Search results
Results from the WOW.Com Content Network
For example, the fact that any convergent sequence in a metric space is a Cauchy sequence is a direct consequence of the triangle inequality, because if we choose any x n and x m such that d(x n, x) < ε/2 and d(x m, x) < ε/2, where ε > 0 is given and arbitrary (as in the definition of a limit in a metric space), then by the triangle ...
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);
When u and v are real numbers, they can be viewed as vectors in , and the triangle inequality expresses a relationship between absolute values. Pythagorean theorem : It states that the area of the square whose side is the hypotenuse (the side opposite the right angle ) is equal to the sum of the areas of the squares on the other two sides.
Euler's inequality, in the form stating that, for all triangles inscribed in a given circle, the maximum of the radius of the inscribed circle is reached for the equilateral triangle and only for it, is valid in absolute geometry. [7]
Osmoregulation is the active regulation of the osmotic pressure of an organism's body fluids, detected by osmoreceptors, to maintain the homeostasis of the organism's water content; that is, it maintains the fluid balance and the concentration of electrolytes (salts in solution which in this case is represented by body fluid) to keep the body fluids from becoming too diluted or concentrated.
If you’re stuck on today’s Wordle answer, we’re here to help—but beware of spoilers for Wordle 1273 ahead. Let's start with a few hints.
In mathematics, the Kantorovich inequality is a particular case of the Cauchy–Schwarz inequality, which is itself a generalization of the triangle inequality. The triangle inequality states that the length of two sides of any triangle, added together, will be equal to or greater than the length of the third side. In simplest terms, the ...
The process of osmosis over a semipermeable membrane.The blue dots represent particles driving the osmotic gradient. Osmosis (/ ɒ z ˈ m oʊ s ɪ s /, US also / ɒ s-/) [1] is the spontaneous net movement or diffusion of solvent molecules through a selectively-permeable membrane from a region of high water potential (region of lower solute concentration) to a region of low water potential ...