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.

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.

The application of the catenary to the construction of arches is attributed to Robert Hooke, whose " true mathematical and mechanical form " in the context of the rebuilding of St Paul's Cathedral alluded to a catenary.

But these are physical representations of the corresponding mathematical entities ; the line and the curve are idealized concepts whose width is 0 ( see Line ).

In the computer science subfields of computer-aided design and computer graphics, the term B-spline frequently refers to a spline curve parametrized by spline functions that are expressed as linear combinations of B-splines ( in the mathematical sense above ).

# Using a mathematical expression, such as a polynomial or a trigonometric function, and a single point on the corresponding curve instead of storing or transmitting the entire graphic curve or a series of points on it.

The Koch snowflake ( also known as the Koch star and Koch island ) is a mathematical curve and one of the earliest fractal curves to have been described.

The idea is based on a mathematical model, the Lissajous curve, which allows the user to keep a continuous flowing form.

The remainder of this article discusses, from a mathematical perspective, some geometric examples of curvature: the curvature of a curve embedded in a plane and the curvature of a surface in Euclidean space.

A sigmoid curve is produced by a mathematical function having an " S " shape.

For example, it can be almost synonymous with mathematical function ( as in learning curve ), or graph of a function ( as in Phillips curve ).

* Cassini oval, mathematical curve

There are at least two different mathematical derivations of the Phillips curve.

So in mathematical terms a curve is defined by four coordinate functions ( where usually denotes the time coordinate ) depending on one parameter.

In the mathematical field of numerical analysis and in computer graphics, a Bézier spline is a spline curve where each polynomial of the spline is in Bézier form.

Transpulmonary thermodilution spans right heart, pulmonary circulation and left heart ; this allows further mathematical analysis of the thermodilution curve, giving measurements of cardiac filling volumes ( GEDV ), intrathoracic blood volume, and extravascular lung water.

In the mathematical subfield of numerical analysis, a Hermite spline is a spline curve where each polynomial of the spline is in Hermite form.

In mathematical physics, a closed timelike curve ( CTC ) is a worldline in a Lorentzian manifold, of a material particle in spacetime that is " closed ," returning to its starting point.

In 1936, Theodore Paul Wright described the effect of learning on labor productivity in the aircraft industry and proposed a mathematical model of the learning curve.

The page on " learning & experience curve models " offers more discussion of the mathematical theory of representing them as deterministic processes, and provides a good group of empirical examples of how that technique has been applied.

Ogee is also a mathematical term, meaning an inflection point ; the aesthetic appeal of the ogee curve forms part of the leitmotif of the Booker-prize winning novel The Line of Beauty.

In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square ( or more generally an n-dimensional hypercube ).

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