Abstract
A cube is one of the most fundamental shapes we can draw and can observe from a drawing. The two visualization methods most commonly applied in mathematics textbooks and education are the axonometric and the perspective representations. However, what we see in the drawing is really a cube or only a general cuboid (i.e., a polyhedron with different edge lengths). In this experimental study, 153 first-year ( 19–20-year-old) students, two-thirds of them being female, were asked to interactively adjust a cuboid figure until they believe what they see is really a cube. We were interested in how coherently people, who are actually students of arts studies and engineering with advanced spatial perception skills in most cases, evaluate these drawings. What we have experienced is that for most people there is a common visual understanding of seeing a cube (and not a general cuboid). Moreover, this common sense is surprisingly close to the conventions applied in axonometric drawings, and to the theoretical, geometric solution in the case of three-point perspective drawings, which is the most realistic visualization method.
Highlights
Most people with average spatial abilities can draw a cuboid, and, vice versa, can observe a cuboid from a line drawing
In spatial line drawings of artistic pieces, design materials and mathematics illustrations, we can distinguish fundamentally two basic approaches: the axonometric type, when the parallel sides of the cube will be parallel in the drawing, and the perspective type, when—due to the classical rules of perspectivity—images of lines of parallel edges meet at one point in some or all of the three directions
It is by no means trivial whether a drawing is well understood by the observer and if this is a correct drawing to provide the specific mathematic knowledge or artistic message [2,3,4]
Summary
Most people with average spatial abilities can draw a cuboid, and, vice versa, can observe a cuboid from a line drawing. In spatial line drawings of artistic pieces, design materials and mathematics illustrations, we can distinguish fundamentally two basic approaches: the axonometric (or oblique) type, when the parallel sides of the cube will be parallel in the drawing, and the perspective type, when—due to the classical rules of perspectivity—images of lines of parallel edges meet at one point (the so-called vanishing point) in some or all of the three directions It is by no means trivial whether a drawing is well understood by the observer and if this is a correct drawing to provide the specific mathematic knowledge or artistic message [2,3,4]. Accurate drawing and understanding of a drawing is of utmost importance to effectively support mathematical performance [7], especially in geometry [8], but its interdisciplinary impact is crucial
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