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Old October 8th, 2009, 08:24 PM
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Default A beautiful, complicated expression equal to 37?

This is a little bit of an unusual question I know, but here goes. My sister works at a bakery as a decorator, and today someone ordered a birthday cake for a math teacher. They want it decorated like notebook paper with an equation or expression that adds up to 37 (the teacher's age). The only other specifications were that it be "attractive, long, and impressive looking." Does anyone have any suggestions? She (and I) would really appreciate the help. She needs any ideas before 11:30 A.M. tomorrow.
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Old October 8th, 2009, 09:19 PM
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This is a little bit of an unusual question I know, but here goes. My sister works at a bakery as a decorator, and today someone ordered a birthday cake for a math teacher. They want it decorated like notebook paper with an equation or expression that adds up to 37 (the teacher's age). The only other specifications were that it be "attractive, long, and impressive looking." Does anyone have any suggestions? She (and I) would really appreciate the help. She needs any ideas before 11:30 A.M. tomorrow.
37=\sqrt{1 + 36 \sqrt{1 + 37 \sqrt{1 + 38 \sqrt{1 + 39 \sqrt{ 1 + \cdots}}}}}
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Old October 8th, 2009, 09:50 PM
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37=\sqrt{1 + 36 \sqrt{1 + 37 \sqrt{1 + 38 \sqrt{1 + 39 \sqrt{ 1 + \cdots}}}}}
That is really nice! Elegant, tastefull, deceptively simple yet so complex! I think that the person who ordered the cake wants something with "lots of different symbols and stuff" (not a math teacher who ordered it) so I may surround it by multiplicands that amount to 1 but look "impressive." Your expression will be the pièce de résistance of her piece of cake.
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Old October 10th, 2009, 05:42 AM
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Hello, sinewave85!

What a marvelous idea!


How about:

. . \bigg[ \ln(e^7) + e^{i\pi}\bigg]^2 + \sum^{\infty}_{n=0}\frac{1}{2^n}


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Old October 10th, 2009, 08:20 AM
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Hello, sinewave85!

What a marvelous idea!


How about:

. . \bigg[ \ln(e^7) + e^{i\pi}\bigg]^2 + \sum^{\infty}_{n=0}\frac{1}{2^n}

That's 38

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Old October 15th, 2009, 03:18 PM
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These thanks are a little tardy, but know that they are very sincere. Thanks so much for the help, NonCommAlg, Soroban, and CaptainBlack! The teacher loved the cake, and my sister earned major points at work. I wondered wherther such a strange question would get any response at all but Math Help Forum came through once again!
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