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The proper symmetry group is then a subgroup of the special orthogonal group SO(n), and is called the rotation group of the figure. In a discrete symmetry group, the points symmetric to a given point do not accumulate toward a limit point. That is, every orbit of the group (the images of a given point under all group elements) forms a discrete ...
The mapping (x, y) → (x, y, 1) defines an inclusion from the Euclidean plane to the projective plane and the complement of the image is the set of points with z = 0. The equation z = 0 is an equation of a line in the projective plane (see definition of a line in the projective plane), and is called the line at infinity.
These transformations preserve angles, map every straight line to a line or circle, and map every circle to a line or circle. The Möbius transformations are the projective transformations of the complex projective line. They form a group called the Möbius group, which is the projective linear group PGL(2, C).
Inversive geometry. In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied.
Example Symbols. NATO Joint Military Symbology is the NATO standard for military map symbols. Originally published in 1986 as Allied Procedural Publication 6 ( APP-6 ), NATO Military Symbols for Land Based Systems, the standard has evolved over the years and is currently in its fifth version (APP-6D). The symbols are designed to enhance NATO 's ...
An object has reflectional symmetry (line or mirror symmetry) if there is a line (or in 3D a plane) going through it which divides it into two pieces that are mirror images of each other. [6] An object has rotational symmetry if the object can be rotated about a fixed point (or in 3D about a line) without changing the overall shape. [7]
Circle MRT line. The Circle Line ( CCL) is a medium-capacity Mass Rapid Transit line in Singapore. It runs in a loop from Dhoby Ghaut station in the city-centre to HarbourFront station in the south via Bishan station in the centre of the country. It also has a branch to Marina Bay station from Promenade station, which will be extended to ...
A Reuleaux triangle [ʁœlo] is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. [1] It is formed from the intersection of three circular disks, each having its center on the boundary of the other two. Constant width means that the separation of every two parallel supporting lines ...