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Dmitrij [34]
3 years ago
13

Can you double a square with a straightedge and a compass?

Mathematics
1 answer:
sergejj [24]3 years ago
8 0
I'd say yes.  If you use the diagonal as a reference.  Take the square and set your compass to the width of the diameter of the square.  Now put it on the page and mark a point.  Put the point of the compass on that mark and make another mark.  Now you can connect the two marks with the straight edge and you have a line that, if you made a square with sides that long, it'd have 2x the area of the first one.  That's because the diagonal is the square root of 2 larger than one side.  Square the square root of 2 and you've got 2.  You lust need to make a perpendicular line to the first one to get the box going.
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It's a geometric sequence.

4,-12,36,... \\ \\
a_1=4 \\
r=\frac{a_2}{a_1}=\frac{-12}{4}=-3 \\ \\
a_n=a_1 \times r^{n-1} \\
a_n=4 \times (-3)^{n-1} \\
a_n=4 \times (-3)^{-1} \times (-3)^n \\
a_n=4 \times (-\frac{1}{3}) \times (-3)^n \\
a_n=-\frac{4}{3}(-3)^n

It's the sum for term 4 through term 15.

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