+0

# Impossible construction?

+5
779
8
+354

Ok look at this image.

I'm 99% certain that this is impossible to construct as joining the bottom left corner with the top left corner creates a 20 degree angle. It also creates a essential trisection of 60 degrees, but i can't tell for sure.

The closest i have gotten to 20 degrees is 19.1.

The two trianges are equlateral.

Apr 21, 2015

#5
+28029
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Start with the large equilateral triangles - they are easy to construct with straight-edge and compass.  Then you can draw the larger circle easily enough - you don't need to use a 20° angle.  The four smallest equilateral triangles are also easy to construct (I'm assuming the four intermediate equilateral triangles created by the intersection of the two large triangles are themselves equal in size to four of the smallest triangles.

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Apr 23, 2015

#1
+1000
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X-X what? sorry my mind just exploded.

Apr 21, 2015
#2
+101771
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I don't know where you want the 20 degree angle.  If the 2 big triangles are equilateral then they have to be congruent because they have the same height.   ???

Apr 22, 2015
#3
+354
+5

I mean with a unmarked staight edge and compass, how could I contruct an accurate version or not.

Apr 22, 2015
#4
+101771
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I will include your question in the wrap - maybe someone will take up your challenge :)

Does it have to be a ruler and pair of compasses?

It might be fun to try and construct it using co-ordinate geometry and Desmos graphing calculator :)

Apr 23, 2015
#5
+28029
+8

Start with the large equilateral triangles - they are easy to construct with straight-edge and compass.  Then you can draw the larger circle easily enough - you don't need to use a 20° angle.  The four smallest equilateral triangles are also easy to construct (I'm assuming the four intermediate equilateral triangles created by the intersection of the two large triangles are themselves equal in size to four of the smallest triangles.

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Alan Apr 23, 2015
#6
+101771
+5

The 20 degree angle was a major part of radio's request Alan

Apr 23, 2015
#7
+28029
+5

I read this as an attempt to do a straight-edge and compass construction (as per the ancient Greeks).  However, the angle indicated isn't in fact 20° - see image below:

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Apr 23, 2015
#8
+101771
0

Thanks Alan,

There you go radio.  You cannot construct it at 20 degrees because it is NOT 20 degrees.

Its value is totally predefined !

Apr 24, 2015