United States
Main article: Republicanism in the United States
A distinct set of definitions for the word republic evolved in the United States. In common parlance a republic is a state that does not practice direct democracy but rather has a government indirectly controlled by the people. This understanding of the term was originally developed by James Madison, and notably employed in Federalist Paper No. 10. This meaning was widely adopted early in the history of the United States, including in Noah Webster's dictionary of 1828. It was a novel meaning to the term; representative democracy was not an idea mentioned by Machiavelli and did not exist in the classical republics.[44] Also, there is evidence that contemporaries of Madison considered the meaning of the word to reflect the definition found elsewhere, as is the case with a quotation of Benjamin Franklin taken from the notes of James McHenry. Where the question is put forth, "a Republic or a Monarchy?"[45]
The term republic does not appear in the Declaration of Independence, but does appear in Article IV of the Constitution which "guarantee to every State in this Union a Republican form of Government." What exactly the writers of the constitution felt this should mean is uncertain. The Supreme Court, in Luther v. Borden (1849), declared that the definition of republic was a "political question" in which it would not intervene. In two later cases, it did establish a basic definition. In United States v. Cruikshank (1875), the court ruled that the "equal rights of citizens" were inherent to the idea of a republic.
However, the term republic is not synonymous with the republican form. The republican form is defined as one in which the powers of sovereignty are vested in the people and are exercised by the people, either directly, or through representatives chosen by the people, to whom those powers are specially delegated. In re Duncan, 139 U.S. 449, 11 S.Ct. 573, 35 L.Ed. 219; Minor v. Happersett, 88 U.S. (21 Wall.) 162, 22 L.Ed. 627. [46]
Beyond these basic definitions the word republic has a number of other connotations. W. Paul Adams observes that republic is most often used in the United States as a synonym for state or government, but with more positive connotations than either of those terms.[47] Republicanism is often referred to as the founding ideology of the United States. Traditionally scholars believed this American republicanism was a derivation of the liberal ideologies of John Locke and others developed in Europe.
A political philosophy of republicanism that formed during the Renaissance period, and initiated by Machiavelli, was thought to have had little impact on the founders of the United States. In the 1960s and 1970s a revisionist school[citation needed] led by the likes of Bernard Bailyn began to argue that republicanism was just as or even more important than liberalism in the creation of the United States.[48] This issue is still much disputed and scholars like Isaac Kramnick completely reject this view.[49]
(double check the link you posted, the United States is NOT included in the list of Federal Republics until AFTER 2009 when Obama became President). 
