By Howard Eves
From the book's preface:
Since writing the preface of the 1st variation of this paintings, the gloomy plight there defined of starting collegiate geometry has brightened significantly. The pendulum turns out certainly to be swinging again and a goodly quantity of good textual fabric is showing.
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Additional info for A Survey of Geometry (Revised Edition)
It is a number U such that each set in the collection is contained in a ball of radius U. circumradius The radius of a circumcircle or circumsphere. circumscribed circle See circumcircle. circumscribed cone of a pyramid A cone that has the same vertex as the pyramid and has as its base a circle that is circumscribed about the base of the pyramid. circumsphere A sphere that intersects every vertex of a polyhedron or polytope. Not every polyhedron has a circumsphere. circumtangential triangle For a given triangle, there are exactly three points with the property that the line connecting the point to its isogonal conjugate point is tangent to the circumcircle of the circular reasoning – circumtangential triangle glossary 29 glossary cissoid – coaxial triangle.
Crossing point A break in an arc in a knot diagram that allows another arc to pass through. cross joins The lines AB′ and A′B are the cross joins of the ordered pair of points A and A′ and the ordered pair of points B and B′. cross multiply See rule of three. 5. cross polytope A polytope whose vertices are the endpoints of the segments of a cross. cross product The cross product of two vectors v and w is the vector, denoted v w, that is perpendicular to the plane determined by v and w, has length equal to the area of the parallelogram glossary 44 coversed sine – cross product cross ratio – crystal system glossary formed by v and w, and has direction so that v, w, and v w form a right-handed system.
Constant is the term used to describe a variable that represents a number with a fixed but unknown, rather than varying, value. A constant function has the same value for every point in the domain. constant curvature, surface of A surface with constant nonzero Gaussian curvature. constant of inversion The square of the radius of inversion. constant of proportionality See dilation. constrained triangulation A triangulation that must include certain specified edges. constructible number If a given segment can be constructed with compass and straightedge starting with a segment of length one, the measure of the segment is a constructible number.