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Anonymous
(Hard?) Geometry Problem 2017-08-26 08:04:23 Post No. 9129741
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(Hard?) Geometry Problem 2017-08-26 08:04:23 Post No. 9129741
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How the fuck do I solve this, /sci/?
Assume you're given a rectangular sheet of paper with corners labelled as pictured. Your task is to fold B onto B' such that [math]\overline{AE}[/math] has minimal length.
Once you've done that, assuming you were told the ratio of [math]\overline{AB}:\overline{BC}[/math], what is the ratio of [math]\overline{BE}:\overline{EC}[/math]?
Keep in mind this is a question primarily about folding paper. So [math]\overline{BE} =\overline{B'E}[/math]. That's what the circle illustrates. Furthermore, the red triangle and the blue triangle are congruent right triangles.
I am a turbobrainlet. Prove you're at least smarter than me.
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>>9129741
It's quite trivial. But why would I be helping a redditor?
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>>9129741
Without loss of generality let
[math] A = (0,a) [/math]
[math] B = (0,0) [/math]
[math] E = (1,0) [/math]
then
[math] B' = \left( \frac{2 a^2}{a^2 - 1}, \frac{2 a}{a^2 - 1} \right) [/math]
[math] C = \left( \frac{2 a^2}{a^2 - 1} , 0 \right)[/math]
[math] D = \left( 0 , \frac{2 a}{a^2 - 1} \right) [/math]
So the ratio is just
[math] \frac{1}{\frac{2 a^2}{a^2 - 1} - 1} = \frac{a^2 - 1}{a^2 + 1} [/math]
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>>9129992
Did you know about \\ in latex?
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