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ORTHOPTIC SURFACE

From the Greek orthos "right" and optikos "relating to sight". |

The *orthoptic* surface of a surface is the locus of the points through which pass 3 planes tangent to the surface and perpendicular 2 by 2.

Examples:

- the orthoptic surface of a sphere with radius *R* is a concentric sphere with radius .

- more generally, the orthoptic surface of a centered quadric is a sphere called *orthoptic sphere* or *Monge sphere*.

- The orthoptic surface of the elliptic paraboloid is a plane called directrix plane????

A similar notion, bearing the same name, is that of *orthoptic surface* of a *subset* of the space: locus of the vertices of the right trihedra that circumscribe X (i.e. containing X, and the three faces of which meet X).

Example: the orthoptic of a circle with radius *R* is a sphere with the same center and radius .

But for some authors, the orthoptic *sphere* of a conic is the locus of the vertices of the cones of revolution with right angle at the vertex in which the conic is included.

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