Looking at Solid Geometry Through Perspective

“Much attention should be given to the visualization of spatial figures and relations, to the representation of three-dimensional figures on paper, and to the solution of problems in mensuration,” says the Joint Commission among its suggestions on solid geometry in its report on “The Place of Mathematics in Secondary Education.”* These ideas are incorporated in the notion of perspective. Perspective may be regarded as a practical means for securing a rigorous reciprocal metrical relationship between the shapes of objects as definitely located in space and their pictorial representation. It may be regarded as the rationalization of sight. This Commission further points out that “the problems in mensuration offer opportunity for correlation of solid geometry with arithmetic, algebra, and trigonometry. Part of the importance of the geometry of the sphere comes from the perspective that it makes possible.”