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Van Hiele model. In mathematics education, the Van Hiele model is a theory that describes how students learn geometry. The theory originated in 1957 in the doctoral dissertations of Dina van Hiele-Geldof and Pierre van Hiele (wife and husband) at Utrecht University, in the Netherlands. The Soviets did research on the theory in the 1960s and ...
Congruence (geometry) Relationship between two figures of the same shape and size, or mirroring each other. The two triangles on the left are congruent. The third is similar to them. The last triangle is neither congruent nor similar to any of the others. Congruence permits alteration of some properties, such as location and orientation, but ...
Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure. Two congruent shapes are similar, with a scale factor of 1. However, some school textbooks specifically exclude congruent triangles from their definition of similar triangles by insisting that the sizes must be ...
In this tiling of the plane by congruent squares, the green and violet squares meet edge-to-edge as do the blue and orange squares. In geometry, Keller's conjecture is the conjecture that in any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes that share an entire (n − 1)-dimensional face with each other.
Mental rotation is the ability to rotate mental representations of two-dimensional and three-dimensional objects as it is related to the visual representation of such rotation within the human mind. [1] There is a relationship between areas of the brain associated with perception and mental rotation.
A simplicial line arrangement (left) and a simple line arrangement (right). In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons, the cells of the arrangment, line segments and rays, the edges of the arrangement, and ...
The Ebbinghaus illusion or Titchener circles is an optical illusion of relative size perception. Named for its discoverer, the German psychologist Hermann Ebbinghaus (1850–1909), the illusion was popularized in the English-speaking world by Edward B. Titchener in a 1901 textbook of experimental psychology, hence its alternative name. [1] In ...
Euclidean tilings are usually named after Cundy & Rollett’s notation. [1] This notation represents (i) the number of vertices, (ii) the number of polygons around each vertex (arranged clockwise) and (iii) the number of sides to each of those polygons. For example: 3 6; 3 6; 3 4.6, tells us there are 3 vertices with 2 different vertex types ...