document.write( "Question 1159776: A gift has the dimensions of 𝟓𝟎 𝐜𝐦 × 𝟑𝟓 𝐜𝐦 × 𝟓 𝐜𝐦. You have wrapping paper with dimensions of 𝟕𝟓 𝐜𝐦 ×
\n" ); document.write( "𝟔𝟎 𝐜𝐦. Do you have enough wrapping paper to wrap the gift? Why or why not? \n" ); document.write( "

Algebra.Com's Answer #782849 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " Let's assume for a minute that such wrapping is possible.\r
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\n" ); document.write( "\n" ); document.write( " I will show that it leads to a contradiction, which will prove that wrapping is not possible.\r
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document.write( "Let's assume that the box is wrapped.\r\n" );
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document.write( "Mark the point at the center of the 50 cm by 35 cm face of the box.\r\n" );
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document.write( "Using pencil, draw the straight segments along the longest path on the box surface until you return to the same point,\r\n" );
document.write( "moving perpendicularly to 35 cm edges.\r\n" );
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document.write( "The length of this longest path is  25 + 5 + 50 + 5 + 25 = 110 centimetres.\r\n" );
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document.write( "If you then un-wrap the paper, you will get a straight line segment on it, whose total length is 110 centimetres.\r\n" );
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document.write( "But it is NOT POSSIBLE : the longest straight segment on this piece of paper is its diagonal, \r\n" );
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document.write( "whose length is   = 90.05 centimetres (rounded).\r\n" );
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document.write( "This contradiction PROVES my statement.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Here in the forum some tutors assume \"it may be this way, or may be that way . . . \"\r
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\n" ); document.write( "\n" ); document.write( "I hope you do understand, that the solution I found for you is a \r
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\n" ); document.write( "            * BRILLIANT *
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\n" ); document.write( "\n" ); document.write( "and there is NO any other way to discuss . . . \r
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\n" ); document.write( "\n" ); document.write( "Actually, it is a brilliant problem and a brilliant solution of the Math circle level,
\n" ); document.write( "for a special session of the Math circle.\r
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\n" ); document.write( "\n" ); document.write( "Let me tell you one story from Physics.     // Once upon a time . . . \r
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\n" ); document.write( "\n" ); document.write( "In one country, let's call it \"country N\", were there two physicists, X and Y.\r
\n" ); document.write( "\n" ); document.write( "The X was a worldwide recognized, very authoritative person (in that sense that he was
\n" ); document.write( "very respectful for his knowledge, skills and talents - a kind of moral and scientific authority). \r
\n" ); document.write( "\n" ); document.write( "The Y was, how to say it, a row professor, without world wide fame.\r
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\n" ); document.write( "\n" ); document.write( "And there was the third physicist, Z, in an abroad country.\r
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\n" ); document.write( "\n" ); document.write( "It happened, that Z made a world-wide scale discovery in Physics, for which he obtained the Nobel prize.\r
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\n" ); document.write( "\n" ); document.write( "When Y learned about it, he came to X (they were close friends) and said\r
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\n" ); document.write( "\n" ); document.write( "\"my dear X, I am very disappointed by myself. The matter is that I made this discovery two years
\n" ); document.write( "before Z did it; but I didn't give importance to it and did not publish it . . . \"\r
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\n" ); document.write( "\n" ); document.write( "For it, master X replied: \"Do not tell to ANYBODY about it.\r
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\n" ); document.write( "\n" ); document.write( "Because it is not a shame do not make this discovery --- thousands of people did not make it.\r
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\n" ); document.write( "\n" ); document.write( "But it is a real shame TO MAKE this discovery and do not give importance to it.\"\r
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\n" ); document.write( "\n" ); document.write( "End of the story.\r
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