ♠♦❞❡r♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✶✳✹ ❆ ♦r✐❣❡♠ ❞♦ ❏✉r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✶✵ ✷✳✶ ❏✉r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷ ❖s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✷✳✶ ❖ ❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❈♦♥tí♥✉❛ ✲ ❙❈❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✷✳✷ ❖ ❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❉❡s❝♦♥tí♥✉❛ ✲ ❙❈❉ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✷✳✸ ❆ ❞✐st✐♥çã♦ ❡♥tr❡ ♦ ❘❡❣✐♠❡ ❞❡ ❏✉r♦s ❙✐♠♣❧❡s ❡ ♦ ❘❡❣✐♠❡
❞❡ ❏✉r♦s ❈♦♠♣♦st♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✸ ✲ ❖ ❘❡❣✐♠❡ ❞❡ ❏✉r♦s ❙✐♠♣❧❡s ✭❘❏❙✮ ✷✶
❙✉♠ár✐♦
✸✳✸ ❏✉r♦ ❊①❛t♦ ❡ ❏✉r♦ ❈♦♠❡r❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✹ ❱❛❧♦r ❆t✉❛❧ ❡ ❱❛❧♦r ❋✉t✉r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✹ ✲ ❖ ❘❡❣✐♠❡ ❞❡ ❏✉r♦s ❈♦♠♣♦st♦s ✭❘❏❈✮ ✷✼
✹✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✹✳✷ ❏✉r♦s ❈♦♠♣♦st♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✹✳✸ ◗✉❛♥❞♦✱ ♥♦ ❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❉❡s❝♦♥tí♥✉❛✱ t❡♠♣♦ ♥ã♦
é ✉♠❛ ✈❛r✐á✈❡❧ ❞✐s❝r❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✺ ✲ ❖s ♠❛✐s ✈❛r✐❛❞♦s t✐♣♦s ❞❡ ❚❛①❛s ✸✻
✺✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✺✳✷ ❚❛①❛ ◆♦♠✐♥❛❧ ❡ ❚❛①❛ ❊❢❡t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✺✳✸ ❚❛①❛ Pr♦♣♦r❝✐♦♥❛❧ ❡ ❚❛①❛ ❊q✉✐✈❛❧❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✺✳✸✳✶ ❚❛①❛s Pr♦♣♦r❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✺✳✸✳✷ ❚❛①❛s ❊q✉✐✈❛❧❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✺✳✸✳✸ ❚❛①❛ ❞❡ ❏✉r♦s ❡♠ ✉♠ s✐st❡♠❛ ■♥✢❛❝✐♦♥ár✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✻ ✲ ❘❡♥❞❛s ❈♦st❛♥t❡s ✹✹
❙✉♠ár✐♦
✼ ✲ ❙✐st❡♠❛s ❞❡ ❆♠♦rt✐③❛çã♦ ✽✹
✼✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✼✳✷ ❚❛❜❡❧❛ Pr✐❝❡ ✲ ❙✐st❡♠❛ ❋r❛♥❝ês ❞❡ ❆♠♦rt✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✼✳✸ ❙✐st❡♠❛ ❞❡ ❆♠♦rt✐③❛çã♦ ❈♦♥st❛♥t❡ ✲ ❙❆❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✼✳✹ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦ ❙✐st❡♠❛ ❋r❛♥❝ês ✲ Pr✐❝❡ ✲ ❡ ♦ ❙❆❈ ✳ ✳ ✳ ✳ ✳ ✽✼ ✼✳✺ ❙✐st❡♠❛ ❞❡ ❆♠♦rt✐③❛çã♦ ❈r❡s❝❡♥t❡ ✲ ❙❛❝r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸
✽ ✲ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✾✼
❘❡❢❡rê♥❝✐❛s ✶✵✵
❆P✃◆❉■❈❊ ✲ ❖ ❘❏❙✱ ♦ ❘❏❈ ❡ ♦ ❊♥s✐♥♦ ▼é❞✐♦ ✶✵✷
✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✳✷ ❆ ❢✉♥çã♦ ❆✜♠✱ ❛ Pr♦❣r❡ssã♦ ❆r✐t♠ét✐❝❛ ❡ ♦ ❏✉r♦ ❙✐♠♣❧❡s ✳ ✳ ✳ ✳ ✶✵✹ ✳✸ ❆ ❋✉♥çã♦ ❊①♣♦♥❡♥❝✐❛❧✱ ❛ Pr♦❣r❡ssã♦ ●❡♦♠étr✐❝❛ ❡ ♦ ❏✉r♦ ❈♦♠✲
■♥tr♦❞✉çã♦ ✶
■♥tr♦❞✉çã♦
➱ ❝♦♠✉♠✱ ❞❡♥tr♦ ❞♦ ❡st✉❞♦ ❞❛ ❊❝♦♥♦♠✐❛ ❈♦♥t❡♠♣♦râ♥❡❛✱ ❞❡♣❛r❛r♠♦s ♥❛ t❡♦r✐❛ ❝♦♠ ♦ t❡r♠♦ ❈❛♣✐t❛❧ ❡♠ s✐t✉❛çõ❡s ❜❡♠ ❞✐❢❡r❡♥t❡s✳ ❯♠❛ ❞❡❧❛s ❞✐③ r❡s♣❡✐t♦ ❛ ✉♠ ❞♦s ❢❛t♦r❡s ❜ás✐❝♦s ❞❛ ♣r♦❞✉çã♦✱ q✉❡ s❡r✈❡ ❝♦♠♦ ✉♠❛ ❡str❛té❣✐❛ ❛ s❡r ✉t✐❧✐③❛❞❛ ♣❡❧❛s ♣❡ss♦❛s ♣❛r❛ ❡①tr❛✐r ❞❛ ♥❛t✉r❡③❛ ♣r♦❞✉t♦s ❡♠ ❢♦r♠❛s ❞❡ ❜❡♥s✳ ◆♦✉tr❛✱ ♦ ❈❛♣✐t❛❧ s❡ r❡❧❛❝✐♦♥❛ à ❞✐str✐❜✉✐çã♦ ❞♦s ❜❡♥s❀ s✉r❣❡ ❝♦♠♦ ❢♦♥t❡ ❞❡ ❢✉♥❞♦s ❞❡ r❡♥❞❛ ❡ r❡♥❞✐♠❡♥t♦s✳ ▼❛s ♥✉♠❛ ♦✉ ♥♦✉tr❛ s✐t✉❛çã♦ é s❡♥s♦ ❝♦♠✉♠ q✉❡ ♦ ❈❛♣✐t❛❧✱ ❝♦♠♦ r❡s✉❧t❛❞♦ ❞♦ tr❛❜❛❧❤♦ ❝♦❧❡t✐✈♦✱ ❢❛③ ❝♦♠ q✉❡ ❣r❛✈✐t❡ ❡♠ t♦r♥♦ ❞❡ s✐ ✉♠❛ ❣r❛♥❞❡ ♣❛rt❡ ❞♦ ♣r♦❞✉t♦ ♥❛❝✐♦♥❛❧✱ tr❛♥s♣♦♥❞♦ ♣❛r❛ ♦ s❡✉ ♣r♦♣r✐❡tár✐♦ ✉♠❛ r❡♥❞❛✱ q✉❡ ♦✉s❛❞❛♠❡♥t❡✱ ❞❡♥♦♠✐♥❛♠♦s ❞❡ ❥✉r♦s✳
➱ ✐♥❞✐s❝✉tí✈❡❧ q✉❡ ♦ ❈❛♣✐t❛❧✱ q✉❛♥❞♦ ❜❡♠ ❛❞♠✐♥✐str❛❞♦✱ ♣r♦❞✉③ ❜❡♥s✱ q✉❡ ♣♦r s✉❛ ✈❡③✱ tr❛♥s♣♦rt❛ ❜❡♥s ♣❛r❛ ♦ s❡✉ ♣r♦♣r✐❡tár✐♦✱ ♠♦str❛♥❞♦ ❛ r❡❝✐♣r♦❝✐✲ ❞❛❞❡ ❡♥tr❡ ❛s ❞✉❛s r❡❢❡rê♥❝✐❛s✿ ♦ ❈❛♣✐t❛❧ ♣r♦✈♦❝❛ ❛ ♣r♦❞✉çã♦ ❞❡ ❜❡♥s ❛ s❡✉ ♣r♦♣r✐❡tár✐♦ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ❡❧❡ t❡r ♣r♦❞✉③✐❞♦ ❜❡♥s✳
❆ tr❛♥s❢♦r♠❛çã♦ ❞❛ ❊❝♦♥♦♠✐❛ ❡♠ ❈✐ê♥❝✐❛ ♠♦str♦✉ q✉❡ ♦s três ❢❛t♦r❡s ❜ás✐❝♦s ❞❛ ♣r♦❞✉çã♦✿ ❚❡rr❛ ✭◆❛t✉r❡③❛✮✱ ❚r❛❜❛❧❤♦ ✭▼ã♦✲❞❡✲♦❜r❛✮ ❡ ❈❛♣✐t❛❧ r❡❝❡❜❡♠ s✉❛s r❡s♣❡❝t✐✈❛s r❡♠✉♥❡r❛çõ❡s ❝♦♠♦ t✐♣♦s ❞❡ r❡♥❞❛s✿ r❡♥❞❛ ❞❛ t❡rr❛✱ s❛❧ár✐♦ ❞♦s ❝♦❧❛❜♦r❛❞♦r❡s ❡ ❏✉r♦s ❞♦ ❈❛♣✐t❛❧✱ s❡♥❞♦ ♦ ú❧t✐♠♦✱ ♦ ♣❛❣❛♠❡♥t♦ ❛❞q✉✐r✐❞♦ ♣❡❧♦s s❡r✈✐ç♦s ♣r♦❞✉③✐❞♦s ❞❡✈✐❞♦ ❛♦ ❈❛♣✐t❛❧ ❜❡♠ ❞✐str✐❜✉í❞♦ ♥❛ tr❛♥s❢♦r♠❛çã♦ ❞❡ ❜❡♥s ❡✴♦✉ s❡r✈✐ç♦s✳
■♥tr♦❞✉çã♦ ✷
◆❡st❡ ❝❛s♦✱ t♦r♥❛✲s❡ ❞❡ s✉♠❛ ✐♠♣♦rtâ♥❝✐❛ q✉❡ ❡♥t❡♥❞❛♠♦s q✉❡ ❛ ♣❛❧❛✈r❛ ❜❡♥s t❛♠❜é♠ ♣♦❞❡ s❡r s✉❜st✐t✉í❞❛ ♣❡❧❛ ♣❛❧❛✈r❛ s❡r✈✐ç♦s ❡✱ ♥❡st❡ ❝❛s♦✱ ❏✉r♦s s❡r✐❛♠ ❛ r❡♠✉♥❡r❛çã♦ ❞❡ ✉♠ ❈❛♣✐t❛❧ ❛♣❧✐❝❛❞♦ ♥❛ ♣r♦❞✉çã♦ ❞❡ ✉♠ ❜❡♠ ♦✉ s❡r✈✐ç♦✳
◆❛ ❛t✉❛❧✐❞❛❞❡✱ q✉❛♥❞♦ s♦❧✐❝✐t❛♠♦s ♣❛r❛ ❛ ❣r❛♥❞❡ ♠❛✐♦r✐❛ ❞❛s ♣❡ss♦❛s ♦ q✉❡ ❡❧❛s ❡♥t❡♥❞❡♠ ♣♦r ❥✉r♦s✱ ❛ r❡s♣♦st❛ ❡♥❝♦♥tr❛❞❛ ❡ ❡s♣❡r❛❞❛ é✿ ❖ ♣r❡ç♦ ❞♦ ❞✐♥❤❡✐r♦✳ ◆❡st❡ ❝❛s♦✱ s❡ ❛♥❛❧✐s❛r♠♦s ❢r✐❛♠❡♥t❡ ❛ r❡s♣♦st❛ ❡ ❝r✉③❛r♠♦s ❝♦♠ ❛s ❞❡✜♥✐çõ❡s ❝✐❡♥tí✜❝❛s s❡❣✉♥❞♦ ✈ár✐♦s ❛✉t♦r❡s✱ ♣♦❞❡♠♦s ❛❝❡✐tá✲❧❛ ❡ ♣❛ssá✲❧❛ à ❢r❡♥t❡ ❝♦♠♦ ✈❡r❞❛❞❡✐r❛✳
❚♦❞❛ ♣❡ss♦❛ q✉❡ ❢❛③ ❛ ❣r❛✈✐t❛çã♦ ♥♦ ❡♥t♦r♥♦ ❞❡ ✉♠ ❈❛♣✐t❛❧ ❡st❛rá s✉❥❡✐t❛ ❛ ✉♠❛ ❞❛s ❞✉❛s s✐t✉❛çõ❡s✿ ❣❛st❛✲♦ ❧❡✈❛♥❞♦ r❡♥❞❛ ❛ q✉❡♠ ♦ r❡❝❡❜❡✉ ♦✉ ❡♠♣r❡❣❛✲ ♦ ♣❛r❛ ♦❜t❡r ✉♠ r❡s❣❛t❡ ❢✉t✉r♦✱ ❡✈✐❞❡♥t❡♠❡♥t❡✱ ♠❛✐♦r q✉❡ ❛ q✉❛♥t✐❛ ✐♥✐❝✐❛❧ ❛♣❧✐❝❛❞❛✳
◆♦ss❛ q✉❡stã♦ ♥ã♦ s❡rá ❡①♣❧♦r❛r ♦ ✏❣❛♥❤♦✑ s♦❜r❡ ✉♠ ❈❛♣✐t❛❧ ✐♥✈❡st✐❞♦ ♥✉♠ ❡♠♣r❡❡♥❞✐♠❡♥t♦ q✉❡ ♣r♦❞✉③ ❜❡♥s ♦✉ s❡r✈✐ç♦s✳ ◆♦ss♦ ❡s❝♦♣♦ s❡rá ❛✈❛❧✐❛r ❛ r❡♠✉♥❡r❛çã♦ ❞❡ ✉♠ ❈❛♣✐t❛❧ q✉❛♥❞♦ ❛♣❧✐❝❛❞♦ ♥✉♠❛ ✐♥st✐t✉✐çã♦ ✜♥❛♥❝❡✐r❛ ♦✉ ✈✐❝❡✲✈❡rs❛✱ q✉❛♥❞♦ ❛ ✐♥st✐t✉✐çã♦ ✜♥❛♥❝❡✐r❛ ♦ ❡♠♣r❡st❛✱ ♠♦str❛♥❞♦ ♦s ❞♦✐s t✐✲ ♣♦s ♠❛✐s ❝♦♠✉♥s ❞❡ s❡ ✈❛❧♦r✐③❛r ♦ ❈❛♣✐t❛❧ ❡ ❛♥❛❧✐s❛♥❞♦ q✉❛♥❞♦ ✉♠ ♦✉ ♦✉tr♦ ♣r♦✈♦❝❛ ♦ ❛♥❛t♦❝✐s♠♦✱ q✉❡ é ❛ ✐♥❝✐❞ê♥❝✐❛ ❞❡ ❥✉r♦s s♦❜r❡ ♦s ❥✉r♦s ❛❝r❡s❝✐❞♦s ❛♦ s❛❧❞♦ ❞❡✈❡❞♦r✱ ❡♠ r❛③ã♦ ❞❡ ♥ã♦ t❡r❡♠ s✐❞♦ ♣❛❣♦s✳ ❖s ❥✉r♦s ♦❜t✐❞♦s✱ ♣♦r ♠❡✐♦ ❞❡st❛ ♣rát✐❝❛✱ sã♦ s♦♠❛❞♦s ❛♦ ❈❛♣✐t❛❧ ❡ s❡rá ❛ ❜❛s❡ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛ ♥♦✈❛ ❝♦♥t❛❜✐❧✐③❛çã♦ ❞❡ ❥✉r♦s✳
❖ ❆rt✐❣♦ ✶✾✷✱ ➓✸♦✱ ❞❛ ❈♦♥st✐t✉✐çã♦ ❋❡❞❡r❛❧ ✭❇r❛s✐❧✱ ✶✾✽✽✮ q✉❡ ❞❡✜♥✐❛ t❛✐s ♦♣❡r❛çõ❡s ❢♦✐ r❡✈♦❣❛❞♦ ❡♠ ✷✵✵✸ ❡✱ ❛ ♣❛rt✐r ❞❛í✱ ❡①✐st❡♠ ✈ár✐❛s ❥✉r✐s♣r✉❞ê♥❝✐❛s s♦❜r❡ ❛ ✈❛❧✐❞❛❞❡ ♦✉ ♥ã♦ ❞❡ss❛ ❝♦❜r❛♥ç❛✳
❆ ✜♥❛❧✐❞❛❞❡ ♥ã♦ s❡rá ❛♥❛❧✐s❛r ❛ ❧❡❣❛❧✐❞❛❞❡ ♦✉ ♥ã♦ ❞♦ ❛♥❛t♦❝✐s♠♦✱ ♠❛s s✐♠✱ ✈❡r✐✜❝❛r ♦✉ ♥ã♦ s✉❛ ❡①✐stê♥❝✐❛ ❞❡♥tr♦ ❞❡ ❝♦♥tr❛t♦s ♦✉ ✈❛❧✐❞❛çã♦ ❞❡ r❡♠✉♥❡r❛✲ çõ❡s s♦❜r❡ ♦ ❈❛♣✐t❛❧✳
■♥tr♦❞✉çã♦ ✸
✭r❡♥❞❛s✮✳
✶ ✲ ❯♠ ♣♦✉❝♦ ❞❡ ❍✐stór✐❛ ✹
✶ ✲ ❯♠ ♣♦✉❝♦ ❞❡ ❍✐stór✐❛
✶✳✶ ❆ ♦r✐❣❡♠ ❞♦ ❞✐♥❤❡✐r♦
❍á ♠❛✐s ❞❡ ✺ ✵✵✵ ❛♥♦s ❛♥t❡s ❞❡ ❈r✐st♦✱ ❝❛r♥❡ s❛❧❣❛❞❛✱ ♣❡❧❡s ❞❡ ❛♥✐♠❛✐s✱ s❛❧✱ ❣r❛õs✱ ❡♥tr❡ ♦✉tr❛s ❝♦✐s❛s✱ ❢♦r❛♠ ❢❡rr❛♠❡♥t❛s ❞❡ tr♦❝❛ ❡♥tr❡ ❛s ♣❡ss♦❛s✱ q✉❡ ❢❛③✐❛♠ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s s✉❛s ♥❡❝❡ss✐❞❛❞❡s ❜ás✐❝❛s✳ P❛r❛ ❛q✉❡❧❡s q✉❡ t✐♥❤❛♠ ❡①❝❡ss♦ ❞❡ ✉♠✱ tr♦❝❛✈❛♠ ♣❡❧❛ ❢❛❧t❛ ❞♦ ♦✉tr♦✳ ❆ ❡st❡ ♣r♦❝❡ss♦ ❞❡ tr♦❝❛s ❛♣❛r❡❝❡✉ ❛ ♣r✐♠❡✐r❛ ♠♦❡❞❛✿ ❊s❝❛♠❜♦✳ ✶
P❡r❝❡❜❡♠♦s q✉❡ ♥❛ ♣ró♣r✐❛ ❞❡✜♥✐çã♦ ❞❛ ♣r✐♠❡✐r❛ ♠♦❡❞❛ ❞❡♣❛r❛♠♦s✲♥♦s ❝♦♠ ❛ ♣❛❧❛✈r❛ ✏❞✐♥❤❡✐r♦✑ ♣❛r❛ ❞❡✜♥✐✲❧❛✳
P❛r❛ ❱❡rs✐❣♥❛ss✐ ✭✷✵✶✷✱ ♣✳ ✾✼✮✱ ✏✭❉✐♥❤❡✐r♦✮ ✳✳✳ ❙❡ ♥ã♦ ❢♦r ❡s❝❛ss♦ ♥ã♦ t❡♠ ❣r❛♥❞❡ ✈❛❧♦r❀ s❡ ♥ã♦ t❡♠ ✈❛❧♦r✱ ♥ã♦ é ❞✐♥❤❡✐r♦✳
❖ ❞✐♥❤❡✐r♦ ❢♦✐ ✉♠❛ ❝r✐❛çã♦ ❢❡✐t❛ ❝♦♠ ♠✉✐t♦ ❛rt✐❢í❝✐♦ ❡ ❞❡str❡③❛✳ P❡r♠✐t❡ q✉❡ ❛❧❣✉é♠ q✉❡ ♥ã♦ t❡♥❤❛ ❞❡t❡r♠✐♥❛❞♦ ♣r♦❞✉t♦ tr♦q✉❡ ♣♦r ♦✉tr♦ s❡♠ ♥❡❝❡ss✐t❛r ❛ r❡❛❧✐③❛çã♦ ❞♦ ❡s❝❛♠❜♦❀ ❝♦♠♦ ♣♦r ❡①❡♠❧♦✱ ♣❡r♠✐t❡ q✉❡ ✉♠ ♠é❞✐❝♦ ❝♦♠♣r❡ ❝❛r♥❡ s❡♠ ♣r❡❝✐s❛r ❢❛③❡r ❛ ❝♦♥s✉❧t❛ ❝♦♠ ♦ ❛ç♦✉❣✉❡✐r♦✳ ❋♦✐ ❝r✐❛❞♦ ♥❛ ●ré❝✐❛ ❛♥t✐❣❛ ❡ ♥ós ♥♦s ✈❛❧❡♠♦s ❞❡st❛ ❝r✐❛çã♦ ❛té ♦s ❞✐❛s ❞❡ ❤♦❥❡✳ ❊❧❡ s❡ r❡s✉♠❡ ♥❛ s✉❛ ♣ró♣r✐❛ r❛③ã♦ ❞❡ s❡r ❡ ♥ós ♣r❡❝✐s❛♠♦s ♥♦s ✈❛❧❡r ❞❛ ❝❡rt❡③❛ ❞❡ q✉❡ ♥ã♦ ✈❡♠♦s s❡✉ ✈❛❧♦r ♠❛s ❛❝r❡❞✐t❛♠♦s ♥❡❧❡✳ ❆❝r❡❞✐t❛♠♦s q✉❡ q✉❛♥❞♦ s✉❜st✐t✉✐♠♦s ✉♠ ❜❡♠ ♦✉ ✉♠ s❡r✈✐ç♦ ♣♦r ✉♠ ♥ú♠❡r♦ ❡①♣r❡ss♦ ❡♠ ✉♠ ♣❛♣❡❧ ♦✉ ♠❡t❛❧✱ ❡st❡ ♥ú♠❡r♦ ✭♣❛♣❡❧ ♦✉ ♠❡t❛❧✮ s❡rá s✉❜st✐t✉✐❞♦ ♥♦✈❛♠❡♥t❡✱ ❡ ❛ss✐♠ s✉❝❡ss✐✈❛♠❡♥t❡✱
✶❙❡❣✉♥❞♦ ❉✐❝✐♦✿ ❉✐❝✐♦♥ár✐♦ ❖♥❧✐♥❡ ❞❡ P♦rt✉❣✉ês✱ ❬❊s❝❛♠❜♦❪✿ ❚r♦❝❛ ❞❡ ♠❡r❝❛❞♦r✐❛s s❡♠
✶ ✲ ❯♠ ♣♦✉❝♦ ❞❡ ❍✐stór✐❛ ✺
❛❝r❡❞✐t❛♥❞♦ ❝♦♠ ✈❡❡♠ê♥❝✐❛ ♥❛ s✉❛ ✈❡r❛❝✐❞❛❞❡✳ ❆ ✐ss♦✱ ❛ ❝❡rt❡③❛ ❞❛q✉✐❧♦ q✉❡ ♥ã♦ s❡ ✈ê✱ ❞❡♥♦♠✐♥❛♠♦s ❋é✳
P❡r❝❡❜❡♠♦s q✉❡ ♣❛r❛ s❡r ✏❞✐♥❤❡✐r♦✑ é ♥❡❝❡ssár✐♦ q✉❡ s❡❥❛ ❛❧❣♦ q✉❡ t♦❞♦s ♥❡❝❡ss✐t❛♠ ❡ q✉❡✐r❛♠ ❡ q✉❡ s❡❥❛ ❛❧❣♦ ❡s❝❛ss♦ ♦✉ ❞❡ ❞✐❢í❝✐❧ ♣♦ss❡❀ ❡ ♥❡st❡ ❝❛s♦✱ ✏❛❧✐♠❡♥t♦s✑ s❡ ❡♥❝❛✐①❛ ♠✉✐t♦ ❜❡♠❀ ♣♦✐s ❞❡s❞❡ ❛ ✐♥tr♦❞✉çã♦ ❞♦ ❤♦♠❡♠ s♦❜r❡ ❛ s✉♣❡r❢í❝✐❡ ❞♦ ♣❧❛♥❡t❛✱ ♦ ❛❧✐♠❡♥t♦ é ✉♠ ❣r❛♥❞❡ ✐♥str✉♠❡♥t♦ ❞❡ tr♦❝❛✳
➱ ❝❧❛r♦ q✉❡ ♥❛ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ ❛ ❛❣r✐❝✉❧t✉r❛ ❡ ❛ ❝❛ç❛ é ♠❛✐s ❞♦ q✉❡ ó❜✲ ✈✐♦ q✉❡ ❛ s❡❣✉♥❞❛ s❡ s✉❜♠❡t❡ às ♥❡❝❡ss✐❞❛❞❡s ❞❛ ♣r✐♠❡✐r❛✱ ✉♠❛ ✈❡③ q✉❡ ♦s ♣r♦✈❡♥t♦s ❞❛ ❝❛ç❛ ❡r❛♠ ❝♦♥s✉♠✐❞♦s ❡♠ ♣♦✉❝♦s ❞✐❛s✱ ❡♥q✉❛♥t♦ q✉❡ ♦s ❞❛ ❛❣r✐✲ ❝✉❧t✉r❛ ♣♦❞✐❛♠ s❡r ❡st♦❝❛❞♦s✳ P♦r ✐ss♦ ❛ ♥♦ss❛ ❛✜r♠❛çã♦ ❞❡ q✉❡ ✏à ❛❣r✐❝✉❧t✉r❛ ❞❡✈❡♠♦s ❛ ❛♣❛r✐çã♦ ❞♦ ❞✐♥❤❡✐r♦✑✳
➱ ❞❡ ❢á❝✐❧ ❡♥t❡♥❞✐♠❡♥t♦ q✉❡ ❛q✉❡❧❡s q✉❡ ❝✉❧t✐✈❛✈❛♠ ❛ t❡rr❛ ❡ ♥❡❧❛ ♣❧❛♥t❛✲ ✈❛♠ ♣♦❞❡r✐❛♠ ❡st♦❝❛r ♦s ❣rã♦s ❡ ♣♦st❡r✐♦r♠❡♥t❡ ♥❡❣♦❝✐á✲❧♦s❀ ❡♥q✉❛♥t♦ ❝♦♠ ❛ ❝❛ç❛ ❡r❛ ♥❡❝❡ssár✐♦ ❝♦♥s✉♠✐r ♦ ♣r♦❞✉t♦ ✜♥❛❧ ❝♦♠ ♠❛✐s r❛♣✐❞❡③✱ ❞❡✈✐❞♦ à s✉❛ ♣❡r❡❝✐✈✐❞❛❞❡✳ ◆❡st❡ ❝❛s♦✱ ❛s ♣❡ss♦❛s q✉❡ ♥❡❝❡ss✐t❛✈❛♠ ❞❡ ❝♦♠✐❞❛ ❛ tr♦❝❛✈❛♠ ♣❡❧♦ tr❛❜❛❧❤♦✱ ♠♦str❛♥❞♦ ❞❡st❛ ♠❛♥❡✐r❛ q✉❡ ❛ ❝♦♠✐❞❛ ❢♦✐ ✉♠❛ ❞❛s ♣r✐♠❡✐r❛s ❢♦r♠❛s ❞❡ ❞✐♥❤❡✐r♦✳
❉❡✈✐❞♦ ❛♦ ❢❛t♦ ❞♦ ✐♥❝ô♠♦❞♦ ❡♠ ❝❛rr❡❣❛r ♦s s❛❝♦s ❞❡ ❛❧✐♠❡♥t♦s✱ ♦s ♣♦✈♦s ❞❛ ❇❛❜✐❧ô♥✐❛ ❝r✐❛r❛♠ ❞❡♣ós✐t♦s ♦♥❞❡ ❣✉❛r❞❛✈❛♠ ♦s ❛❧✐♠❡♥t♦s ❡ r❡❣✐str❛✈❛♠ ♥✉♠❛ tá❜✉❛ ❞❡ ❛r❣✐❧❛ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❛❧✐♠❡♥t♦s q✉❡ ❤❛✈✐❛♠ ♥♦ ❡st♦q✉❡✳ ❉❡ss❛ ❢♦r♠❛ s✉r❣✐r❛♠ ♦s ❜❛♥❝♦s ❡ ♦ ❞✐♥❤❡✐r♦ q✉❡ t❡♠♦s ❤♦❥❡✳
❚❛♥t♦ ❛ ❛r❣✐❧❛ q✉❛♥t♦ ♦s ❛❧✐♠❡♥t♦s ❡r❛♠ ❞❡ ♣♦✉❝♦ ❞✉r❛❜✐❧✐❞❛❞❡✳ ❆ss✐♠✱ t♦r♥♦✉✲s❡ ♥❡❝❡ssár✐♦ ❛ ❝r✐❛çã♦ ❞❡ ♦✉tr❛ ❝♦✐s❛ q✉❡ ♣✉❞❡ss❡ s✉❜st✐t✉í✲❧♦s✱ ♠❛s q✉❡ ♠❛♥t✐✈❡ss❡ ❛ ❝❛r❛❝t❡ríst✐❝❛ q✉❡ s❡r✐❛ ♥❡❝❡ssár✐❛✳ ❆♣❛r❡❝❡✉ ♦ ✏❙❛❧✑❀ ❞✐❢í❝✐❧ ❞❡ ❛❞q✉✐r✐r ❡ ❢á❝✐❧ ❞❡ ❝❛rr❡❣❛r✳ ❉❛í ❛ ♦r✐❣❡♠ ❞♦ t❡r♠♦ ✏s❛❧ár✐♦✑✱ q✉❡ ♣❡r❞✉r❛ ❛té ♦s ❞✐❛s ❞❡ ❤♦❥❡✳ ❖s r♦♠❛♥♦s ❧❡❣✐♦♥ár✐♦s r❡❝❡❜✐❛♠ s❡✉s s❛❧ár✐♦s ❡♠ ❙❛❧✳
✶ ✲ ❯♠ ♣♦✉❝♦ ❞❡ ❍✐stór✐❛ ✻
✶✳✷ ❖s t✐♣♦s ❞❡ ❞✐♥❤❡✐r♦
❆ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ♦❜t❡r ❛❧❣♦ ❞❡ tr❛♥s♣♦rt❡ ♠❛✐s ❢á❝✐❧ ❛ ✜♠ ❞❡ s❡ ❢❛③❡r ❛s tr♦❝❛s✱ ❛ ❤✉♠❛♥✐❞❛❞❡ ❛❝❛❜♦✉ ♣♦r ❛❞♦t❛r ♦ ♣r✐♠❡✐r♦ ♠❡t❛❧ ❝♦♠♦ ❞✐♥❤❡✐r♦✿ ♦ ❝♦❜r❡✳ P♦ré♠✱ ❞❡✈✐❞♦ à ❢❛❝✐❧✐❞❛❞❡ ❞❡ s❡ ❡♥❝♦♥tr❛r ♦ r❡❢❡r✐❞♦ ♠❡t❛❧✱ ❡st❡ ❢♦✐ ❧♦❣♦ s✉❜st✐t✉í❞♦ ♣❡❧❛ ♣r❛t❛✱ q✉❡ s❡ ✐♠♣ôs ♣♦r s❡r ❞❡ ♠❛✐s ❞✐❢í❝✐❧ ❛❝❡ss♦ q✉❡ ♦ ❝♦❜r❡✳ ▼❛s✱ ❞❡✈✐❞♦ à ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ✈❛❧♦r✐③❛r ♠❛✐s ♦s ♦❜❥❡t♦s ❡ ❛s ♣r♦♣r✐❡❞❛❞❡s✱ ❝❤❡❣❛r❛♠✲s❡ ❛♦ ♦✉r♦✱ q✉❡ ❡r❛ ❞❡ ❞✐❢í❝✐❧ ❛q✉✐s✐çã♦✳
❆ss✐♠✱ ♣♦r ♠✉✐t♦ t❡♠♣♦✱ ❛ ✉t✐❧✐③❛çã♦ ❞♦s três ♠❡t❛✐s ✜❝❛r❛♠ ❞❡✜♥✐❞❛s ❡♠ ❢✉♥çã♦ ❞❡ s✉❛ r❛r✐❞❛❞❡✱ ♥ã♦ ❝♦rr♦sã♦✱ ♣r❛t✐❝✐❞❛❞❡ ❞❡ ♠❛♥✉s❡✐♦✱ ❜❡❧❡③❛ ❡✱ ❛❝✐♠❛ ❞❡ t✉❞♦✱ ✈❛❧♦r ❡❝♦♥ô♠✐❝♦✳
❙❡❣✉♥❞♦ ❲❡❛♥t❤❡r❢♦r❞ ✭✷✵✵✺✮✱ ❡♠ ♠❡❛❞♦s ❞♦ sé❝✉❧♦ ❱■■ ❛✳❈✳ ❛♣❛r❡❝❡♠ ♦s ♣r✐♠❡✐r♦s ♦❜❥❡t♦s ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s ♠❛✐s ♣ró①✐♠❛s ❞❛s ♠♦❡❞❛s✱ ❝♦♠ ✈❛❧♦r❡s ♣ré✲❞❡✜♥✐❞♦s ♥❛ s✉❛ ❝✉♥❤❛❣❡♠ ❡ ❛ ❣❛r❛♥t✐❛ ❞❛ ♠❛r❝❛ ❞❡ q✉❡♠ ❛s ✐♠♣r✐♠✐✉ ❝✉♥❤❛❞❛s ❡♠ s✐ ♠❡s♠❛s✳
◆♦ ✐♥í❝✐♦ ❞❛ ❝✐✈✐❧✐③❛çã♦ ❜❛❜✐❧ô♥✐❝❛ s❡✉s s❛❝❡r❞♦t❡s ❡r❛♠ ❛♣r❡❝✐❛❞♦r❡s ❞❛ ❛s✲ tr♦♥♦♠✐❛ ❡ ❝♦♥✈❡♥❝✐❛♠ ♦s s❡✉s s❡❣✉✐❞♦r❡s ❞❡ q✉❡ ♦ ❙♦❧ ❡st❛✈❛ ❧✐❣❛❞♦ ❛♦ ♦✉r♦ ❛ss✐♠ ❝♦♠♦ ❛ ♣r❛t❛ ❡st❛✈❛ ❧✐❣❛❞❛ à ▲✉❛✱ ❡ ✐ss♦ ❢❡③ ❝♦♠ q✉❡ ❛ ❤✉♠❛♥✐❞❛❞❡ s❡ ❧✐❣❛ss❡✱ ❞❡ ❛❧❣✉♠❛ ❢♦r♠❛✱ ❛ ❡ss❡s ♠❡t❛✐s✱ ♦ q✉❡ ♦s ❧❡✈❛r✐❛♠ ♠❛✐s ❛✐♥❞❛ ❛ s❡r❡♠ ❝♦♥s✐❞❡r❛❞♦s ❝♦♠♦ ✐♥str✉♠❡♥t♦s ❞❡ tr♦❝❛s ❡ ❞❡ ♣❡♥❤♦r✳
❆s ♠♦❡❞❛s ❞❡ ♣r❛t❛✱ ♦✉r♦ ❡ ❜r♦♥③❡ ❡r❛♠ ❧✐❣❛❞❛s ❞✐r❡t❛♠❡♥t❡ ❛♦ s❡✉ ✈❛❧♦r r❡❛❧✱ ✐ss♦ ❞✉r♦✉ ♣♦r ♠✉✐t♦ t❡♠♣♦✳ ❊ ❞✉r❛♥t❡ ❡st❡ t❡♠♣♦✱ ❛té ♦ sé❝✉❧♦ ♣❛ss❛❞♦✱ ♦s ♣❛✐s❡s ❝✉♥❤❛✈❛♠ ♠♦❡❞❛s ❞❡ss❡s ♠❡t❛✐s✱ ❣✉❛r❞❛♥❞♦✲❛s ❡ ❝♦❧♦❝❛♥❞♦ ♣❛r❛ ❝✐r❝✉❧❛r ♠♦❡❞❛s ❝♦♠ ♠❡t❛✐s ♠❛✐s ❜❛r❛t♦s✱ ♣♦ré♠✱ ♠❛♥t❡♥❞♦ ❡♠ s❡✉ ♣♦❞❡r q✉❛♥t✐❞❛❞❡ ❞❡ ♦✉r♦ ❡ ♣r❛t❛ ❡q✉✐✈❛❧❡♥t❡ às q✉❛♥t✐❞❛❞❡s q✉❡ ❡r❛♠ ❧❛♥ç❛❞❛s ♥♦ ♠❡r❝❛❞♦✳
◆ã♦ ❞❡♠♦r♦✉ ♠✉✐t♦ ❡ s✉r❣✐✉ ♦ ♣❛♣❡❧✲♠♦❡❞❛✱ ❡ ❛ ❝✉♥❤❛❣❡♠ ❞❡ ♠♦❡❞❛s ♠❡✲ tá❧✐❝❛s t♦r♥♦✉✲s❡ r❡str✐t❛ ❛ ✈❛❧♦r❡s ♣❡q✉❡♥♦s✱ ♥❡❝❡ssár✐♦s ♣❛r❛ ❝♦♠♣r❛ ❞❡ ♠❡r✲ ❝❛❞♦r✐❛s ❞❡ ❜❛✐①♦ ✈❛❧♦r ♦✉ ♠❡s♠♦ ♣❛r❛ tr♦❝♦✳
✶ ✲ ❯♠ ♣♦✉❝♦ ❞❡ ❍✐stór✐❛ ✼
♠♦❡❞❛s ♥❛ ❈❤✐♥❛ ❞❡s❞❡ ♦ ❛♥♦ ❞❡ ✾✻✵✱ ♣♦ré♠ ❡st❛s ♥ã♦ s❡ ❞✐ss✐♠✐♥❛r❛♠ ♣❡❧♦ ♠✉♥❞♦❀ ♣♦r ✐ss♦ ♥ã♦ ❢♦r❛♠ ♠❛✐s ✉t✐❧✐③❛❞❛s✳
❍✐st♦r✐❝❛♠❡♥t❡ ♦s r❡❣✐str♦s ♠♦str❛♠ q✉❡ ❛s ♥♦t❛s ❛♣❛r❡❝❡r❛♠ ♥❛ ❙✉é❝✐❛ ✭❊✉r♦♣❛✮ ♥♦ ❛♥♦ ❞❡ ✶✻✻✶✱ ❡✱ ❞❡ ❧á ♣❛r❛ ❝á✱ s♦❢r❡r❛♠ ❛s ❡✈♦❧✉çõ❡s ❡ ❛❞❡q✉❛çõ❡s ♥❡❝❡ssár✐❛s ❛ ❝❛❞❛ P❛ís✳
P❛r❛ ❲❡❛t❤❡r❢♦r❞ ✭✶✾✾✾✱ ♣✳ ✷✶✵✮
❬✳✳✳❪ ❡st❛♠♦s ❡♥tr❛♥❞♦ ♥❛ t❡r❝❡✐r❛ ❢❛s❡ ❞❛ r❡✈♦❧✉çã♦ ♠♦♥❡tá✲ r✐❛✿ ❈♦♠ ❛ ✐♥❢♦r♠át✐❝❛✱ ♦ ❞✐♥❤❡✐r♦ s❡ tr❛♥s❢♦r♠♦✉ ❡♠ ✐♠✲ ♣✉❧s♦s ❡❧❡trô♥✐❝♦s ✐♥✈✐sí✈❡✐s✱ ❧✐✈r❡s ❞♦ ❡s♣❛ç♦✱ ❞♦ t❡♠♣♦ ❡ ❞♦ ❝♦♥tr♦❧❡ ❞❡ ❣♦✈❡r♥♦s ❡ ❝♦r♣♦r❛çõ❡s✳
P❡r❝❡❜❡♠♦s q✉❡✱ ❝♦♠ ✉♠ s✐♠♣❧❡s ❝❛rtã♦✱ ♣♦❞❡♠♦s ❢❛③❡r ♣❛❣❛♠❡♥t♦s ❡ r❡❝❡✲ ❜✐♠❡♥t♦s✱ ❜❡♠ ❝♦♠♦✱ s❡♠ s❛✐r ❞❡ ♥♦ss❛s ♣ró♣r✐❛s r❡s✐❞ê♥❝✐❛s✱ q✉❛s❡ t♦❞❛s ❛s ♦♣❡r❛çõ❡s ❜❛♥❝ár✐❛s✱ ❛s q✉❛✐s✱ ❡♠ t❡♠♣♦s ♥ã♦ tã♦ r❡♠♦t♦s✱ r❡✈❡rí❛♠♦s ❡♥❢r❡♥✲ t❛r ✜❧❛s ❡ ❛t❡♥❞✐♠❡♥t♦✳
✶✳✸ ❖ ❞✐♥❤❡✐r♦ ♠♦❞❡r♥♦
◆❛ ❛t✉❛❧✐❞❛❞❡✱ t♦❞❛s ❛s ♠♦❡❞❛s ❡ ❝é❞✉❧❛s q✉❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♣❛ís ❡♠✐t❡ ❢♦r♠❛ ♦ s❡✉ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦ ❡ ♠♦♥❡tár✐♦✳ ❈❛❞❛ ♣❛ís t❡♠ ✉♠ ❢♦r♠❛ ♣ró♣r✐❛ ❞❡ ❧❡❣✐s❧❛r ❡st❛ ❡♠✐ssã♦ ❡ ❞❡ ✈❛❧♦r✐③❛r s✉❛ ✉♥✐❞❛❞❡ ♠♦♥❡tár✐❛ ❛ ♣❛rt✐r ❞❡ ✉♠ ✈❛❧♦r ❞❡ r❡❢❡rê♥❝✐❛✳
➱ ♠✉✐t♦ ❝♦♠✉♠ q✉❡ ♦s ✈❛❧♦r❡s ♠♦♥❡tár✐♦s ♠❛✐s ❡❧❡✈❛❞♦s s❡❥❛♠ ❡①♣r❡ss♦s ❡♠ ❝é❞✉❧❛s ❡ q✉❡ ♦s ♠❛✐s ❜❛✐①♦s✱ ❡♠ ♠♦❡❞❛s✳
✶ ✲ ❯♠ ♣♦✉❝♦ ❞❡ ❍✐stór✐❛ ✽
❆ ❣❧♦❜❛❧✐③❛çã♦ r❡♣♦rt❛✲♥♦s à ❝♦♠♣❛r❛çã♦ ❞✐ár✐❛ ❡♥tr❡ ♦s ✈❛❧♦r❡s ♠♦♥❡tár✐♦s ✉t✐❧✐③❛❞♦s ♣❡❧♦s ♣❛ís❡s ❞✐t♦s ❞❡s❡♥✈♦❧✈✐❞♦s✱ ♣❛ís❡s ❡♠ ❢❛s❡ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ ♦s ♣❛ís❡s s✉❜❞❡s❡♥✈♦❧✈✐❞♦s✳ ➱ ❝❧❛r♦ q✉❡ ❛ s✉♣r❡♠❛❝✐❛ ❡♥tr❡ ❡❧❡s é ❡✈✐❞❡♥t❡ ❡ q✉❡ ♥❛ ❡s❝❛❧❛ ❛s❝❡♥❞❡♥t❡ ❞❡ ❝❛❞❛ ✉♠ ♥❛ s✉❛ ✐♥s❡rçã♦ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❝♦❧♦❝❛ ❛ ✈❛❧♦r✐③❛çã♦ ❞❡ s❡✉ ❞✐♥❤❡✐r♦ ❡♠ ❢✉♥çã♦ ❞❛ s✉❛ ❜❛❧❛♥ç❛ ❝♦♠❡r❝✐❛❧ ❡ ❞❡ s❡✉ ♣r♦❞✉t♦ ✐♥t❡r♥♦ ❜r✉t♦✳
❖ ❜♦♠ s❡♥s♦ ❧❡✈❛ ♦ ♣❛ís ❛ ❡♠✐t✐r ❞✐♥❤❡✐r♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ❝♦❜r✐r s❡✉ P■❇✱ ❞❡ ❢♦r♠❛ ❛ ♣♦❞❡r ❢❛③❡r ❝♦♠ q✉❡ t✉❞♦ ♦ q✉❡ s❡❥❛ ♣r♦❞✉③✐❞♦ ❡♠ ❜❡♥s ❡ s❡r✈✐ç♦s t❡♥❤❛ ❞✐♥❤❡✐r♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ♣❛❣á✲❧♦❀ é ❝❧❛r♦ q✉❡ ❡①✐st❡♠ ❞✉❛s s✐t✉❛çõ❡s ❛❞✈❡rs❛s à r❡❛❧✐❞❛❞❡✿ s❡ ♦ ♠❡r❝❛❞♦ ✐♥t❡r♥♦ r❡❝❡❜❡ ♠❛✐s ❞✐♥❤❡✐r♦ q✉❡ ♦ P■❇ ❤❛✈❡rá ✉♠ ❡①❝❡ss♦ ❞❡ ❞✐♥❤❡✐r♦ ♥♦ ♠❡r❝❛❞♦ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛s ♣❡ss♦❛s ❝♦♠♣r❛rã♦ ♠❛✐s❀ ❞❡ss❛ ❢♦r♠❛✱ ♦ ❝♦♥s✉♠✐s♠♦ ❧❡✈❛rá ❛ ✉♠ ❛✉♠❡♥t♦ ❝♦♥tí♥✉♦ ❡ ❣❡♥❡r❛❧✐③❛❞♦ ❞♦s ♣r❡ç♦s ❞♦s ❜❡♥s ❡ s❡r✈✐ç♦s✱ ♣r♦✈♦❝❛♥❞♦ ♦ q✉❡ é ❝❤❛♠❛❞♦ ❞❡ ✐♥✢❛çã♦✳ ❈❛s♦ ♦❝♦rr❛ ♦ ❝♦♥trár✐♦ ❡ ♦ ♣❛ís ❝♦❧♦q✉❡ ♥♦ ♠❡r❝❛❞♦ ✉♠❛ q✉❛♥t✐❞❛❞❡ ♠❡♥♦r ❞❡ ❞✐♥❤❡✐r♦ q✉❡ ❛ ♣r♦❞✉③✐❞❛ ♣❡❧♦s ❜❡♥s ❡ s❡r✈✐ç♦s✱ ❤❛✈❡rá ✉♠❛ ❢❛❧t❛ ❞❡ ❞✐♥❤❡✐r♦ ♥♦ ♠❡r❝❛❞♦ ❡ ❛s ♣❡ss♦❛s✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♥ã♦ t❡rã♦ ♣♦❞❡r ❞❡ ❝♦♠♣r❛✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ❛s ✐♥❞ústr✐❛s ♥ã♦ ♣r♦❞✉③❛♠✱ ♣r♦✈♦❝❛♥❞♦ ✉♠❛ r❡❝❡ssã♦✳
❆❝r❡❞✐t❛♠♦s q✉❡ é ❞❡ s✉♠❛ ✐♠♣♦rtâ♥❝✐❛ q✉❡ s❡ ❝r✐❡ s✐t✉❛çõ❡s ♦♥❞❡ ❤❛❥❛ ♦ ❡q✉✐❧í❜r✐♦ ❞❛ ❜❛❧❛♥ç❛ ❞❡ ♣❛❣❛♠❡♥t♦s✱ ✐♠♣♦rt❛çã♦✴❡①♣♦rt❛çã♦✱ ❡✱ ❛❝✐♠❛ ❞❡ t✉❞♦✱ ✉♠ ❝♦♥tr♦❧❡ ♥❛ ❡♠✐ssã♦ ❞♦ ❞✐♥❤❡✐r♦ ❛ ✜♠ ❞❡ ♠❛♥t❡r ❛ ❡❝♦♥♦♠✐❛ ❡stá✈❡❧ ❡ ♣r♦✈♦❝❛r ✉♠ ❝r❡s❝✐♠❡♥t♦ ❡❝♦♥ô♠✐❝♦ ♥♦ ♣❛ís✳
✶✳✹ ❆ ♦r✐❣❡♠ ❞♦ ❏✉r♦
❖s ✐♥❞í❝✐♦s ❞❛ ♦r✐❣❡♠ ❞♦ ❏✉r♦ r❡♠♦♥t❛♠ ❞❡ ✷✵✵✵ ❛✳❈✳ ♥❛ ❝✐✈✐❧✐③❛çã♦ ❜❛❜✐❧ô✲ ♥✐❝❛✱ ♦♥❞❡ ❛s ♥❡❣♦❝✐❛çõ❡s ❡r❛♠ ❢❡✐t❛s ❛tr❛✈és ❞❡ ❣rã♦s✳
✶ ✲ ❯♠ ♣♦✉❝♦ ❞❡ ❍✐stór✐❛ ✾
♣r❡s❡♥t❡ ❞♦ ♠❡s♠♦ ❡ ❛ ♣r♦❥❡çã♦ ♣❛r❛ ♦ ✈❛❧♦r ❢✉t✉r♦✳ ❙❡❣✉♥❞♦ ❇♦❤r♥ ✲ ❇❛✇❡r❦✱ ❊✉❣❡♥ ❱♦♥ ✭✶✾✽✻✱ ♣✳✸✵✵✮
❆ r❡❧❛çã♦ ❞❡ ♥❡❝❡ss✐❞❛❞❡ ❡ ❝♦❜❡rt✉r❛ ♥♦ ♣r❡s❡♥t❡ ❡ ♥♦ ❢✉✲ t✉r♦✱ ❛ s✉❜❛✈❛❧✐❛çã♦ ❡①❝❡ss✐✈❛ ❞❡ ❛❧❡❣r✐❛s ❡ tr✐st❡③❛s ❢✉t✉r❛s✱ ❡ ❛ s✉♣❡r✐♦r✐❞❛❞❡ té❝♥✐❝❛ ❞❡ ❜❡♥s ♣r❡s❡♥t❡s ❢❛③❡♠ ❝♦♠ q✉❡✱ ♣❛r❛ ❛ ❣r❛♥❞❡ ♠❛✐♦r✐❛ ❞❛s ♣❡ss♦❛s✱ ♦ ✈❛❧♦r ❞❡ ✉s♦ s✉❜❥❡✲ t✐✈♦ ❞❡ ❜❡♥s ♣r❡s❡♥t❡s s❡❥❛ ♠❛✐♦r ❞♦ q✉❡ ♦ ❞❡ ❜❡♥s ❢✉t✉r♦s ❞❛ ♠❡s♠❛ ❡s♣é❝✐❡✳ ❉❡ss❛ s✐t✉❛çã♦ ❞❡ ❛✈❛❧✐❛çõ❡s s✉❜❥❡t✐✈❛s r❡s✉❧t❛✱ ♥♦ ♠❡r❝❛❞♦ ❡♠ ❣❡r❛❧✱ ✉♠❛ s✉♣❡r✐♦r✐❞❛❞❡ ❞♦s ❜❡♥s ♣r❡s❡♥t❡s r❡❧❛t✐✈❛♠❡♥t❡ ❛ ✈❛❧♦r ❞❡ tr♦❝❛ ♦❜❥❡t✐✈♦ ❡ ♣r❡ç♦ ❞❡ ♠❡r❝❛❞♦✳ ❊ss❛ s✉♣❡r✐♦r✐❞❛❞❡ r❡tr♦❛❣❡ ❡ ❢❛③ ❝♦♠ q✉❡ ❢❛ç❛♠ ✉♠❛ ❛✈❛❧✐❛çã♦ s✉❜❥❡t✐✈❛ ✭❞♦ ✈❛❧♦r ❞❡ tr♦❝❛✮ ♠❛✐s ❛❧t❛ ❞♦s ❜❡♥s ♣r❡s❡♥t❡s t❛♠❜é♠ ❛q✉❡❧❛s ♣❡ss♦❛s q✉❡✱ ♣♦r s✉❛s ❝♦♥✲ ❞✐çõ❡s ♣❡ss♦❛✐s ❝❛s✉❛✐s✱ ♥ã♦ ❛tr✐❜✉❡♠ ❛ ❡ss❡s ❜❡♥s ♣r❡s❡♥t❡s ✉♠ ✈❛❧♦r ❞❡ ✉s♦ s✉❜❥❡t✐✈♦ ♠❛✐♦r✳ ❆♦ ✜♥❛❧✱ ❛s t❡♥❞ê♥❝✐❛s ♥✐✈❡❧❛❞♦r❛s ❞♦ ♠❡r❝❛❞♦ ❢❛③❡♠ ❝♦♠ q✉❡ ❛ ✐♥❢❡r✐♦r✐❞❛❞❡ ❞♦ ✈❛❧♦r ❞♦s ❜❡♥s ❢✉t✉r♦s ❛♣r❡s❡♥t❡ ✉♠❛ ♣r♦♣♦rçã♦ r❡❣✉❧❛r ❝♦♠ ♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ q✉❡ ♦s s❡♣❛r❛ ❞♦ ♣r❡s❡♥t❡✳ P♦r ❝♦♥✲ s❡❣✉✐♥t❡✱ ♥❛ ❊❝♦♥♦♠✐❛ ❞❛ ♥❛çã♦ ❤á ✉♠❛ ✐♥❢❡r✐♦r✐❞❛❞❡ ❣❡r❛❧ ❞♦s ❜❡♥s ❢✉t✉r♦s✱ ♥♦ t♦❝❛♥t❡ ❛♦ ✈❛❧♦r s✉❜❥❡t✐✈♦✳ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ q✉❡ ♦s s❡♣❛r❛ ❞♦ ♣r❡s❡♥t❡✳
P♦❞❡♠♦s ❡♥t❡♥❞❡r ❡ss❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❜❡♥s ❢✉t✉r♦s ❡ ♣r❡s❡♥t❡s ❡①❛t❛♠❡♥t❡ ❝♦♠♦ ♦ ✐♥í❝✐♦ ❞♦ ♠❛♥❛♥❝✐❛❧ q✉❡ ♦r✐❣✐♥❛ ❏✉r♦✳ ❈♦♠♦ ❢❛t♦r ❞❡ r❡❧❡✈â♥❝✐❛✱ t❡♠ ❝♦♠♦ ♠❛✐s s✐♠♣❧❡s ❡♥t❡♥❞✐♠❡♥t♦ ♦ ❡♠♣rést✐♠♦ ✭✈❡r❞❛❞❡✐r❛ tr♦❝❛ ❞❡ ❜❡♥s ♣r❡✲ s❡♥t❡s ♣♦r ❜❡♥s ❢✉t✉r♦s✮✱ ♦♥❞❡ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ♣❡ss♦❛ ❳ ✭❞❡♥♦♠✐♥❛❞❛ ❝r❡❞♦r✮ ❞á ❛ ✉♠❛ ♣❡ss♦❛ ❨ ✭❞❡♥♦♠✐♥❛❞❛ ❞❡✈❡❞♦r❛✮ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ q✉❛♥t✐❛ ❞❡ ❜❡♥s ♣r❡s❡♥t❡s✱ tr❛♥s❢❡r✐♥❞♦ à s❡❣✉♥❞❛ ❧✐✈r❡ ❛r❜ítr✐♦ s♦❜r❡ ❛ q✉❛♥t✐❛ ❞❛❞❛✱ ♣♦ré♠✱ ❡♠ ♦♣♦s✐çã♦✱ ♦ ❞❡✈❡❞♦r ❨ ❞á ❛ ❳ ✉♠❛ ❣❛r❛♥t✐❛ ❡①❛t❛ ❞❡ ♠❡s♠❛ ❡s♣é❝✐❡ ✭♦✉ ❣ê♥❡r♦✮✱ ♣♦ré♠ ❢✉t✉r♦s✱ tr❛♥s❢❡r✐♥❞♦ ♦ ❧✐✈r❡ ❛r❜ítr✐♦ à ❳✳
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✶✵
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s
❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦
✷✳✶ ❏✉r♦
❆ ▼❛t❡♠át✐❝❛ ❋✐♥❛♥❝❡✐r❛ t❡♠ ❝♦♠♦ ❛❧✈♦ ♣r✐♥❝✐♣❛❧ ❛ ❛♥á❧✐s❡ ❞❡ q✉❛♥t✐❛s ♠♦♥❡tár✐❛s q✉❡ sã♦ ♣❡r♠✉t❛❞❛s ❡♠ ✐♥t❡r✈❛❧♦s ❞✐❢❡r❡♥t❡s ❛♦ ❧♦♥❣♦ ❞❛ ❧✐♥❤❛ ❞♦ t❡♠♣♦✳ ❆♣❡s❛r ❞❡ ❛❧❣✉♥s ❛✉t♦r❡s ♥ã♦ ❝♦♥❝♦r❞❛r❡♠ q✉❡ ♦ ❞✐♥❤❡✐r♦ s❡❥❛ ♣r♦❞✉t✐✈♦ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✱ ❛ ❣r❛♥❞❡ ♠❛✐♦r✐❛ ❝♦♥❝♦r❞❛ q✉❡ s✐♠ ❡ ❛ ♣rát✐❝❛ ❞♦ ❡st✉❞♦ ❞❡ q✉❛♥t✐❞❛❞❡s ♠♦♥❡tár✐❛s ❡♠ t❡♠♣♦s ❞✐❢❡r❡♥t❡s t♦r♥♦✉✲s❡ ❛❧✈♦ ❞❡ ❡st✉❞♦s ❡ ❞❡❜❛t❡s ❝❛❧♦r♦s♦s ❡♥tr❡ ❛✉t♦r❡s✳ P♦ré♠✱ t♦❞♦s sã♦ ✉♥â♥✐♠❡s ❡♠ ❝♦♥❝♦r❞❛r q✉❡ ❛ ▼❛t❡♠át✐❝❛ ❋✐♥❛♥❝❡✐r❛ ♣♦❞❡ s❡r ❞❡s❝r✐t❛ ❝♦♠♦ ♦ q✉❡ ❛✜r♠❛ ❋❛r♦ ✭✶✾✽✷✱ ♣✳ ✶✸✮ ✏❬✳✳✳❪ ♦ ❡st✉❞♦ ❞❛ ❡✈♦❧✉çã♦ ❞♦ ❞✐♥❤❡✐r♦ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✑✳ ❙❡❣✉♥❞♦ ❙✐✈❛ ✭✶✾✾✷✮ ♦s ❢❛t♦r❡s ❜ás✐❝♦s ❞❛ ♣r♦❞✉çã♦ s❡ ❛❣r✉♣❛♠ ❡♠ três ✐t❡♥s✿ ❚r❛❜❛❧❤♦ ✭❈♦♥tr✐❜✉✐çã♦ ❞♦ s❡r ❤✉♠❛♥♦✱ ♥❛ ♣r♦❞✉çã♦✱ ❡♠ ❢♦r♠❛ ❞❡ ❛t✐✲ ✈✐❞❛❞❡ ❢ís✐❝❛ ❡ ♠❡♥t❛❧✮❀ ❈❛♣✐t❛❧ ✭é ♦ ❝♦♥❥✉♥t♦ ❞❡ ❡q✉✐♣❛♠❡♥t♦s✱ ❢❡rr❛♠❡♥t❛s ❡ ♠áq✉✐♥❛s✱ ♣r♦❞✉③✐❞♦s ♣❡❧♦ ❤♦♠❡♠✱ q✉❡ ♥ã♦ s❡ ❞❡st✐♥❛♠ à s❛t✐s❢❛çã♦ ❞❛s ♥❡❝❡ss✐❞❛❞❡s ❛tr❛✈és ❞♦ ❝♦♥s✉♠♦✱ ♠❛s ❝♦♥❝♦rr❡♠ ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡ ❜❡♥s ❡ s❡r✈✐ç♦s✱ ❛✉♠❡♥t❛♥❞♦ ❛ ❡✜❝✐ê♥❝✐❛ ❞♦ tr❛❜❛❧❤♦ ❤✉♠❛♥♦✮ ❡ ❘❡❝✉rs♦s ◆❛t✉r❛✐s ✭❡❧❡♠❡♥t♦s ❞❛ ♥❛t✉r❡③❛ ✉t✐❧✐③❛❞♦s ♣❡❧♦ ❤♦♠❡♠ ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ ❝r✐❛r ❜❡♥s✮✳ P❛r❛ ❋❛r♦ ✭✶✾✽✷✮✱ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❛ ❡❝♦♥♦♠✐❛✱ ❛ r❡♠✉♥❡r❛çã♦ ❛ q✉❛❧q✉❡r tít✉❧♦ ❛tr✐❜✉í❞❛ ❛♦ ❢❛t♦r ❈❛♣✐t❛❧ é ❞❡♥♦♠✐♥❛❞❛ ❏✉r♦✳
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✶✶
t✐❛ ♥✉♠ ❞❡t❡r♠✐♥❛❞♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦✱ ❝♦st✉♠❛♠♦s ❝♦❜r❛r ✉♠❛ ❝❡rt❛ ✐♠♣♦r✲ tâ♥❝✐❛✱ à q✉❛❧ ❝❤❛♠❛♠♦s ❏✉r♦✱ ❞❡ ♠❛♥❡✐r❛ q✉❡ ❛♦ s❡ ✜♥❞❛r ♦ ♣r❛③♦ ❡st✐♣✉❧❛❞♦✱ ♣❛ss❛r❡♠♦s ❛ t❡r ♥ã♦ s♦♠❡♥t❡ ❛ q✉❛♥t✐❛ ✐♥✐❝✐❛❧ ❡♠♣r❡st❛❞❛✱ ♠❛s t❛♠❜é♠ ♦s ❛❝rés❝✐♠♦s q✉❡ ❢❛ç❛ ❛ ❝♦♠♣❡♥s❛çã♦ ❞❛ ♥ã♦ ✉t✐❧✐③❛çã♦ ❞♦ ❈❛♣✐t❛❧ ♣♦r ♥ós✱ ❡①❛✲ t❛♠❡♥t❡ ❞✉r❛♥t❡ t♦❞♦ ♦ ♣❡rí♦❞♦ ❡♠ q✉❡ ♥ã♦ ✜❝❛♠♦s ❞❡ ♣♦ss❡ ❞❡❧❡✳
❖ ❏✉r♦ ❛ s❡r ❝♦❜r❛❞♦ ♥✉♠❛ ❞❡t❡r♠✐♥❛❞❛ tr❛♥s❛çã♦ ✜♥❛♥❝❡✐r❛ é ❡❢❡t✉❛❞♦ ♠❡❞✐❛♥t❡ ✉♠ í♥❞✐❝❡✱ ✉♠ ❝♦❡✜❝✐❡♥t❡✱ q✉❡ ❡①♣r❡ss❛ ♦ ✈❛❧♦r ❞♦ ❈❛♣✐t❛❧ ❛ s❡r ❡♠✲ ♣r❡❣❛❞♦ ♥❛ tr❛♥s❛çã♦✳ ❆ ❡st❡ í♥❞✐❝❡ ✭❝♦❡✜❝✐❡♥t❡✮ ❞❛♠♦s ♦ ♥♦♠❡ ❞❡ t❛①❛ ❞❡ ❥✉r♦s✱ q✉❡ s❡rá s❡♠♣r❡ r❡❢❡r✐❞❛ ❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ❡ q✉❡ r❡♣r❡s❡♥t❛ ♥❛❞❛ ♠❛✐s ♥❛❞❛ ♠❡♥♦s q✉❡ ♦ ♣r❡ç♦ ❞♦ ❈❛♣✐t❛❧ q✉❡ ❡stá s❡♥❞♦ ♥❡❣♦✲ ❝✐❛❞♦ ♥❛q✉❡❧❡ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦✳ ❊st❛ t❛①❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ✭♦✉ ❞❡❝r❡s❝✐♠❡♥t♦✮✱ T C✱ é ♦❜t✐❞❛ ❢❛③❡♥❞♦ ♦ q✉♦❝✐❡♥t❡ ❡♥tr❡ ❛ ❞✐❢❡r❡♥ç❛ ❞❡ ✈❛❧♦r❡s ✭❢✉t✉r♦ ♠❡♥♦s ❛t✉❛❧✮ ♣❡❧♦ ✈❛❧♦r ❛t✉❛❧✿
T C = V alorF uturo−V alorAtual
V alorAtual ✳
❆s t❛①❛s ❞❡ ❥✉r♦s ♣♦❞❡♠ s❡r ❡♠♣r❡❣❛❞❛s ❞❡ ❞✉❛s ❢♦r♠❛s✿ ❢♦r♠❛ ✉♥✐tár✐❛✱ q✉❡ ♠♦str❛ ♦ ✈❛❧♦r ❞❡ ❝❛❞❛ ✉♥✐❞❛❞❡ ❞♦ ❝❛♣✐t❛❧ ❡♠♣r❡❣❛❞♦ ♥❛q✉❡❧❡ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ♦✉ ❢♦r♠❛ ♣❡r❝❡♥t✉❛❧ ✭♠❛✐s ✉t✐❧✐③❛❞❛✮✱ q✉❡ ♠♦str❛ ♦ ✈❛❧♦r ❞❡ ❝❛❞❛ ✶✵✵ ✉♥✐❞❛❞❡s ❞♦ ❝❛♣✐t❛❧ ❡♠♣r❡❣❛❞♦ ♥♦ r❡❢❡r✐❞♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦✳
✷✳✷ ❖s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦
❊♥t❡♥❞❡♠♦s ♣♦r ❈❛♣✐t❛❧✐③❛çã♦ ♦ ♣r♦❝❡ss♦ ♣❡❧♦ q✉❛❧ ♦s ❏✉r♦s sã♦ ✐♥❝♦r♣♦r❛❞♦s ❛♦ ❈❛♣✐t❛❧ q✉❡ ❡stá s❡♥❞♦ ❝♦❧♦❝❛❞♦ ❡♠ ❡st✉❞♦✳ ❯♥✐✈❡rs❛❧♠❡♥t❡ t❡♠♦s ❞♦✐s t✐♣♦s ❞❡ ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦✱ ❛ s❛❜❡r✿ ❖ ❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❈♦♥tí♥✉❛ ❡ ♦ ❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❉❡s❝♦♥tí♥✉❛✳
✷✳✷✳✶ ❖ ❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❈♦♥tí♥✉❛ ✲ ❙❈❈
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✶✷
♦✉ s❡❥❛✱ ♦ ❈❛♣✐t❛❧ ❛✉♠❡♥t❛ ❝♦♥t✐♥✉❛♠❡♥t❡ q✉❛♥❞♦ ♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ❞❡✐①❛ ❞❡ s❡r ✉♠❛ ✈❛r✐á✈❡❧ ❞✐s❝r❡t❛ ❡ t❡♥❞❡ ❛ s❡r ✉♠❛ ✈❛r✐á✈❡❧ r❡❛❧✳ ❆ ❝❛❞❛ s❡❣✉♥❞♦✱ ❛ ❝❛❞❛ ❞é❝✐♠♦ ❞❡ s❡❣✉♥❞♦✱ ♦s ❥✉r♦s sã♦ ✐♥❝♦r♣♦r❛❞♦s ❛♦ ❈❛♣✐t❛❧✳
❆ ♥♦♠❡♥❝❧❛t✉r❛ ❛ s❡r ✉t✐❧✐③❛❞❛ ❡♠ ♥♦ss❛s ❝♦♥s✐❞❡r❛çõ❡s s❡rá✿ i= t❛①❛ ❞❡ ❥✉r♦s ♥❛ ❢♦r♠❛ ✉♥✐tár✐❛❀
n=t❡♠♣♦ ♥❛ ♠❡s♠❛ ✉♥✐❞❛❞❡ ❛ q✉❡ s❡ r❡❢❡r❡ ❛ t❛①❛❀ C ♦✉ C0 = ❈❛♣✐t❛❧ ♦✉ q✉❛♥t✐❛ ✐♥✐❝✐❛❧❀
J ♦✉ Jn = ❏✉r♦s r❡❢❡r❡♥t❡s ❛♦ ❈❛♣✐t❛ C à t❛①❛ ❞❡ ❏✉r♦s i ♥♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ n❀
Cn =▼♦♥t❛♥t❡ ✭s♦♠❛ ❞♦ ❈❛♣✐t❛❧ ❝♦♠ ♦s ❏✉r♦s r❡❢❡r❡♥t❡s ❛♦ ♣❡rí♦❞♦ ❝♦♥s✐✲ ❞❡r❛❞♦✮✳
❱❛♠♦s ❝♦♥s✐❞❡r❛rC ♦ ✈❛❧♦r ❞❡ ✉♠ ❝❡rt♦ ❈❛♣✐t❛❧ ♥✉♠ ❞❡t❡r♠✐♥❛❞♦ ♠♦♠❡♥t♦ ❞♦ t❡♠♣♦n✳
❙❛❜❡♠♦s q✉❡ ♥♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦
n+ ∆n
❤❛✈❡rá ✉♠❛ ✐♥❝♦r♣♦r❛çã♦ ❞❡ ❥✉r♦sJnr❡❢❡r❡♥t❡ à ✉t✐❧✐③❛çã♦ ❞♦ ❈❛♣✐t❛❧ C ♥❡st❡ ♣❡rí♦❞♦✱ ❞❡ ❢♦r♠❛ q✉❡✱ ❛♦ ✜♥❛❧ ❞♦ ♣❡rí♦❞♦n+ ∆n t❡r❡♠♦s ✉♠ ♠♦♥t❛♥t❡
Cn =C+Jn✳
❙❛❜❡♠♦s ♣❡❧❛ ❞❡✜♥✐çã♦ ❞❡ t❛①❛ ❞❡ ❝r❡s❝✐♠❡♥t♦✿ ❚❈ ✱ q✉❡ ♣❛r❛ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ✉♥✐tár✐♦✱ ❛ t❛①❛ ❞❡ ❝r❡s❝✐♠❡♥t♦T C✱ q✉❡ s❡rá ❛ t❛①❛ ❞❡ ❥✉r♦si ♥❡st❡ ♣❡rí♦❞♦✱ s❡rá ❞❛❞❛ ♣♦r✿
i= Cn−C
C ✳
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✶✸
Jn =Cn−C✳
▲♦❣♦✱ ❛ t❛①❛ ❞❡ ❥✉r♦s ♥♦ ♣❡rí♦❞♦ ✉♥✐tár✐♦ ❝♦♥s✐❞❡r❛❞♦ s❡rá ❞❛❞❛ ♣♦r✿
i= Jn C❀
❡✱ ❝❛s♦ ♦ ♣❡rí♦❞♦ ♥ã♦ s❡❥❛ ✉♥✐tár✐♦✱ ♠❛s s❡❥❛ ✉♠ ♣❡rí♦❞♦ n✱ ❛ t❛①❛ ❞❡ ❥✉r♦s s❡rá ❞❛❞❛ ♣♦r✿
i= Jn (C).(n)✳
❈♦♥s✐❞❡r❛♥❞♦ ✉♠ ✐♥t❡r✈❛❧♦ ✐♥✜♥✐t❛♠❡♥t❡ ♣❡q✉❡♥♦ ❞❡ t❡♠♣♦ dn✱ ♣♦❞❡♠♦s s✉❜st✐t✉✐r ♦ ❛❝rés❝✐♠♦Jn ♣❡❧❛ ❞✐❢❡r❡♥❝✐❛❧ dCn✳
❈❤❛♠❛♥❞♦ ❛ t❛①❛ ❞❡ ❥✉r♦s r❡❧❛t✐✈❛ ❛ ❡st❡ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ✐♥✜♥✐t❛♠❡♥t❡ ♣❡q✉❡♥♦ ❝♦♠♦ t❛①❛ ✐♥st❛♥tâ♥❡❛ ❞❡ ❥✉r♦ ❡ ❛ r❡♣r❡s❡♥t❛♥❞♦ ♣♦r i✱ ♣♦❞❡♠♦s ❡s❝r❡✈❡r✿
i= dCn (Cn).(dn)
dCn❂(i).(Cn).(dn)✱
q✉❡ é ✉♠❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✱ ♠♦str❛♥❞♦✲♥♦s ❝♦♠ ✐ss♦ q✉❡ ❛ ❢r❛çã♦ ❞❡ ❥✉r♦s ❝♦rr❡s♣♦♥❞❡♥t❡ à ❛♣❧✐❝❛çã♦ é ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ✐♥✜♥✐t❛♠❡♥t❡ ♣❡q✉❡♥♦ ❡ t❛♠❜é♠ ❛♦ ❈❛♣✐t❛❧ ❡♠ q✉❡stã♦✱ ❡✱ ♠❛✐s ❛✐♥❞❛✱ ❛ ❝♦♥st❛♥t❡ ❞❡ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ ❡♥tr❡ ❛s ❣r❛♥❞❡③❛s é ❛ t❛①❛ ❞❡ ❥✉r♦s ✐♥st❛♥tâ♥❡❛i✳
❘❡s♦❧✈❡♥❞♦ ❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ t❡r❡♠♦s✿ Z
dCn= Z
(i).(Cn).dn =⇒
Z dCn
Cn =
Z
(i).dn =⇒ln(Cn) = (i).(n) +K✳ ❊♠ q✉❡ ln(Cn) r❡♣r❡s❡♥t❛ ♦ ❧♦❣❛r✐t♠♦ ♥❛t✉r❛❧ ❞❡ Cn ❡ K ✉♠❛ ❝♦♥st❛♥t❡ ❞❡
✐♥t❡❣r❛çã♦✳
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✶✹
ln(Cn) = (i).(n) +ln(K)✳
❙❛❜❡♠♦s q✉❡ ♥❛ é♣♦❝❛ ③❡r♦(n= 0)✱ ♦ ❈❛♣✐t❛❧ é ♦ ✐♥✐❝✐❛❧✱ q✉❡ ❝❤❛♠❛r❡♠♦s ❞❡ C0✱ ❡ q✉❡ é ✉♠ ✈❛❧♦r ❝♦♥❤❡❝✐❞♦✱ ♣♦✐s é ❞❡❧❡ q✉❡ s❡ tr❛t❛ ♥♦ss♦ ❡st✉❞♦✳ ❆ss✐♠✱ t♦♠❛♥❞♦ ❛ s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❡ ❢❛③❡♥❞♦n= 0 ❡ Cn =C0 t❡r❡♠♦s✿
ln(C0) = (i).0 +ln(K)✱
q✉❡ ♥♦s ❧❡✈❛ ❡♠C0 =K✱ ♠♦str❛♥❞♦ q✉❡ ❛ ❝♦♥st❛♥t❡ ❞❡ ✐♥t❡❣r❛çã♦ é ♦ ❧❛❣❛r✐t♠♦ ♥❛t✉r❛❧ ❞♦ ❝❛♣✐t❛❧ ✐♥✐❝✐❛❧✳
❱♦❧t❛♥❞♦ à ❢ór♠✉❧❛✱ ♣♦❞❡r❡♠♦s ❡♥tã♦ ❡s❝r❡✈❡r✿
ln(Cn) = (i).(n) +ln(K)
ln(Cn) = (i).(n) +ln(C0)
ln(Cn)−ln(C0) = (i).(n) ln(Cn
C0) = (i).(n) Cn
C0
= e(i).(n)
Cn = C0.e(i).(n)
❡♠ q✉❡ ✏e✑ é ♦ ❛❧❣❛r✐s♠♦ ❞❡ ◆❡♣❡r✱ ♥ú♠❡r♦ ■rr❛❝✐♥❛❧✱ q✉❡ ♣♦❞❡ s❡r ♦❜t✐❞♦ ❛tr❛✈és ❞❛ ❢ór♠✉❧❛✿
e=
∞
X
i=0
1
n! = 2,718 281 828...✳
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✶✺
❖ ❣rá✜❝♦ q✉❡ s❡ s❡❣✉❡ ♠♦str❛ ♠❛✐s ❝❧❛r❛♠❡♥t❡ ❛ ✈❛r✐❛çã♦ ❞❛ ❢✉♥çã♦✳ ◆❛s ♦r❞❡♥❛❞❛s t❡♠♦s ♦ ❝❛♣✐t❛❧ ✐♥✐❝✐❛❧ ♣❛r❛ ❛ ❞❛t❛ n = 0 ❡✱ ❛ ❝❛❞❛ ✐♥t❡r✈❛❧♦ ✐♥✜✲ ♥✐t❡s✐♠❛❧ ❞❡ ❛❝rés❝✐♠♦ ❞❡ t❡♠♣♦ n ✭♥❛s ❛❜s❝✐ss❛s✮✱ t❡r❡♠♦s ✉♠ ♠♦♥t❛♥t❡ Cn q✉❡ é ♦❜t✐❞♦ ❛tr❛✈és ❞❛ ❢✉♥çã♦✿
Cn =C0.e(i).(n)
❋✐❣✉r❛ ✷✳✶✿ ❊①♣♦♥❡♥❝✐❛❧ ❞❡ ✉♠❛ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♥tí♥✉❛
◆♦t❡ q✉❡ ♦s ❥✉r♦s ❢♦r♠❛❞♦s ❡♠ q✉❛❧q✉❡r ✐♥st❛♥t❡ s❡rá ❞❛❞♦ ♣❡❧❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦ ▼♦♥t❛♥t❡Cn ❡ ♦ ❝❛♣✐t❛❧ ✐♥✐❝✐❛❧C0✱ ❧❡✈❛♥❞♦✲♥♦s ❛✿
Jn = Cn−C0 Jn = C0.(ei.n)−C0 Jn = C0.(ei.n−1).
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✶✻
t❡♠♣♦ ♣❡r❢❡✐t❛♠❡♥t❡ ❞❡✜♥✐❞♦ ❝♦♠ ✐♥í❝✐♦ ❡ ✜♠✱ ♦s ❥✉r♦s sã♦ ❢♦r♠❛❞♦s ❞❡ ✉♠❛ ♠❛♥❡✐r❛ ❝♦♥tí♥✉❛ ❡ ✐♥✐♥t❡rr✉♣t❛✱ ❡①♣♦♥❡♥❝✐❛❧♠❡♥t❡ ❝r❡s❝❡♥t❡✳
✷✳✷✳✷ ❖ ❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❉❡s❝♦♥tí♥✉❛ ✲ ❙❈❉
❊st❡ é ♦ ❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❛❞♦t❛❞♦ r❡❛❧♠❡♥t❡ ♥❛ ♣rát✐❝❛✳ ❖s ❥✉r♦s só sã♦ ✐♥❝♦r♣♦r❛❞♦s ❛♦ ❝❛♣✐t❛❧ ♥♦ ✜♥❛❧ ❞♦ ♣❡rí♦❞♦ ❛ q✉❡ s❡ r❡❢❡r❡ ❛ t❛①❛ ♦✉ ❛ ❝❛♣✐t❛❧✐③❛çã♦✳ ❖ ❝❛♣✐t❛❧ ❛♣❧✐❝❛❞♦ r❡❝❡❜❡ ❛♦ ✜♥❛❧ ❞❡ ❝❛❞❛ ♣❡rí♦❞♦ ✜♥✐t♦ ❞❡ t❡♠♣♦ ♦ ❛❝rés❝✐♠♦ ❞♦s ❥✉r♦s✱ q✉❡ é ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ ❛ ❡ss❡ ❝❛♣✐t❛❧ ❡✱ ❝♦♠♦ ♥♦ ❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❈♦♥tí♥✉❛✱ ❛ ❝♦♥st❛♥t❡ ❞❡ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ ❡♥tr❡ ❡❧❡s é ❛ t❛①❛ ❞❡ ❥✉r♦s ♣❛r❛ ♦ ♣❡rí♦❞♦ ❝♦♥s✐❞❡r❛❞♦✳
❙❡❥❛Cn✉♠ ❝❛♣✐t❛❧ ❝♦♥s✐❞❡r❛❞♦ ♥✉♠❛ ❞❡t❡r♠✐♥❛❞❛ é♣♦❝❛ ❞❛ ❧✐♥❤❛ ❞♦ t❡♠♣♦ n✳ ❆♣ós ✉♠ ♣❡rí♦❞♦ ❛ q✉❡ s❡ r❡❢❡r❡ ❛ t❛①❛ ♦ ♥♦✈♦ t❡♠♣♦ s❡rá n+ 1 ❡ ♦ ❝❛♣✐t❛❧ q✉❡ ♥❛ é♣♦❝❛n ❡r❛ Cn s♦❢r❡rá ✉♠ ❛❝rés❝✐♠♦ ♣♦r ✉♥✐❞❛❞❡ ❡q✉✐✈❛❧❡♥t❡ à t❛①❛ i✱ ❡ ♥❡st❡ ❝❛s♦✱ s❡rá ❛❝r❡s❝✐❞♦ ❞❡ Cn.i ✱ s❡♥❞♦ ❡st❡ ❛❝rés❝✐♠♦ ♦s ❥✉r♦s r❡❢❡r❡♥t❡s ❛ ❡st❡ ♣❡rí♦❞♦ ✉♥✐tár✐♦❀ ♦✉ s❡❥❛✿
J = (Cn).(i)✳ ❆ss✐♠✱ ♦ ♠♦♥t❛♥t❡Cn+1 ❢♦r♠❛❞♦ ♥❛ é♣♦❝❛n+ 1 s❡rá✿
Cn+1 = Cn+Cn.i
Cn+1−Cn.(1 +i) = 0
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✶✼
C1 = C0.(1 +i)
C2 = C1.(1 +i)
C3 = C2.(1 +i)
C4 = C3.(1 +i)
... = ...
Cn = Cn−1.(1 +i)
(C1).(C2).(C3). ... .(Cn−1).(Cn) = C0.(1 +i).C1.(1 +i).C2.(1 +i). ... .Cn−1.(1 +i)
Cn = C0.(1 +i)n
❢♦r♥❡❝❡♥❞♦✲♥♦s ♦ ♠♦♥t❛♥t❡ ✭❛ s♦♠❛ ❞♦ ❝❛♣✐t❛❧ ♠❛✐s ♦s ❥✉r♦s r❡❢❡r❡♥t❡s ❛♦ ♣❡rí♦❞♦✮ ♥♦ ❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❉❡s❝♦♥tí♥✉❛ ❛♣❧✐❝❛❞♦ ❛ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ t❛①❛i ♣♦r ✉♠ ♣❡rí♦❞♦ ✜♥✐t♦ ❞❡n ✈❡③❡s ❛ q✉❡ s❡ r❡❢❡r❡ ❛ t❛①❛ ❞❛❞❛✳
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✶✽
❋✐❣✉r❛ ✷✳✷✿ ●rá✜❝♦ ❞❡ ✉♠❛ ❝❛♣✐t❛❧✐③❛çã♦ ❞❡s❝♦♥tí♥✉❛
❉❡ss❛ ❢♦r♠❛✱ ♦ t♦t❛❧ ❞❡ ❥✉r♦s ❢♦r♠❛❞♦s ❡♥tr❡ ♦ t❡♠♣♦n = 0❡ ♦ t❡♠♣♦ ✐❣✉❛❧ ❛n s❡rá✿
Jn = Cn−C0
Jn = C0.(1 +i)n−C0
Jn = C0.[(1 +i)n−1].
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✶✾
❋✐❣✉r❛ ✷✳✸✿ ●rá✜❝♦ ❞❡ ✉♠❛ ❝❛♣✐t❛❧✐③❛çã♦ ❞❡s❝♦♥tí♥✉❛ s✐♠♣❧❡s
✷✳✷✳✸ ❆ ❞✐st✐♥çã♦ ❡♥tr❡ ♦ ❘❡❣✐♠❡ ❞❡ ❏✉r♦s ❙✐♠♣❧❡s ❡ ♦
❘❡❣✐♠❡ ❞❡ ❏✉r♦s ❈♦♠♣♦st♦s
❉❡ ❛❝♦r❞♦ ❝♦♠ ❛s ❝♦♥s✐❞❡r❛çõ❡s ❞❛ s✉❜s❡çã♦ ❛♥t❡r✐♦r✱ ♦ ❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛✲ ❧✐③❛çã♦ ❉❡s❝♦♥tí♥✉❛ ♣♦❞❡ ❛❝♦rr❡r ❞❡ ❞✉❛s ❢♦r♠❛s✿ ♦s ❏✉r♦s sã♦ ✐♥❝♦r♣♦r❛❞♦s à q✉❛♥t✐❛ ✐♠❡❞✐❛t❛♠❡♥t❡ ❛♥t❡r✐♦r ❡ ❛♠❜♦s ♣❛ss❛♠ ❛ r❡♥❞❡r ❥✉r♦s ♥♦✈❛♠❡♥t❡ ♦✉ ♦s ❏✉r♦s sã♦ ❞❡✈✐❞♦s s♦♠❡♥t❡ à q✉❛♥t✐❛ ✐♥✐❝✐❛❧ ❛♣❧✐❝❛❞❛ ❡ ❝♦♥st❛♥t❡s ❛♦ ❧♦♥❣♦ ❞❡ t♦❞♦ ♣r♦❝❡ss♦✳ ❊st❡s ❝❛s♦s sã♦ ❞❡✜♥✐❞♦s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❝♦♠♦✿ ❘❡❣✐♠❡ ❞❡ ❏✉r♦s ❈♦♠♣♦st♦s ✭❘❏❈✮ ❡ ♦ ❘❡❣✐♠❡ ❞❡ ❏✉r♦s ❙✐♠♣❧❡s ✭❘❏❙✮✳
❆ ♣r✐♥❝✐♣❛❧ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❡❧❡s é q✉❡✱ ♥♦ ♣r✐♠❡✐r♦ r❡❣✐♠❡✱ ♦s ❥✉r♦s r❡❢❡r❡♥t❡s ❛ ✉♠ ♣❡rí♦❞♦ sã♦ ✐♥❝♦r♣♦r❛❞♦s ❛♦ ❝❛♣✐t❛❧ ❛♥t❡r✐♦r ❡✱ ❛ ♣❛rt✐r ❞❛í✱ ❝❛♣✐t❛❧ ♠❛✐s ❥✉r♦s ♣❛ss❛♠ ❛ r❡♥❞❡r ❥✉r♦s ♥♦ ♣❡rí♦❞♦ s❡❣✉✐♥t❡❀ é ♦ ❢❛♠♦s♦ ❥✉r♦ s♦❜r❡ ❥✉r♦✳ ❏á ♥♦ s❡❣✉♥❞♦✱ ♦s ❥✉r♦s sã♦ s❡♠♣r❡ ❞❡✈✐❞♦s s♦♠❡♥t❡ s♦❜r❡ ❛ q✉❛♥t✐❛ ✐♥✐❝✐❛❧ ❛♣❧✐❝❛❞❛✱ ♦✉ s❡❥❛✱ sã♦ ❝♦♥st❛♥t❡s ❞✉r❛♥t❡ t♦❞♦ ♦ ♣❡rí♦❞♦ ❞❡ ❛♣❧✐❝❛çã♦✳
✷ ✲ ❏✉r♦s ♥❛ ❛t✉❛❧✐❞❛❞❡ ❡ ♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✷✵
❙✐st❡♠❛ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❉❡s❝♦♥tí♥✉❛ ❝♦♠ ❥✉r♦s s✐♠♣❧❡s ❡ ❝♦♠♣♦st♦s✱ ♠♦str❛✲ r❡♠♦s ✉♠ q✉❛❞r♦ ♦♥❞❡ ❛ q✉❛♥t✐❛ ✐♥✐❝✐❛❧ ❛♣❧✐❝❛❞❛ s❡rá ❛ ♠❡s♠❛ ✭R$ 1 000,00✮✱ ♣♦r ✉♠ ♠❡s♠♦ ♣❡rí♦❞♦ ❡ ✉♠❛ ♠❡s♠❛ t❛①❛✱ q✉❡✱ ♣❛r❛ ❢❛❝✐❧✐❞❛❞❡ ❞❡ ❡♥t❡♥❞✐✲ ♠❡♥t♦✱ ✉s❛r❡♠♦s ✶✪ ❛♦ ♣❡rí♦❞♦✳ ◆❡st❡ q✉❛❞r♦ ♣♦❞❡rá s❡r ♦❜s❡r✈❛❞♦ ♣❡rí♦❞♦ ❛ ♣❡rí♦❞♦ ❡✱ ❝♦♠ ✏s❛❧t♦s✑ ❞❡ ♣❡rí♦❞♦s✱ ♦ ♠♦♥t❛♥t❡Cn q✉❡ é ❢♦r♠❛❞♦ ✉t✐❧✐③❛♥❞♦ ❝❛❞❛ ✉♠ ❞♦s ❙✐st❡♠❛s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❡ ❘❡❣✐♠❡ ❞❡ ❏✉r♦s ❞❛s ❢♦r♠❛s ❝✐t❛❞❛s✳ ❚❛❜❡❧❛ ✷✳✶✿ ❚❛❜❡❧❛ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ♦s ❞♦✐s t✐♣♦s ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❡ ♦s ❞♦✐s s✐st❡♠❛s ❞❡ ❥✉r♦s✿
Cn
♥ ❈❛♣✐t❛❧✐③❛çã♦ ❈♦♥tí♥✉❛ ❈❛♣✐t❛❧✐③❛çã♦ ❉❡s❝♦♥tí♥✉❛ ❏✉r♦s ❈♦♠♣♦st♦s ❏✉r♦s ❙✐♠♣❧❡s
✵ ✶ ✵✵✵✱✵✵ ✶ ✵✵✵✱✵✵ ✶ ✵✵✵✱✵✵
✶ ✶ ✵✶✵✱✵✺ ✶ ✵✶✵✱✵✵ ✶ ✵✶✵✱✵✵
✷ ✶ ✵✷✵✱✷✵ ✶ ✵✷✶✱✶✵ ✶ ✵✷✵✱✵✵
✸ ✶ ✵✸✵✱✹✺ ✶ ✵✸✵✱✸✵ ✶ ✵✸✵✱✵✵
✹ ✶ ✵✹✵✱✽✶ ✶ ✵✹✵✱✻✵ ✶ ✵✹✵✱✵✵
✺ ✶ ✵✺✶✱✷✼ ✶ ✵✺✶✱✵✶ ✶ ✵✺✵✱✵✵
✻ ✶ ✵✻✶✱✽✹ ✶ ✵✻✶✱✺✷ ✶ ✵✻✵✱✵✵
✼ ✶ ✵✼✷✱✺✶ ✶ ✵✼✷✱✶✹ ✶ ✵✼✵✱✵✵
✽ ✶ ✵✽✸✱✷✾ ✶ ✵✽✷✱✽✻ ✶ ✵✽✵✱✵✵
✾ ✶ ✵✾✹✱✶✼ ✶ ✵✾✸✱✻✾ ✶ ✵✾✵✱✵✵
✶✵ ✶ ✶✵✺✱✶✼ ✶ ✶✵✹✱✻✸ ✶ ✶✵✵✱✵✵
✷✵ ✶ ✷✷✶✱✹✵ ✶ ✷✷✵✱✶✾ ✶ ✷✵✵✱✵✵
✸✵ ✶ ✸✹✾✱✽✻ ✶ ✸✹✼✱✽✺ ✶ ✸✵✵✱✵✵
✹✵ ✶ ✹✾✶✱✽✷ ✶ ✹✽✽✱✽✻ ✶ ✹✵✵✱✵✵
✺✵ ✶ ✻✹✽✱✼✷ ✶ ✻✹✹✱✻✸ ✶ ✺✵✵✱✵✵
✶✵✵ ✷ ✼✶✽✱✷✽ ✷ ✼✵✹✱✽✶ ✷ ✵✵✵✱✵✵
❖❜s❡r✈❛✲s❡ ❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦s ♠♦♥t❛♥t❡s ❡ ❥✉r♦s ❢♦r♠❛❞♦s ♣❛r❛ ❝❛❞❛ ✉♠ ❞♦s s✐st❡♠❛s ❡ r❡❣✐♠❡s ❛❞♦t❛❞♦s✳ ❖ ❝♦♥❢r♦♥t♦ ❞❡ss❡s ✈❛❧♦r❡s t✉♠✉❧t✉❛ ♦ ♠❡r❝❛❞♦ ✜♥❛♥❝❡✐r♦✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♥♦ tr♦❝❛❞✐❧❤♦ ❞❡ ♣❛❧❛✈r❛s ❡ ♣r♦♣❛❣❛♥❞❛s ❡♥❣❛♥♦s❛s ❛♦ s❡ ♦❢❡r❡❝❡r ❡♠♣rést✐♠♦s ♦✉ ❢❛③ê✲❧♦s✳
