In the following paper it is shown that in a certain definite sense, exactly an odd number of squares can be inscribed in every such curve which does not contain an infinite number of inscribed squares.

In accordance with this, other civilizations, including more " successful " ones, should exist an infinite number of times on the " preceding " and the " following " pages of the Book of the Universe.

On the other hand, for integer order α, the following relationship is valid ( note that the Gamma function becomes infinite for negative integer arguments ):

Hippolyte Taine wrote in 1866: " There may not be in the world an example of another genius so universal, so incapable of fulfilment, so full of yearning for the infinite, so naturally refined, so far ahead of his own century and the following centuries.

The basic question about a set of Wang tiles is whether it can tile the plane or not, i. e., whether copies of the tiles can be arranged to fill an infinite plane, following the adjacency rules.

It begins at an infinite distance from the pole in the centre ( for θ starting from zero r = a / θ starts from infinity ), it winds faster and faster around as it approaches the pole, the distance from any point to the pole, following the curve, is infinite.

In " Essay on the Funding System " ( 1820 ) Ricardo studied whether it makes a difference to finance a war with £ 20 million in current taxes or to issue government bonds with infinite maturity and annual interest payment of £ 1 million in all following years financed by future taxes.

This future visibility limit is calculated at a comoving distance of 19 billion parsecs ( 62 billion light years ), which implies the number of galaxies that we can ever theoretically observe in the infinite future ( leaving aside the issue that some may be impossible to observe in practice due to redshift, as discussed in the following paragraph ) is only larger than the number currently observable by a factor of 2. 36 .< ref name =" mapofuniverse "> The comoving distance of the future visibility limit is calculated on p. 8 of Gott et al.

If G is infinite, the division by | G | may not be well-defined ; in this case the following statement in cardinal arithmetic holds:

Common interpretations of Islamic architecture include the following: The concept of God or Allah's infinite power is evoked by designs with repeating themes which suggest infinity.

To illustrate his thoughts he used the following example: Suppose an object C, on which an infinite small plane zz and a sphere centered about zz is drawn.

Consider the following test case: The field f has been on for infinite time and is switched off at t = 0

In the case of " John believes everything that Mary says ", if we try to capture the content of John's beliefs, we would need to form an infinite conjunction such as the following:

The deflationist response is that the assertion that truth is a norm of assertion can be stated only in the form of the following infinite conjunction:

* For all elements x of P and all subsets S of P, the following infinite distributivity law holds:

The following sample program is to demonstrate Thue's nondeterminism ( and to show an example of an infinite loop, besides ).

dimensional factor in the following sense: it is contained in any other infinite dimensional factor, and any infinite dimensional factor contained in R is isomorphic to R.

The following table lists various thermodynamic quantities calculated in the limit of low temperature and high temperature, and in the limit of infinite particle number.

Hartman, following Georg Cantor, uses infinite cardinalities.

Also, commands that produce a potentially infinite amount of output, such as the yes command, cannot be used in a pseudo-pipeline, since they would run until the temporary disk space is exhausted, so the following processes in the pipeline could not even start to run.

Each task is an infinite loop and can be in any one of the following five states:

In mathematics, the Viète formula, named after François Viète ( 1540 – 1603 ), is the following infinite product representating the mathematical constant π:

The first book assumes that gamemasters will set their campaigns after the Patternfall war ; that is, after the end of the fifth book in the series, The Courts of Chaos, but uses material from the following books to describe those parts of Zelazny's cosmology that were featured there in more detail.

The series has retained a cult following.

The public image of rail travel was severely damaged following the series of significant accidents after privatisation.

In 1893 the same printer brought several more drawings for Weatherly ’ s Our Dear Relations, another book of rhymes, and the following year Potter successfully sold a series of frog illustrations and verses for Changing Pictures, a popular annual offered by the art publisher Ernest Nister.

Zahir-ud-din Muhammad Babur ( 14 February 148326 December 1530 ; sometimes also spelt Baber or Babar ) was a conqueror from Central Asia who, following a series of setbacks, finally succeeded in laying the basis for the Mughal dynasty in the Indian Subcontinent and became the first Mughal emperor.

This was in effect a series of two conferences: ( i ) between James and the Bishops ; ( ii ) between James and the Puritans on the following day.

The series was canceled after the following season, but leftover episodes aired as late as the next June.

The following year, in November 1963, the Plaza Theater in New York started a year-long series of Chaplin's films, including Monsieur Verdoux and Limelight, which now gained excellent reviews from American critics.

M * A * S * H would be toned down and brought to television in the following decade as a long-running series.

In 626 BC, following the death of Ashurbanipal, a series of bitter wars broke out in the Assyrian Empire over who should rule.

In 1905, President Theodore Roosevelt threatened to ban the sport following a series of player deaths from injuries suffered during games. The deaths and injuries were a result of the mass formations and gang tackling that characterized the sport in its early years.

The thirty-nine regiments of the Indian Army were reduced to twenty-one as the result of a series of amalgamations immediately following World War I.

Through a series of derivations, de Donder showed that if we consider a mixture of chemical species with the possibility of chemical reaction, it can be proven that the following relation holds:

* Trudeau was awarded the US Army ’ s Commander ’ s Award for Public Service in 2006 for his series of strips about BD ’ s recovery following the loss of his leg in Iraq.

In the 1924 national election, the Munich cultural journal Süddeutsche Monatshefte published a series of articles blaming the SPD and trade unions for Germany's defeat in World War I, which came out during the trial of Adolf Hitler and Ludendorff for high treason following the Beer Hall Putsch in 1923.

The model of decision making I am proposing has the following feature: when we are faced with an important decision, a consideration-generator whose output is to some degree undetermined produces a series of considerations, some of which may of course be immediately rejected as irrelevant by the agent ( consciously or unconsciously ).

By 1987, with Yzerman, now the captain following the departure of Danny Gare, joined by Petr Klima, Adam Oates, Gerard Gallant, defenseman Darren Veitch and new head coach Jacques Demers, the Wings won a playoff series for only the second time in the modern era.

" Munch's paintings of the following year included sketchy tavern scenes and a series of bright cityscapes in which he experimented with the pointillist style of Georges Seurat.

By 1951, 87 subroutines in the following categories were available for general use: floating point arithmetic ; arithmetic operations on complex numbers ; checking ; division ; exponentiation ; routines relating to functions ; differential equations ; special functions ; power series ; logarithms ; miscellaneous ; print and layout ; quadrature ; read ( input ); nth root ; trigonometric functions ; counting operations ( simulating repeat until loops, while loops and for loops ); vectors ; and matrices.

In mathematics, the Fibonacci numbers or Fibonacci series or Fibonacci sequence are the numbers in the following integer sequence:

They defeated the American League champion Cleveland Indians in the 1997 series, which was notable for shortstop Edgar Renteria driving in second baseman Craig Counsell for the series-clinching run in the eleventh inning of the seventh and deciding game and the " fire sale " which occurred in the off-season following the dramatic win.

Madero was arrested and a short time later assassinated along with his Vice-President, José María Pino Suárez on the 22nd of February 1913, following the series of events known as the Ten Tragic Days ( la Decena Tragica ).

* The books in Lemony Snicket's A Series of Unfortunate Events conclude with supposed letters from Snicket himself to his editor, containing a summary of his submitted manuscript for the following book in the series.

The following year the calendar was combined with that of Formula One, so the series became support races for the Grand Prix.

In 2003, a fan ( Les Braun ) published GW11 Omega Project on the internet, finishing the Third Edition series by closely following Eastland's original storyline.