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Matematica E Simpla • View topic - Se poate indoi o coala de 50 de ori?

Matematica E Simpla

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 Post subject: Se poate indoi o coala de 50 de ori?
PostPosted: Wed Dec 03, 2008 4:25 pm 
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Enunt:
Se poate indoi o coala de 50 de ori?


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 Post subject: Re: Se poate indoi o coala de 50 de ori?
PostPosted: Wed Dec 03, 2008 4:32 pm 
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Joined: Wed Oct 22, 2008 6:27 pm
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Rezolvare:
Categoric ca nu!

Sa notam cu d grosimea initiala a colii. Dupa prima indoire, grosimea colii indoite devine d * 2, dupa a doua indoire devine d * 4, iar dupa a 50-a indoire devine d * (2 la puterea 50).

Cam cat de groasa este o coala? Daca un top de 500 de coli are cam 5 centimetri, rezulta ca grosimea unei coli este cam 1/100 dintr-un centimetru.
Deci, d = 1/100 * 1 cm = 1/100 * 1/100 m = 1/10000 m
Cam cat este 2 la puterea 50? Folosind un calculator electronic, obtinem:
2 la puterea 50 = 1125899906842624. Daca inmultim cu d, obtinem grosimea colii, dupa 50 de indoiri:
112589990684.2624 m = 112 589 990.6842624 km. Asta inseamna, cu aproximatie, 113 milioane de km. Raza Pamantului este cam de 6300 de km, deci diametrul Pamantului este cam de 6300 * 2 = 12 600 km. Cu alte cuvinte, coala noastra, dupa 50 de indoiri, va fi de 8935 de ori mai mare decat diametrul Pamantului!

Exista persoane care au castigat diverse bauturi alcoolice punand pariu cu prietenii ca nu se poate indoi o coala de 50 de ori :)


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