Warning: tricky quickie quiz?

You are given unmarked straightedge, a comapass, and a sheet of paper with drawings.

http://i20.tinypic.com/25u7bjo.jpg

Now the quiz (please, pay attention):

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The curves in the graph accurately depict functions sin(x), cos(x), and ln(x). Which one is cos(x)?

1)

2)

3)

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What is area of right angle triangle ABC:

1) AB + BC

2) 1/2 AB x BC

3) AB x BC x CA

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Can you trisect angle DEF?

1) Yes

2) No, imposssible

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Can you double the volume of cube of edge PQ?

1) Yes

2) No, imposssible

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Can you qudrature circle s cetered at point O?

1) Yes

2) No, imposssible

Warning: tricky quickie quiz?

First, let's skip the obvious preliminaries, 1) is the Cosine function, and 2) is almost the correct formula, which is (1/2) AC x BC. The next questions are:

Can you trisect an angle?

Can you construct the cube root of 2?

Can you construct any rational multiple of 蟺?

Those are classic problems of construction by straightedge and compass only, and all of them have been proven impossible to do without resorting to other tricks, such as marking the straightedge or making folds with the paper.

Addendum: All right, I get it, the trick is to make use of the log and trig functions to do the necessary constructions. When I have time, I'll get back to this. Circle quadrature, for example, becomes easy since we know that the Cos(x) function intersects the axis at 蟺/2, so it's all a matter of geometric ratios to apply it to the circle s given. Likewise, use the Log graph to find (1/3)Log(2), and thence 2^(1/3), and finally use the trig functions to find Sin(胃/3) or Cos(胃/3), and go construct the triangle with the angle desired. The only thing I don't get is the right triangle problem.

Addendum 2: If AB and BC are vectors, then the area is 1/2 of the vector cross product, so the answer would be 2). However, the vector cross product is a vector, not a scalar, with magnitude equal to the area of the parallogram formed by AB and BC.

Warning: tricky quickie quiz?

I took another look at this question only after I realized it was you, Alexander. Report It

Warning: tricky quickie quiz?

Congradulations Locust:D Report It

Warning: tricky quickie quiz?

3:sin is 2, cos is 1 so In must be 3

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2: A=bh/2 (is this a joke?)

Ok, its a trick so it is 3

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How about moving D down instead?

Or F up?

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"Why, I've seen as many as six impossssssssssible things before breakfast!"

-Lewis Carroll, "Through the Looking Glass"

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Perhaps with square roots and pies?

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Are you going to block me?

:D

Warning: tricky quickie quiz?

q1

1)

q2

2) actually AC*CB/2

q3

maybe 2)

q4

1)

q5

1)