Polygon problem

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peterhitter

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The base of the rotating tower has a shape of equilateral polygon. If the tower rotates by 28,5°, then it looks the same from the left & from the right side. How many sides does the rotating tower need to have this property? (We are asked for the smallest possible number of the sides)

I tried to divide 360 by 28,5° but it gave me 12,63... and since polygon cannot have 12,63 sides that answer does not make sense. And I do not have any other idea. Thanks in advance for your help.
 
peterhitter said:
The base of the rotating tower has a shape of equilateral polygon. If the tower rotates by 28,5°, then it looks the same from the left & from the right side. How many sides does the rotating tower need to have this property? (We are asked for the smallest possible number of the sides)

I tried to divide 360 by 28,5° but it gave me 12,63... and since polygon cannot have 12,63 sides that answer does not make sense. And I do not have any other idea. Thanks in advance for your help.
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The 28.5° is a bogus measurement since it is not really tied into anything.

For example, suppose you were facing a particular direction and this problem was given but with a rotation of a degrees. If the complete situation were rotated b degrees, then the situation would be the same. That is the 28.5 is a reference between you and the tower, having nothing to do with the shape of the tower.

So, the actual problem is suppose you are looking at tower with a shape of equilateral polygon. Could you walk around the polygon so that, at some point, it looked the same from the left as from the right. That is, does any equilateral polygon have an orientation with left-right symmetry and, if so, what is the one with the smallest number of sides?
 
Last edited:
Ishuda said:
The 28.5° is a bogus measurement since it is not really tied into anything.

For example, suppose you were facing a particular direction and this problem was given but with a rotation of a degrees. If the complete situation were rotated b degrees, then the situation would be the same. That is the 28.5 is a reference between you and the tower, having nothing to do with the shape of the tower.

So, the actual problem is suppose you are looking at tower with a shape of equilateral polygon. Could you walk around the polygon so that, at some point, it looked the same from the left as from the right. That is, does any equilateral polygon have an orientation with left-right symmetry and, if so, what is the one with the smallest number of sides?
Click to expand...
Yeah it is a strange measurment since this is supposed to be a tricky question, but still I can't seem to find any polygon with this crazy property.
 
Sorry, I meant regular polygon as you said with all sides of the same length and all angles of the same value
 
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