We devote a chapter to the binomial distribution not only because it is a mathematical model for an enormous variety of real life phenomena, but also because it has important properties that recur in many other probability models.

But, up to now, no one has attempted to analyze its inherent mathematical properties, or the numerical significance of its numbers -- singly or in combination -- and then tried to consider these in the light of Old Chinese cosmological concepts.

The importance of this 5 can largely be explained by the natural mathematical properties of the middle number and its special relationship to all the rest of the numbers -- quite apart from any numerological considerations, which is to say, any symbolic meaning arbitrarily assigned to it.

Whereas the primary meanings of the Lo Shu diagram seemed to have been based on its inner mathematical properties -- and we shall see that even its secondary meanings rested on some mathematical bases -- the urgent desire to place everything into categories of fives led to other groupings based on other numbers, until an exaggerated emphasis on mere numerology pervaded Chinese thought.

Although the primary mathematical properties of the middle number at the center of the Lo Shu, and the interrelation of all the other numbers to it, might seem enough to account for the deep fascination which the Lo Shu held for the Old Chinese philosophers, this was actually only a beginning of wonders.

There are typically three mathematical forms for the radial functions R ( r ) which can be chosen as a starting point for the calculation of the properties of atoms and molecules with many electrons.

He held that the Absolute Infinite had various mathematical properties, including the reflection principle which says that every property of the Absolute Infinite is also held by some smaller object.

The triangle demonstrates many mathematical properties in addition to showing binomial coefficients.

Constructed languages such as Esperanto, programming languages, and various mathematical formalisms are not necessarily restricted to the properties shared by human languages.

The study of condensed matter physics involves measuring various material properties via experimental probes along with using techniques of theoretical physics to develop mathematical models that help in understanding physical behavior.

Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows ( also called morphisms, although this term also has a specific, non category-theoretical meaning ), where these collections satisfy some basic conditions.

These physical properties are then represented by tensors, which are mathematical objects that have the required property of being independent of coordinate system.

Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the spontaneity of processes.

In the 19th century, several disparate mathematical properties were understood that would later be seen as consequences of compactness.

Synchronous CDMA exploits mathematical properties of orthogonality between vectors representing the data strings.

The mathematical properties of the catenary curve were first studied by Robert Hooke in the 1670s, and its equation was derived by Leibniz, Huygens and Johann Bernoulli in 1691.

volume ) and its position in time ( perceived as a scalar dimension along the t-axis ), as well as the spatial constitution of objects within — structures that correlate with both particle and field conceptions, interact according to relative properties of mass — and are fundamentally mathematical in description.

Graph ( mathematics ) | Graphs like this are among the objects studied by discrete mathematics, for their interesting graph property | mathematical properties, their usefulness as models of real-world problems, and their importance in developing computer algorithm s.

This observation motivates the theoretical concept of an abstract data type, a data structure that is defined indirectly by the operations that may be performed on it, and the mathematical properties of those operations ( including their space and time cost ).

The ellipse and some of its mathematical properties.

The exactly opposite properties of the two kinds of electrification justify our indicating them by opposite signs, but the application of the positive sign to one rather than to the other kind must be considered as a matter of arbitrary convention, just as it is a matter of convention in mathematical diagram to reckon positive distances towards the right hand.

These descriptions refer to the mathematical properties of the filter ( that is, the frequency and phase response ).

Using mathematical rules and procedures based on properties of reducible configurations, Appel and Haken found an unavoidable set of reducible configurations, thus proving that a minimal counterexample to the four-color conjecture could not exist.

One of the early ( and portable ) languages that had 4GL properties was Ramis developed by Gerald C. Cohen at Mathematica, a mathematical software company.

It is organized by the students of the Faculty of Engineering and Technology in the month of March with the aim of promoting the spirit of innovation and discovery among the participants and features competitions in coding, robotics, hardware designing, and even mathematical puzzles.

Mathematical games differ from mathematical puzzles in that all mathematical puzzles require math to solve them whereas mathematical games may not require a knowledge of mathematics to play them or even to win them.

Recreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.

They have specific rules, as do multiplayer games, but mathematical puzzles don't usually involve competition between two or more players.

Logic puzzles are a common type of mathematical puzzle.

Conway's Game of Life and fractals are also considered mathematical puzzles, even though the solver only interacts with them by providing a set of initial conditions.

Sometimes, mathematical puzzles are referred to as mathematical games as well.

* Project Eureka-collection of mathematical problems and puzzles

Reflected binary codes were applied to mathematical puzzles before they became known to engineers.

As in many mathematical puzzles, finding a solution is made easier by solving a slightly more general problem: how to move a tower of h ( h = height ) disks from a starting peg A ( f = from ) onto a destination peg C ( t = to ), B being the remaining third peg and assuming t ≠ f.

* Romantic mathematical puzzles

The notebooks additionally contained a number of mathematical calculations and puzzles.

For example there are thousands of computer puzzle games and many letter games, word games and mathematical games which require solutions to puzzles as part of the gameplay.

Her book In Code ( 2001 ), co-written with her father, mathematician David Flannery, retells the story of the making and breaking of the algorithm and of the enjoyment that she got, as a child and throughout her life, from solving mathematical puzzles.

Logic puzzles are a common type of mathematical puzzle.

Conway's Game of Life and fractals, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions.

It also created a series of mathematical puzzles that were posted among the advertising placards on San Francisco Muni buses.