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3D Trihedron

A more flexible set of axes. I will adopt this system for now.
Each axis slides along one meridian. Arrows indicate the direction of positive rotation. I adopt the following notation: Capital letters X, Y, Z denote the 3-dimensional vectors: X Y Z are mutually perpendicular unit vectors forming a right-handed coordinate system. Barred letters are projections: are the projections of X Y Z on the view plane (the coordinates of are the ordinary GGB coordinates.) I have begun with a coordinate-free representation. I submit without proof that the axes are bound by the following constraints: The two constraints can also be stated this way: Let determine an ellipse with center O, major axis the unit perpendicular to , and minor axis of . Then are conjugate radii on the ellipse. And likewise are conjugate on the ellipses determined by , respectively. Update: So. I made that up, to respect freedom of motion. Today I find this is Gauss' Fundamental Theorem of Normal Axonometry. This was problem #74 in Heinrich Dorrie's 100 Great Problems of Elementary Mathematics.. ___________________ Unit Sphere [list]
  • Setup: http://www.geogebratube.org/material/show/id/101282
  • → Trihedron:
  • Base Object: http://www.geogebratube.org/material/show/id/105255
  • Spherical Coordinates {link}
  • Meridian, (Horizon Points)
  • Latitude, (Horizon Points)