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Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
Birkhoff's axiomatic system was utilized in the secondary-school textbook by Birkhoff and Beatley. [2] These axioms were also modified by the School Mathematics Study Group to provide a new standard for teaching high school geometry, known as SMSG axioms. A few other textbooks in the foundations of geometry use variants of Birkhoff's axioms. [3]
[2] By itself, at least granted the axiom of choice, the existence of a scale on a pointset is trivial, as A can be wellordered and each φ n can simply enumerate A. To make the concept useful, a definability criterion must be imposed on the norms (individually and together).
Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building. [1] In such cases the scale is dimensionless and exact throughout the model or drawing. The scale can be expressed in four ways: in words (a lexical scale), as a ratio, as a fraction and as a graphical (bar) scale.
Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.
Quizlet was founded in October 2005 by Andrew Sutherland, who at the time was a 15-year old student, [2] and released to the public in January 2007. [3] Quizlet's primary products include digital flash cards , matching games , practice electronic assessments , and live quizzes.
Scale analysis (or order-of-magnitude analysis) is a powerful tool used in the mathematical sciences for the simplification of equations with many terms. First the approximate magnitude of individual terms in the equations is determined.
In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning, such as preserving distances, angles, or ratios (scale).
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