Hi, *****
If you double the size of a cube, its edge length goes up by the cube root of 2, and therefore its surface area (and thus, the amount of paper required to wrap it) increases by the cube root of 4. The same thing applies to other shapes so long as the doubled shape is similar (in the Euclidean-geometrical sense of the word) to the original, and isn't one of those monsters that all the kids (like Helge and Georg) keep going on about.
*** Now that's also pretty interesting :) The answer I was looking for was the value of x such that the area under y=x^2 is equal to the area under y=sqrt(x) between the origin and x (area=4/3). Because I'm very paranoid and a little rusty when it comes to actually performing such calculations I checked it online via this rather nice tool: http://newgraph.seriesmathstudy.com/ On 28 Dec 2011, at 05:14, Robert Munafo wrote:
Ummm... Amount of wrapping paper to wrap a double-size box.
If you double the size of a cube, its edge length goes up by the cube root of 2, and therefore its surface area (and thus, the amount of paper required to wrap it) increases by the cube root of 4. The same thing applies to other shapes so long as the doubled shape is similar (in the Euclidean-geometrical sense of the word) to the original, and isn't one of those monsters that all the kids (like Helge and Georg) keep going on about.
Or, if you want something more approximate, how about 3/(e-1) + sin(1) - 1 = 1.5874011054...
Is that it? (-:
- Robert
On Tue, Dec 27, 2011 at 19:03, David Makin <makinmagic@tiscali.co.uk> wrote:
Hi all,
Just came across/worked out something and the result was interesting at least to me anyway even though it's something pretty simple ;) So here's a quick challenge question:
What's special about the cube root of 4 relating to areas ?
bye Dave
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun