InterpolationIn the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.
Ancient Greek astronomyAncient Greek astronomy is the astronomy written in the Greek language during classical antiquity. Greek astronomy is understood to include the Ancient Greek, Hellenistic, Greco-Roman, and late antique eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as Hellenistic astronomy, while the pre-Hellenistic phase is known as Classical Greek astronomy.
History of astronomyAstronomy is the oldest of the natural sciences, dating back to antiquity, with its origins in the religious, mythological, cosmological, calendrical, and astrological beliefs and practices of prehistory: vestiges of these are still found in astrology, a discipline long interwoven with public and governmental astronomy. It was not completely separated in Europe (see astrology and astronomy) during the Copernican Revolution starting in 1543. In some cultures, astronomical data was used for astrological prognostication.
Polynomial interpolationIn numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each . There is always a unique such polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials.
Multivariate interpolationIn numerical analysis, multivariate interpolation is interpolation on functions of more than one variable (multivariate functions); when the variates are spatial coordinates, it is also known as spatial interpolation. The function to be interpolated is known at given points and the interpolation problem consists of yielding values at arbitrary points . Multivariate interpolation is particularly important in geostatistics, where it is used to create a digital elevation model from a set of points on the Earth's surface (for example, spot heights in a topographic survey or depths in a hydrographic survey).
Egyptian astronomyEgyptian astronomy began in prehistoric times, in the Predynastic Period. In the 5th millennium BCE, the stone circles at Nabta Playa may have made use of astronomical alignments. By the time the historical Dynastic Period began in the 3rd millennium BCE, the 365 day period of the Egyptian calendar was already in use, and the observation of stars was important in determining the annual flooding of the Nile. The Egyptian pyramids were carefully aligned towards the pole star, and the temple of Amun-Re at Karnak was aligned on the rising of the midwinter Sun.
Babylonian astronomyBabylonian astronomy was the study or recording of celestial objects during the early history of Mesopotamia. Babylonian astronomy seemed to have focused on a select group of stars and constellations known as Ziqpu stars. These constellations may have been collected from various earlier sources. The earliest catalogue, Three Stars Each, mentions stars of the Akkadian Empire, of Amurru, of Elam and others. A numbering system based on sixty was used, a sexagesimal system.
Chinese astronomyAstronomy in China has a long history stretching from the Shang dynasty, being refined over a period of more than 3,000 years. The ancient Chinese people have identified stars from 1300 BCE, as Chinese star names later categorized in the twenty-eight mansions have been found on oracle bones unearthed at Anyang, dating back to the mid-Shang dynasty. The core of the "mansion" (宿 xiù) system also took shape around this period, by the time of King Wu Ding (1250–1192 BCE).
Bilinear interpolationIn mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals. Bilinear interpolation is performed using linear interpolation first in one direction, and then again in another direction.
Railway signalA railway signal is a visual display device that conveys instructions or provides warning of instructions regarding the driver’s authority to proceed. The driver interprets the signal's indication and acts accordingly. Typically, a signal might inform the driver of the speed at which the train may safely proceed or it may instruct the driver to stop. Application of railway signals Originally, signals displayed simple stop or proceed indications. As traffic density increased, this proved to be too limiting and refinements were added.
