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Basic abstract diagram of a staple, with parts labelled. Shown in isometric-projection pseudo-perspective (not true perspective view). Date: 2010: Source: Self-made SVG file, based loosely on File:Staplediagram.JPG. Converted from the following PostScript vector source code:
The pedal curve of C with respect to a pedal point P is the locus of points X such that the line through X orthogonal to PX is tangent to C. (Salmon 1879, p.96) pencil A 1-dimensional linear system. See pencil (mathematics) and Lefschetz pencil. pentad A set of 5 points pentahedron A union of 5 planes, in particular the Sylvester pentahedron of ...
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
These subsets subdivide the plane into shapes of the following three types: [1] The cells or chambers of the arrangement are two-dimensional regions not part of any line. They form the interiors of bounded convex polygons or unbounded convex regions. These are the connected components of the points that would remain after removing all points on ...
The same set of points can often be constructed using a smaller set of tools. For example, using a compass, straightedge, and a piece of paper on which we have the parabola y=x 2 together with the points (0,0) and (1,0), one can construct any complex number that has a solid construction. Likewise, a tool that can draw any ellipse with already ...
The Pythagorean triple (4,3,5) is associated to the rational point (4/5,3/5) on the unit circle. In mathematics, the rational points on the unit circle are those points (x, y) such that both x and y are rational numbers ("fractions") and satisfy x 2 + y 2 = 1. The set of such points turns out to be closely related to primitive Pythagorean triples.
Moritz Pasch first defined a geometry without reference to measurement in 1882. His axioms were improved upon by Peano (1889), Hilbert (1899), and Veblen (1904). [1]: 176 Euclid anticipated Pasch's approach in definition 4 of The Elements: "a straight line is a line which lies evenly with the points on itself". [2]
The Cartesian square of a set X is the Cartesian product X 2 = X × X. An example is the 2-dimensional plane R 2 = R × R where R is the set of real numbers: [1] R 2 is the set of all points (x,y) where x and y are real numbers (see the Cartesian coordinate system).
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