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Hermann Rorschach created the inkblot test in 1921. (Photo from c. 1910). The use of interpreting "ambiguous designs" to assess an individual's personality is an idea that goes back to Leonardo da Vinci and Botticelli. [9]
Given a metric space (loosely, a set and a scheme for assigning distances between elements of the set), an isometry is a transformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between the elements in the original metric space.
The origin of a Cartesian coordinate system. In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space. In physical problems, the choice of origin is often arbitrary, meaning any choice of origin will ultimately give the same ...
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object
Antipodal symmetry is an alternative name for a point reflection symmetry through the origin. [14] Such a "reflection" preserves orientation if and only if k is an even number. [15] This implies that for m = 3 (as well as for other odd m), a point reflection changes the orientation of the space, like a mirror-image symmetry.
The type of symmetry is determined by the way the pieces are organized, or by the type of transformation: 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]
Thus, a d-variate distribution is defined to be mirror symmetric when its chiral index is null. The distribution can be discrete or continuous, and the existence of a density is not required, but the inertia must be finite and non null. In the univariate case, this index was proposed as a non parametric test of symmetry. [2]
In group theory, the rotation axes and mirror planes are called "symmetry elements". These elements can be a point, line or plane with respect to which the symmetry operation is carried out. The symmetry operations of a molecule determine the specific point group for this molecule. Water molecule with symmetry axis