Detailed examinations of the history of the mathematical developments of non-European civilizations, such as the mathematics of ancient Japan, Iraq, Egypt, and of Islamic, Hebrew, and Incan civilizations, have also been presented.

* Detailed explanation of differences between Molokan, Prygun and Dukh-i-zhinik faiths, and between Molokan used as a religious and ethnic term

* Detailed explanation of the Orisha Yemonja-Olokun

* " Annals of Aman " — Detailed chronology from the creation of the world through the end of the First Age, including an explanation of time reckoning in Valian Years.

* Detailed explanation of Paul Graham's formulas by Tim Peters

* The Line Pickelhaube ( Detailed explanation of Pickelhaube and use of Tombak for economic reasons )

* Detailed explanation of relativistic aberration

Detailed explanation of techniques used in verre églomisé at goldreverre

* Detailed explanation of relativistic aberration

* Detailed explanation and instruction for the MCAS

The working principle of a yupana is unknown, but in 2001 an explanation of the mathematical basis of these instruments was proposed by Italian mathematician Nicolino De Pasquale.

Isaac Newton's ( 1642 – 1727 ) mathematical explanation of universal gravitation explained the behavior both of objects here on earth and of objects in the heavens in a way that promoted a worldview in which the natural universe is controlled by laws of nature.

At the time of discovery, Ørsted did not suggest any satisfactory explanation of the phenomenon, nor did he try to represent the phenomenon in a mathematical framework.

* Radiosity, by Allen Martin ( a slightly more mathematical explanation of radiosity )

Some consider statistics to be a mathematical body of science pertaining to the collection, analysis, interpretation or explanation, and presentation of data, while others consider it a branch of mathematics concerned with collecting and interpreting data.

" If we mistakenly confuse precision with accuracy, then we might be misled into thinking that an explanation expressed in precise mathematical or graphical terms is somehow more rigorous or useful than one that takes into account particulars of history, institutions or business strategy.

This supplied a mathematical explanation for the apparent computational difficulty of finding optimal tours.

There is no explanation for the particular values that physical constants appear to have throughout our universe, such as Planck's constant h or the gravitational constant G. Several conservation laws have been identified, such as the conservation of charge, momentum, angular momentum and energy ; in many cases, these conservation laws can be related to symmetries or mathematical identities.

It argues for the existence of mathematical entities as the best explanation for experience, thus stripping mathematics of being distinct from the other sciences.

However, Eudoxus ' importance to Greek astronomy is considerable, as he was the first to attempt a mathematical explanation of the planets.

In 1989, David Hamilton Wright developed a mathematical explanation for mutualism using the Lotka – Volterra equation.

Newton's laws of motion, together with his law of universal gravitation and the mathematical techniques of calculus, provided for the first time a unified quantitative explanation for a wide range of physical phenomena.

Eudoxus of Cnidus, who worked with Plato, developed a less mythical, more mathematical explanation of the planets ' motion based on Plato's dictum stating that all phenomena in the heavens can be explained with uniform circular motion.

From his experimental work with Hodgkin, Huxley developed a set of differential equations that provided a mathematical explanation for nerve impulses — the " action potential ".

Zelikin proposed ( 2006 ) an explanation ( with strict mathematical background ) based on the hypothesis of plasma superconductivity.

Rucker often uses his novels to explore scientific or mathematical ideas ; White Light examines the concept of infinity, while the Ware Tetralogy ( written from 1982 through 2000 ) is in part an explanation of the use of natural selection to develop software ( a subject also developed in his The Hacker and the Ants, written in 1994 ).

Prior to this, all mathematical problems and solutions were written out in words ; the more complicated the problem, the more laborious and convoluted the verbal explanation.

Naturally, as the remainder of this article explains in technical detail, the general concepts described in this non-technical explanation of anti de Sitter space have a much more rigorous and precise mathematical and physical description.

Philosophers and scientists who follow the Bayesian framework for inference use the mathematical rules of probability to find this best explanation.

Beyond point B, mathematical necessity requires that the marginal curve must be below the average curve ( See production theory basics for further explanation.

For a mathematical explanation of this see how variability of individuals is much greater than the variability of their mean.

* Identification numbers and check digit schemes ( a mathematical explanation of various check digit schemes )

It was almost twenty years later, when quantum mechanics was formulated in terms of the Schrödinger equation, that the connection was made to atomic spectra ; a connection with the mathematical physics of vibration had been suspected before, as remarked by Henri Poincaré, but rejected for simple quantitative reasons, absent an explanation of the Balmer series.

* Mathematical problem is a question about mathematical objects and structures that may require a distinct answer or explanation or proof.

Newton was the first to develop a mathematical model for calculating the speed of sound, but it was not correct until Pierre-Simon Laplace accounted for the molecular behavior of gases and introduced the heat capacity ratio.

) The mathematical model works for all fluids: liquids, gases, and slurries.

In the quark model this has no natural explanation — a mystery named the η-η ' mass splitting ( the η is one member of the octet which should have been degenerate in mass with the η ').

However, a study of Dalton's own laboratory notebooks, discovered in the rooms of the Lit & Phil, concluded that so far from Dalton being led by his search for an explanation of the law of multiple proportions to the idea that chemical combination consists in the interaction of atoms of definite and characteristic weight, the idea of atoms arose in his mind as a purely physical concept, forced upon him by study of the physical properties of the atmosphere and other gases.

A complete theoretical explanation of Graham's law was provided years later by the kinetic theory of gases.

In the case of the evaporation of water we are satisfied with the explanation given by the kinetic theory of gases and do not demand that to repeat a well-known jest of Huxley the disappearance of the " aquosity " be also taken into consideration.

The novelisation appears to assume he had actually been shrinking out of existence, and gives the explanation that the flames generated gases that saved him.

A crossflow head gives better performance, but the popular explanation put forward for this — that the gases don't have to change direction and hence are moved into and out of the cylinder more efficiently — is a simplification since there is no continuous flow because of valve opening and closing.

Although other possibilities exist for how these gases emanate energy, such as radiation pressure and interaction with other gas streams, interaction with a massive source of gravity is the simplest explanation.

Maxwell wrote: His theory of impact is faulty, but his explanation of the expansive force of gases pressure is essentially the same as in the dynamical theory, as it now stands.

) could be perfectly imitated in the laboratory, the acid rocks could not, and advanced the explanation that for the crystallization of the latter the gases never absent in natural rock magmas were indispensable mineralizing agents.

Although such proponents of the atomic theory as Amedeo Avogadro and Ludwig Boltzmann made great advances in explaining the behavior of gases, this dispute was not finally settled until Jean Perrin's experimental investigation of Einstein's atomic explanation of Brownian motion in the first decade of the 20th century.

One possible explanation for this was the injection of volcanic gases into the atmosphere by plinian eruptions at Maat Mons.