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Epicentral distance refers to the ground distance from the epicenter to a specified point. [1] Generally, the smaller the epicentral distance of an earthquake of the same scale, the heavier the damage caused by the earthquake. On the contrary, with the increase of epicentral distance, the damage caused by the earthquake is gradually reduced. [2]
Travel-time curve is a graph showing the relationship between the distance from the epicenter to the observation point and the travel time. [2] [3] Travel-time curve is drawn when the vertical axis of the graph is the travel time and the horizontal axis is the epicenter distance of each observation point. [4] [5] [6]
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
Arc length – Distance along a curve; Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric ...
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
That this octagonal figure, whose area is easily calculated, so accurately approximates the area of the circle is just plain good luck. Obtaining a better approximation to the area using finer divisions of a square and a similar argument is not simple. [10] Problem 50 of the RMP finds the area of a round field of diameter 9 khet. [10]
Hence, any distance whose ratio to an existing distance is the solution of a cubic or a quartic equation is constructible. Using a markable ruler, regular polygons with solid constructions, like the heptagon, are constructible; and John H. Conway and Richard K. Guy give constructions for several of them. [20]
The distance of closest approach is sometimes referred to as the contact distance. For the simplest objects, spheres, the distance of closest approach is simply the sum of their radii. For non-spherical objects, the distance of closest approach is a function of the orientation of the objects, and its calculation can be difficult.