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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]
The line segments AB and CD are orthogonal to each other. In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.Whereas perpendicular is typically followed by to when relating two lines to one another (e.g., "line A is perpendicular to line B"), [1] orthogonal is commonly used without to (e.g., "orthogonal lines A and B").
The regular hexagon has D 6 symmetry. There are 16 subgroups. There are 8 up to isomorphism: itself (D 6), 2 dihedral: (D 3, D 2), 4 cyclic: (Z 6, Z 3, Z 2, Z 1) and the trivial (e) These symmetries express nine distinct symmetries of a regular hexagon. John Conway labels these by a letter and group order. [4] r12 is full symmetry, and a1 is no ...
Nine regions of the abdomen can be marked using two horizontal and two vertical dividing lines. The vertical lines are the mid-clavicular lines taken from the mid-point of each clavicle. The upper horizontal line is the subcostal line taken from the inferior parts of the lowest costal cartilages. The lower horizontal line is the intertubercular ...
In chemistry and crystallography, a symmetry element is a point, line, or plane about which symmetry operations can take place. In particular, a symmetry element can be a mirror plane, an axis of rotation (either proper and improper), or a center of inversion. [ 1][ 2][ 3] For an object such as a molecule or a crystal, a symmetry element ...
Asymptote. The graph of a function with a horizontal ( y = 0), vertical ( x = 0), and oblique asymptote (purple line, given by y = 2 x ). A curve intersecting an asymptote infinitely many times. In analytic geometry, an asymptote ( / ˈæsɪmptoʊt /) of a curve is a line such that the distance between the curve and the line approaches zero as ...
In mathematics, a symmetry operation is a geometric transformation of an object that leaves the object looking the same after it has been carried out. For example, a 1 ⁄ 3 turn rotation of a regular triangle about its center, a reflection of a square across its diagonal, a translation of the Euclidean plane, or a point reflection of a sphere through its center are all symmetry operations.
In the three-dimensional case, the situation is more complicated as now one has horizontal and vertical planes in addition to horizontal and vertical lines. Consider a point P and designate a direction through P as vertical. A plane which contains P and is normal to the designated direction is the horizontal plane at P.