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In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent. The AA postulate follows from the fact that the sum of the interior angles of a triangle is always equal to 180°. By knowing two angles, such as 32° and 64° degrees, we know that the next angle is 84°, because 180 ...
Baron Munchausen pulls himself out of a mire by his own hair.. In epistemology, the Münchhausen trilemma is a thought experiment intended to demonstrate the theoretical impossibility of proving any truth, even in the fields of logic and mathematics, without appealing to accepted assumptions.
A spiral similarity taking triangle ABC to triangle A'B'C'. Spiral similarity is a plane transformation in mathematics composed of a rotation and a dilation. [1] It is used widely in Euclidean geometry to facilitate the proofs of many theorems and other results in geometry, especially in mathematical competitions and olympiads.
Similarity measures play a crucial role in many clustering techniques, as they are used to determine how closely related two data points are and whether they should be grouped together in the same cluster. A similarity measure can take many different forms depending on the type of data being clustered and the specific problem being solved.
Similarity is an equivalence relation on the space of square matrices. Because matrices are similar if and only if they represent the same linear operator with respect to (possibly) different bases, similar matrices share all properties of their shared underlying operator: Rank; Characteristic polynomial, and attributes that can be derived from it:
In fluid mechanics, dynamic similarity is the phenomenon that when there are two geometrically similar vessels (same shape, different sizes) with the same boundary conditions (e.g., no-slip, center-line velocity) and the same Reynolds and Womersley numbers, then the fluid flows will be identical.
Time is a criterion commonly appealed to in debate, often referred to as "the test of time". This criterion posits that over time erroneous beliefs and logical errors will be revealed, while if the belief is true, the mere passage of time cannot adversely affect its validity. Time is an inadequate test for truth, since it is subject to similar ...
According to van den Essen, [2] the problem was first conjectured by Keller in 1939 for the limited case of two variables and integer coefficients. The obvious analogue of the Jacobian conjecture fails if k has characteristic p > 0 even for one variable. The characteristic of a field, if it is not zero, must be prime, so at least 2.