ANALOGIE TRIUNGHI TETRAEDRU
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Transcript of ANALOGIE TRIUNGHI TETRAEDRU
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ANALOGIE TRIUNGHI TETRAEDRU
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OARE MATEMATICA ESTE O ŞTIINŢĂ A
ANALOGIILOR?
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O posibilă definiţie
•Analogia Asemănare; Izomorfism
•Două sisteme sunt analoge dacă ele concordă sub aspectul unor relaţii clar definite ale părţilor lor corespunzătoare (G.Polya, Matematica şi raţionamentele plauzibile)
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1.TEOREMA ÎNALŢIMII ÎN TRIUNGHIUL DREPTUNGHIC
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TEOREMA ANALOAGĂ TEOREMEI ÎNĂLŢIMII
Demonstratie:
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1.TEOREMA CATETEI ÎN TRIUNGHIUL DREPTUNGHIC
Intr-un triunghi dreptunghic, cateta este media geometrica a lungimii proiectiei sale pe ipotenuza si ipotenuza.
AB2 = BD áBC Demonstratie: 4 ABD ø 4 ABC
Deci BC
AB= AB
BD AB2 = BD áBC
Pentru cateta AC AC2 = CD áBC
2
0Teorema reciproca 1.Daca intr-un triunghi ABC, AD BC si AB=BD∙BC BAC=90
0 2
Teorema reciproca 2.Daca intr-un triunghi ABC BAC=90 si AB =BD∙BC AD BC
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TEOREMA ANALOAGĂ TEOREMEI CATETEI
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Diferite demonstraţii ale teoremei lui Pitagora
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Prin simplitatea ei si gradul mare de aplicatibilitate, Teorema lui Pitagora a fascinat de-a lungul mileniilor nu numai pe geometrii de profesie, ci si persone de cele mai variate ocupatii. S-au dat peste 2000 de demonstraţii. În cele ce urmeaza prezentăm câteva din aceste demonstraţii:
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(3)
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(Demonstratie data de Leonardo da Vinci)
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Bibliografie1. MIHU CERCHEZ – PITAGORA – EDITURA ACADEMIEI BUCUREŞTI, 1986
2. IOAN DĂNCILĂ – MATEMATICĂ APLICATĂ – EDITURA BOGDANA3. SURSE DE INFORMAŢIE WEB
4. MICULIŢĂ BRÂNZEI – ANALOGII TRIUNGHI TETRAEDRU – EDITURA PARALELA 45, 2000