Heliopolite Nome

The Heliopolite or Thirteenth Nome (Egyptian: Heq-At, lit. "Prospering Scepter") was a province (nome) of Ancient Egypt whose capital was Iunu (the Ptolemaic Heliopolis and modern Ayn Shams, a suburb of Cairo). It formed part of Lower Egypt.

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Nome

Nome may refer to:

See also

Nome (Egypt)

A nome (/noʊm/; from Greek: Νομός, “district”) was a subnational administrative division of ancient Egypt. Today's use of the Greek νομή, nomé rather than the Egyptian term sepat came about during the Ptolemaic period, when use of Greek was widespread in Egypt. The availability of Greek records on Egypt influenced the adoption of Greek terms by later historians.

Ancient Egypt

The division of ancient Egypt into nomes can be traced back to the Predynastic Period (before 3100 BC). These nomes originally existed as autonomous city-states, but later began to unify. According to ancient tradition, the ruler Menes completed the final unification.

Not only did the division into nomes remain in place for more than three millennia, the areas of the individual nomes and their ordering remained remarkably stable. Some, like Xois in the Delta or Khent in Upper Egypt, were first mentioned on the Palermo stone, which was inscribed in the Fifth Dynasty. The names of a few, like the nome of Bubastis, appeared no earlier than the New Kingdom. Under the system that prevailed for most of pharaonic Egypt's history, the country was divided into 42 nomes.

Nome (mathematics)

In mathematics, specifically the theory of elliptic functions, the nome is a special function and is given by

where K and iK ′ are the quarter periods, and ω₁ and ω₂ are the fundamental pair of periods. Notationally, the quarter periods K and iK ′ are usually used only in the context of the Jacobian elliptic functions, whereas the half-periods ω₁ and ω₂ are usually used only in the context of Weierstrass elliptic functions. Some authors, notably Apostol, use ω₁ and ω₂ to denote whole periods rather than half-periods.

The nome is frequently used as a value with which elliptic functions and modular forms can be described; on the other hand, it can also be thought of as function, because the quarter periods are functions of the elliptic modulus. This ambiguity occurs because for real values of the elliptic modulus, the quarter periods and thus the nome are uniquely determined.

The function τ = iK ′/K = ω₁/ω₂ is sometimes called the half-period ratio because it is the ratio of the two half-periods ω₁ and ω₂ of an elliptic function.