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Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distances and angles. The unchanged properties are called invariants. In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
The phase diagram shows, in pressure–temperature space, the lines of equilibrium or phase boundaries between the three phases of solid, liquid, and gas. The curves on the phase diagram show the points where the free energy (and other derived properties) becomes non-analytic: their derivatives with respect to the coordinates (temperature and ...
An example of congruence. The two figures on the left are congruent, while the third is similar to them. The last figure is neither. Congruences alter some properties, such as location and orientation, but leave others unchanged, like distance and angles. The latter sort of properties are called invariants and studying them is the essence of ...
Water (H2O) is a polar inorganic compound that is at room temperature a tasteless and odorless liquid, which is nearly colorless apart from an inherent hint of blue. It is by far the most studied chemical compound [19] and is described as the "universal solvent " [20] and the "solvent of life". [21]
Similarity (geometry) In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.
In mathematics, an isometry (or congruence, or congruent transformation) is a distance -preserving transformation between metric spaces, usually assumed to be bijective. [a] The word isometry is derived from the Ancient Greek: ἴσος isos meaning "equal", and μέτρον metron meaning "measure". If the transformation is from a metric space ...
A water model is defined by its geometry, together with other parameters such as the atomic charges and Lennard-Jones parameters. In computational chemistry, a water model is used to simulate and thermodynamically calculate water clusters, liquid water, and aqueous solutions with explicit solvent. The models are determined from quantum ...
In chemistry, a water cluster is a discrete hydrogen bonded assembly or cluster of molecules of water. [1][2] Many such clusters have been predicted by theoretical models (in silico), and some have been detected experimentally in various contexts such as ice, bulk liquid water, in the gas phase, in dilute mixtures with non-polar solvents, and ...
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