projection of right angle
Proof. Consider the projection of an angle with vertex (http://planetmath.org/Angle) onto the plane . Let be the projection of onto . If neither of the sides of is parallel to , then the lines of the sides intersect the plane in two distinct points and . In order to that the angle of view of the segment seen from the point would be a right angle, must be on a sphere with diameter centered at a point . In order to that the projection angle would be a right angle, the point must be on a circle of the plane having as diameter. But is as the projection of the segment shorter than . It follows that the angle is obtuse and hence cannot be right.
On the other hand, it’s not hard to see that the projection of a right angle is a right angle always when one or both of its sides are parallel to the projection plane.
- 1 E. J. Nyström: Korkeamman geometrian alkeet sovellutuksineen. Kustannusosakeyhtiö Otava, Helsinki (1948).
|Title||projection of right angle|
|Date of creation||2013-03-22 19:20:51|
|Last modified on||2013-03-22 19:20:51|
|Last modified by||pahio (2872)|