Designers and manufacturers have produced models for purchasers who run the gamut from a nautical version of the elderly Pasadena lady who never drove more than five miles an hour on her once-a-month ride around the block, to the sportiest boatman who insists on all the dash, color, flair and speed possible to encompass in a single boat.

When Charlie came up from the beach for his four-o'clock pill, the whole establishment ( gaudy enough when seen through mist and fog ) looked like a floodlit modern painting -- great blocks of dizzy color, punctuated at regular intervals by the glaring white of five community refrigerators.

In 1890, in addition to exposing the flaw in Kempe's proof, Heawood proved the five color theorem and generalized the four color conjecture to surfaces of arbitrary genus — see below.

Heawood noticed Kempe's mistake and also observed that if one was satisfied with proving only five colors are needed, one could run through the above argument ( changing only that the minimal counterexample requires 6 colors ) and use Kempe chains in the degree 5 situation to prove the five color theorem.

He appeared in relatively few color films during the rest of his career, which continued for another five years.

Television viewing spread so rapidly that, by 1987, 99 percent of Japan's households had color television sets and the average family had its set on at least five hours a day.

The arrows indicate the gradients of the potential around the five Lagrange points — downhill toward them (< span style =" color: red ;"> red </ span >) or away from them (< span style =" color: blue ;"> blue </ span >).

With 47 unknown cards, the player will make the straight approximately one time for every five times he doesn't, thus a bet is profitable if six or more of his opponents will call the bet ( he will win once (< font color =" green ">+ 6 bets </ font >) and lose five times (< font color =" red ">- 5 bets </ font >) out of every six hands like this, resulting in an expectation of < font color =" green ">+ 1 bet </ font >).

Of the six players with retired numbers, five were retired for their play with the Phillies and one, 42, was universally retired by Major League Baseball when they honored the fiftieth anniversary of Jackie Robinson's breaking the color barrier.

The players aim to create five vertically, horizontally or diagonally connected stones of their color.

The extra features are integrated memory, PCMCIA, and color LCD controllers connected to an on-die system bus, and five serial I / O channels that are connected to a peripheral bus attached to the system bus.

A Plane ( mathematics ) | planar map with five colors such that no two regions with the same color meet.

After the release of Flowers and Trees, all subsequent Silly Symphony cartoons were in color while Disney was also able to negotiate a two-year deal with Technicolor, giving him the sole right to use their three-strip process, a period eventually extended to five years.

The argument above began by giving an unavoidable set of five configurations ( a single vertex with degree 1, a single vertex with degree 2, ..., a single vertex with degree 5 ) and then proceeded to show that the first 4 are reducible ; to exhibit an unavoidable set of configurations where every configuration in the set is reducible would prove the theorem.

In algebra, the Abel – Ruffini theorem ( also known as Abel's impossibility theorem ) states that there is no general algebraic solution — that is, solution in radicals — to polynomial equations of degree five or higher.

Galois theory can be used to determine which algebraic numbers can be expressed using roots, and to prove the Abel-Ruffini theorem, which states that a general polynomial equation of degree five or higher cannot be solved using roots alone ; this result is also known as " the insolubility of the quintic ".

The bipartite graphs, line graphs of bipartite graphs, and their complements form four out of the five basic classes of perfect graphs used in the proof of the strong perfect graph theorem.

However, in that paper he proved the five color theorem, saying that every planar map can be colored with no more than five colors, using ideas of Kempe.

* P. J. Heawood proves the five colour theorem.

Basic results on algebraic surfaces include the Hodge index theorem, and the division into five groups of birational equivalence classes called the classification of algebraic surfaces.

It involved setting up two intersecting right triangles ; by applying Menelaus ' theorem it was possible to solve one of the six sides, but only if the other five sides were known.

The Braikenridge – Maclaurin theorem may be applied in the Braikenridge – Maclaurin construction, which is a synthetic construction of the conic defined by five points, by varying the sixth point.

This episode includes a reference to Andrew Wiles ' proof of Fermat's Last Theorem, and is considered as a continuity repair for comments made in the Star Trek: The Next Generation episode " The Royale " ( in that 1989 episode, it is mentioned that Fermat's Last Theorem may never be solved ; Wiles would provide the final proof of the theorem five years later ).

In continuum mechanics, " Nemenyi's theorem " proves that, given any net of isothermal curves, there exists a five parameter family of plane stress systems for which these curves are stress trajectories.

The truth of the conjecture for k = 5 implies the four color theorem: for, if the conjecture is true, every graph requiring five or more colors would have a K < sub > 5 </ sub > minor and would ( by Wagner's theorem ) be nonplanar.

It has five subgroups, each of which correspond via the theorem to a subfield of K.

The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the counties of a state, the regions may be colored using no more than five colors in such a way that no two adjacent regions receive the same color.

The five color theorem is implied by the stronger four color theorem, but is considerably easier to prove.

By `` image '' is meant not only a visual presentation, but also remembered sensations of any of the five senses plus the feelings which are immediately conjoined therewith.

and, `` I do think that families are the most beautiful things in all the world '', burst out Jo some five hundred pages later in that popular story of the March family, which had first appeared when Henrietta was eight ; ;

The `` orphaned poems '' mentioned in the letter to Meynell comprised a group of five sonnets, which were published in the 1913 edition of Thompson's works under the heading `` Ad Amicam '', plus certain other completed pieces and rough drafts gathered together in one of the familiar exercise books.

Office workers frequently go out there to lunch and swim during the siesta period, which, during the summer, lasts from two until five in the afternoon, when shops and offices are again open for business.

Although the United States and the U.S.S.R. have been arguing whether there shall be four, five or six top assistants, the most important element in the situation is not the number of deputies but the manner in which these deputies are to do their work.

yet they supported the Eisenhower administration which will cost a small state like ours approximately five million dollars ( matched incidentally by a federal grant ) to initiate.

The enormous plates which had held Mr. Jack's four fried eggs and five strips of bacon were still stacked in the sink.

Certain pianistic traits are common to all five Schnabelian renditions, most notably the `` Schnabel trill '' ( which differs from the conventional trill in that the two notes are struck simultaneously ).

Now cut five Af locking bar spacers ( which run horizontally ).

One or two of the schools have a five year curriculum, but the usual pattern of American education has limited most of them to the four-year plan which seems to be the minimum in acceptable institutions.

Out of many factors which might be cited, five are most important: 1.

If it were wholly random and unrelated, it would be 2.0, assuming the five classes were equal in n, which approximately they are.

If we have five problems whose solution we seek in relatively united fashion, then there are twice as many issues which, I judge, sharply divide us, intergroup relations practitioners and lay people.

We take leave of Pumblechook as he gloats over Pip's loss of fortune, extending his hand `` with a magnificently forgiving air '' and exhibiting `` the same fat five fingers '', one of which he identifies with `` the finger of Providence '' and shakes at Pip in a canting imputation of the latter's `` ingratitoode '' and his own generosity as Pip's `` earliest benefactor ''.

If he is not told which of four or five readings was meant for him, he can more readily assess each item in a larger frame: `` Does that statement really sound as if it were for me, significant in my particular life??

They adopted a program by which Louisiana was divided into five districts.

Operating budget for the day schools in the five counties of Dallas, Harris, Bexar, Tarrant and El Paso would be $451,500, which would be a savings of $157,460 yearly after the first year's capital outlay of $88,000 was absorbed, Parkhouse told the Senate.

Instead, retailers would sign a certificate of correctness, violation of which would carry a penalty of one to five years in prison, plus a $1,000 fine.

The issue which may make it necessary to have a session is the highly sensitive problem of cutting the state's congressional districts from six to five to eliminate one congressional seat.

Leavitt, as he entered the jury room, said he was prepared to answer questions about the $12,500 his liquor firm paid to Stein for `` labor consultant work '' with five unions which organized Leavitt's workers.

Government attorneys, Leavitt said, have questioned him closely about `` five or six loans '' totaling about $40,000 which the liquor company made to Stein in the last year.

All this emphasis on Centrality and on the number 5 as a symbolic expression of the Center, which seems to have begun as far back as 400 B.C., also may conceivably have led to the development of the Five-Elements School and the subsequent efforts to fit everything into numerical categories of five.

but why did the Old Chinese postulate five elements, when the Ancient Near East -- which may have initiated the idea that natural elements exerted influence in human life and activities -- recognized only four??

What concerns him much more is the relationship of diet to the nation's No. 1 killer: coronary artery disease, which accounts for more than half of all heart fatalities and kills 500,000 Americans a year -- twice the toll from all varieties of cancer, five times the deaths from automobile accidents.

The piece is structured into five sections, which culminate in a loose ABA format.