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Thales’ theorem: if AC is a diameter and B is a point on the diameter's circle, the angle ∠ ABC is a right angle.. In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle.
is the diameter of the volume equivalent spherical particle; V 0 {\displaystyle V_{\mathrm {0} }} is the superficial or "empty-tower" velocity which is directly proportional to the average volumetric fluid flux in the channels (q), and porosity ( ε {\displaystyle \mathbf {\varepsilon } } ).
Visualization of the sagitta. In geometry, the sagitta (sometimes abbreviated as sag [1]) of a circular arc is the distance from the midpoint of the arc to the midpoint of its chord. [2]
The method of exhaustion (Latin: methodus exhaustionis) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape.
PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass.
A few steps of the bisection method applied over the starting range [a 1;b 1].The bigger red dot is the root of the function. In mathematics, the bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs.
This is equivalent to the above definition of the 2D mean diameter. However, for historical reasons, the hydraulic radius is defined as the cross-sectional area of a pipe A , divided by its wetted perimeter P , which leads to D H = 4 R H {\displaystyle D_{\text{H}}=4R_{\text{H}}} , and the hydraulic radius is half of the 2D mean radius.
Diameter (group theory), the maximum diameter of a Cayley graph of the group; Equivalent diameter, the diameter of a circle or sphere with the same area, perimeter, or volume as another object; Hydraulic diameter, the equivalent diameter of a tube or channel for fluids; Kinetic diameter, a measure of particles in a gas related to the mean free path