Geometrie Magică - Anul Matematicii 2010 longines kellot myyntiin

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18 Mar 2011 16:42 Cea mai “cool” oră de mate îşi anunţă câştigătorii!
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Nota 3.60 / 10 voturi interes general Geometrie Magică

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Vă propun următoarea activitate: încercaţi să coloraţi o foaie de hârtie pe ambele părţi fără să ridicaţi creionul de pe foaie. Este adevărat că nu aţi reuşit ? La un moment dat a trebuit să ridicaţi creionul pentru a întoarce foaia. Aceasta înseamnă că o suprafaţă are două feţe.


În cele ce urmează vă voi arăta că există şi suprafeţe cu o singură faţă, adică suprafeţe pe care să le puteţi colora fără a fi nevoie să întoarceţi foaia şi fără a ridica creionul de pe foaie.


Pentru aceasta aveţi nevoie de o coală de scris, o foarfecă, lipici, riglă şi ceva îndemânare. Dacă nu vă descurcaţi singuri rugaţi pe unul dintre părinţi să vă ajute.
Iată ce aveţi de făcut:

Tăiaţi de-a lungul colii de hârtie   o   bucată   lată  de  4 cm. Răsuciţi  bucata   obţinută   ca în  figura 2  apoi lipiţi în aşa   fel încât capătul  A să se suprapună cu capătul D şi capătul B să  se suprapună  cu capătul  C  ca în  figura 3 şi să arate ca o brăţară.

 

 

 

 

 

 

Încercaţi să coloraţi fără a ridica creionul de pe foaie. Veţi constata că aţi reuşit să coloraţi întreaga suprafaţă şi nu a fost nevoie să ridicaţi creionul pentru a întoarce foaia.


Banda pe care aţi realizat-o se numeşte banda lui Möbius


Pentru a fi mai convingător, mai tăiaţi o bucată de hârtie, îndoiţi şi lipiţi de această dată capătul A peste capătul C şi B peste D. Încercaţi să o coloraţi fără a ridica creionul. De această dată nu veţi mai reuşi. Va trebui să ridicaţi creionul pentru a trece pe cealaltă parte.
Mai sunt şi  alte lucruri curioase despre această bandă.


Dacă o veţi tăia, de-a lungul ei, împărţind lăţimea în două părţi egale veţi obţine o singură bandă, mai mare.
Dacă o veţi tăia împărţind lăţimea benzii în trei părţi egale veţi obţine două benzi legate.

Încercaţi !  Succes !

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