While at university, Gauss independently rediscovered several important theorems ; his breakthrough occurred in 1796 when he showed that any regular polygon with a number of sides which is a Fermat prime ( and, consequently, those polygons with any number of sides which is the product of distinct Fermat primes and a power of 2 ) can be constructed by compass and straightedge.

While the compass is the primary instrument used to determine one's heading, pilots will usually refer instead to the direction indicator ( DI ), a gyroscopically driven device which is much more stable than a compass.

" While in another comment he stated " On Have a Nice Day, you heard a band that has lost its compass.

While the compass, like any other compass, points north, the direction of prayer is indicated by marks on the perimeter of the dial, corresponding to different cities, or by a second pointer set by the user according to their own location.

While this compass brought the kingdom much prosperity, it was soon abused.

" In a word, the man is everywhere independent, sincere, with sure vision, a decisive note that can sometimes be a little brutal .... While being perfectly healthy he has the neurosis of truthfulness .... The man who has measured with a compass the buttons on a uniform from the time of Frederick, when it is a matter of depicting a modern shoe, waistcoat, or coiffure, does not make them by approximations but totally, in their absolute form and without smallness of means.

While Burt invented the typographer, he is better known for his solar compass.

While the mechanism is not fully understood, it is likely to involve the production of electron – positron pairs, as ordinary matter gains tremendous energy while falling into a stellar remnant .< ref >

While the mechanism is unclear, it appears a local immune reaction is mounted against the tumor.

While the detailed particle physics mechanism responsible for inflation is not known, the basic picture makes a number of predictions that have been confirmed by observation.

While the reliability of this mechanism has not yet been studied for all relevant crop species, recent results in tobacco plants are promising, showing a failed containment rate of transplastomic plants at 3 in 1, 000, 000.

While earlier versions of BIND offered no mechanism to store and retrieve zone data in anything other than flat text files, in 2007 BIND 9. 4 DLZ made available ( as a compile-time option ) zone storage in a variety of database formats including LDAP, Berkeley DB, PostgreSQL, MySQL, and ODBC.

While most MOOs are run by administrative fiat, in summer of 1993 LambdaMOO implemented a petition / ballot mechanism, allowing the community to propose and vote on new policies and other administrative actions.

While the details of the mechanism are uncertain, the stereochemical retention is achieved through a double displacement reaction.

While changes to the chromosome caused by X-ray and mustard gas were readily observable to the early researchers, other changes to the DNA induced by other mutagens were not so easily observable, and the mechanism may be complex and takes longer to unravel.

While the association between serum blood levels of beta-cryptoxanthin and substantially decreased joint disease has been established, neither a convincing mechanism for such protection nor a cause-and-effect have been rigorously studied.

While the consequences of this for the reaction mechanism of chromatin remodeling are not known, the dynamic nature of the system may allow it to respond faster to external stimuli.

While in many lasers the laser process involves the transition of atoms between different electronic energy states, as described in the model above, this is not the only mechanism that can result in laser action.

While Darwin had been criticised for simply accepting female whims as given, Ronald Fisher grasped the underlying mechanism in The Genetical Theory of Natural Selection, in a remark that was not widely understood for another 50 years:

While this study offers a nice way to see the evolution from immature to mature VF, it still does not explain what is the mechanism behind it.

While the complete mechanism of catalase is not currently known, the reaction is believed to occur in two stages:

While the existence of files on a machine does not classify it as a server, the mechanism which shares these files to clients by the operating system is the server.

While the mechanism that causes teratogenicity has been established, the mechanism for therapeutic effects remains unclear.

While they may be blind, they are very efficient hunters with this infrared sensing mechanism, although they can not sense unmoving prey.

While a direct tax should send a clear signal to the consumer, its use as an efficient mechanism to influence consumers ' fuel use has been challenged in some areas:

While a number of insects use frictional vibration mechanisms to generate sound, this particular acoustic mechanism is unique in the animal kingdom.

While he did not coin the specific term, Coase indeed discussed " costs of using the price mechanism " in his 1937 paper The Nature of the Firm, where he first discusses the concept of transaction costs, and refers to the " Costs of Market Transactions " in his seminal work, The Problem of Social Cost ( 1960 ).

While there are many minor differences between manufacturers a player piano is a piano that contains a manually controlled pneumatically operating piano player mechanism.

While shock formation by this process does not normally happen to sound waves in Earth's atmosphere, it is thought to be one mechanism by which the solar chromosphere and corona are heated, via waves that propagate up from the solar interior.

While the precise mechanism of action is still poorly understood, there is evidence that application of gel sheeting may reduce the incidence of abnormal scarring.

While the Chassepot's ballistic performance and firing rates were excellent for the time, burnt paper residues as well as black powder fouling accumulated in the chamber and bolt mechanism after continuous firing.

While ATP appears to be necessary for the occurrence of contraction, its presence and enzymatic hydrolysis of it by the muscle protein myosin are not the only criteria for contraction.

While many Chadians may share that assessment, the uprising appears to be a power struggle within the elite that has long controlled Chad.

While the early, hot universe appears to be well explained by the Big Bang from roughly 10 < sup >− 33 </ sup > seconds onwards, there are several problems.

While the General and Laura are left alone in the ruined chapel, Carmilla appears.

While Duck Hunt does not have a traditional multiplayer mode, the manual states that a second player may plug in a standard NES controller in the other controller port and control the duck that appears.

While the dragon has often served as China's national emblem, internationally the panda appears at least as commonly.

While conceding he is sometimes good, the authors claim Burton's " occasional triumphs only serve to highlight the pathetic waste in most of his films ; for every Equus in which he appears there are at least a half-dozen Cleopatras or Boom! s.

While the first reference to " guising " in North America occurs in 1911, another reference to ritual begging on Halloween appears, place unknown, in 1915, with a third reference in Chicago in 1920.

While some tenets of hacker ethic were described in other texts like Computer Lib / Dream Machines ( 1974 ) by Theodor Nelson, Levy appears to have been the first to document both the philosophy and the founders of the philosophy.

While the term " impi " has become synonymous with the Zulu nation in international popular culture, it appears in various video games such as Civilization III, Civilization IV: Warlords and Civilization: Revolution, where the Impi is the unique unit for the Zulu faction with Shaka as their leader and also as an appearance as unique unit of the Bantu nation in Rise of Nation ( Zulus are among many tribes who make up the Bantu people ).

While on the surface it appears the broker represents the buyer ( not the insurance company ), and typically counsels the buyer on appropriate coverage and policy limitations, in the vast majority of cases a broker's compensation comes in the form of a commission as a percentage of the insurance premium, creating a conflict of interest in that the broker's financial interest is tilted towards encouraging an insured to purchase more insurance than might be necessary at a higher price.

While Coster appears to have experimented with moulds and castable metal type, there is no evidence that he had actually printed anything with this technology.

While the cow is in the care of Mac Cinnfhaelaidh's brother Mac Samthainn, Balor appears in the form of a little red-haired boy and tricks him into giving him the cow.

While " absolute discretion " appears to leave some freedom for manoeuvre for a president in deciding whether to initiate contact with the opposition, " own counsel " has been interpreted by some lawyers as suggesting that no contact whatsoever can take place.

While the name Sigyn is found as a female personal name in Old Norse sources ( Old Norse sigr meaning " victory " and vina meaning " girl-friend "), and though in surviving sources she is largely restricted to a single role, she appears in the 9th century Haustlöng from pagan times, written by the skald Þjóðólfr of Hvinir.

" While it is clear that the Cryptic Corporation has chosen to share this information publicly, no further confirmation — nor any context as to the roles of " Chuck " and " Bob " in the group, or if these names are, indeed, the names of the group's members — appears to have been issued to date.

While the first reference to " guising " in North America occurs in 1911, another reference to ritual begging on Halloween appears, place unknown, in 1915, with a third reference in Chicago in 1920.

; Programming style: While typos in the program code are often caught by the compiler, a bug usually appears when the programmer makes a logic error.

While the name sometimes appears in the forms WINE and wine, the project developers have agreed to standardize on the form Wine.

While clarifying the concept of world has arguably always been among the basic tasks of Western philosophy, this theme appears to have been raised explicitly only at the start of the twentieth century and has been the subject of continuous debate.

While the amendment did not become law, a version of it appears in the Conference Report as an explanatory text about the legislative history and purposes of the bill.

While it thus appears that System A preceded System B, both systems remained in use at least until the 1st century BC.

While Daffy's greed and jealousy of Bugs remains, it appears to be less antagonistic in this show.

While so-called ' pitched ' brick vaulting, which could be constructed without centering, may date back in the Ancient Near East to the 2nd millennium BC, the earliest evidence of the pointed masonry arch appears in late Roman and Sassanian architecture, mostly evidenced in early church building in Syria and Mesopotamia, but occasionally also in secular structures like the Karamagara Bridge.