My good friend asked me Padyta In the previous post if you can get an arbitrary angle on a sheet of paper. If we remember that a square is possible to obtain from this angle, then your question is of great importance. Motivated by this, I cheered and began to analyze the problem.
Build a line perpendicular to another two-dimensional geometry requires the use of ruler and compass and is not a simple process too. One way is by drawing a circle of arbitrary radius from a point on the line (point A) and then another from the intersection of it with the line (point B), the intersection of both circles will give us a point equidistant from both ends (C), then trace another circle with the same radius, centered at this point, and then centered to the intersection with the first (D). Thus we get the point E at the intersection of those two circles (centered at points C and D respectively), this point belongs to the perpendicular to our original line that passes by our vertex A.
However, the "origeometría" allows us to project ourselves into a third dimension and gives us real leaf as an additional element in our abilities, so if we have a straight line either, folding the paper and aligning the line on itself get perpendicular to it immediately.
Now, we achieved our angle, is it possible then to build a perfect square from both lines? The answer, fortunately, is yes, I have here a method for this.
first thing to do is build an angle of 45 ° from both lines, this will allow us to find the 45 ° line through one of our vertices arbitrarily defined. For this, we doubled our angle bisector, aligning two perpendicular lines at the point of their intersection.
then align our line of 45 ° on itself, bending it to pass through the vertex we have defined for our square. A good choice of this summit will allow us to better harness the paper and get the largest possible square from it.
In doing so, we can mark and cut one of the main angles of the square. And as we saw in the previous post, get it from the opposite angle is simple if you double the diagonal aligning it on itself.
It remains then one way to ensure a square of maximum area possible for our piece of paper. A greeting and I hope you liked it;).
Build a line perpendicular to another two-dimensional geometry requires the use of ruler and compass and is not a simple process too. One way is by drawing a circle of arbitrary radius from a point on the line (point A) and then another from the intersection of it with the line (point B), the intersection of both circles will give us a point equidistant from both ends (C), then trace another circle with the same radius, centered at this point, and then centered to the intersection with the first (D). Thus we get the point E at the intersection of those two circles (centered at points C and D respectively), this point belongs to the perpendicular to our original line that passes by our vertex A.
However, the "origeometría" allows us to project ourselves into a third dimension and gives us real leaf as an additional element in our abilities, so if we have a straight line either, folding the paper and aligning the line on itself get perpendicular to it immediately.
Now, we achieved our angle, is it possible then to build a perfect square from both lines? The answer, fortunately, is yes, I have here a method for this.
first thing to do is build an angle of 45 ° from both lines, this will allow us to find the 45 ° line through one of our vertices arbitrarily defined. For this, we doubled our angle bisector, aligning two perpendicular lines at the point of their intersection.
then align our line of 45 ° on itself, bending it to pass through the vertex we have defined for our square. A good choice of this summit will allow us to better harness the paper and get the largest possible square from it.
In doing so, we can mark and cut one of the main angles of the square. And as we saw in the previous post, get it from the opposite angle is simple if you double the diagonal aligning it on itself.
It remains then one way to ensure a square of maximum area possible for our piece of paper. A greeting and I hope you liked it;).
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