Ironically, by today's standard, Gauss's own attempt is not acceptable, owing to implicit use of the Jordan curve theorem.

in light of the Jordan curve theorem and the generalized Stokes ' theorem, F < sub > γ </ sub >( z ) is independent of the particular choice of path γ, and thus F ( z ) is a well-defined function on U having F ( z < sub > 0 </ sub >)

One proof of the impossibility of finding a planar embedding of K < sub > 3, 3 </ sub > uses a case analysis involving the Jordan curve theorem, in which one examines different possibilities for the locations of the vertices with respect to the 4-cycles of the graph and shows that they are all inconsistent with a planar embedding.

Briefly, the path integral along a Jordan curve of a function holomorphic in the interior of the curve, is zero.

From the nineteenth century there is not a separate curve theory, but rather the appearance of curves as the one-dimensional aspect of projective geometry, and differential geometry ; and later topology, when for example the Jordan curve theorem was understood to lie quite deep, as well as being required in complex analysis.

* The curve is said to be simple, or a Jordan arc, if it is injective, i. e. if for all, in, we have implies.

A closed curve is thus a continuous mapping of the circle ; a simple closed curve is also called a Jordan curve.

The Jordan curve theorem states that such curves divide the plane into an " interior " and an " exterior ".

* Jordan curve theorem in topology

Some examples are the Hahn – Banach theorem, König's lemma, Brouwer fixed point theorem, Gödel's completeness theorem and Jordan curve theorem.

In particular, it is impossible to dissect a circle and make a square using pieces that could be cut with scissors ( that is, having Jordan curve boundary ).

Illustration of the Jordan curve theorem.

The Jordan curve ( drawn in black ) divides the plane into an " inside " region ( light blue ) and an " outside " region ( pink ).

In topology, a Jordan curve is a non-self-intersecting continuous loop in the plane, and another name for a Jordan curve is a simple closed curve.

The Jordan curve theorem asserts that every Jordan curve divides the plane into an " interior " region bounded by the curve and an " exterior " region containing all of the nearby and far away exterior points, so that any continuous path connecting a point of one region to a point of the other intersects with that loop somewhere.

The Jordan – Hölder theorem is a more precise way of stating this fact about finite groups.

The Jordan – Hölder theorem and the Schreier refinement theorem describe the relationships amongst all composition series of a single module.

If the group is finite, then eventually one arrives at uniquely determined simple groups by the Jordan – Hölder theorem.

This is expressed by the Jordan – Hölder theorem which states that any two composition series of a given group have the same length and the same factors, up to permutation and isomorphism.

In this context, Jordan developed his theory of measure, Cantor developed what is now called naive set theory, and Baire proved the Baire category theorem.

* Jordan – Schönflies theorem in geometric topology

* Jordan – Hölder theorem in group theory

Issai Schur showed that any finitely generated periodic group that was a subgroup of the group of invertible n x n complex matrices was finite ; he used this theorem to prove the Jordan – Schur theorem.

He is famous for many things including: Hölder's inequality, the Jordan – Hölder theorem, the theorem stating that every linearly ordered group that satisfies an Archimedean property is isomorphic to a subgroup of the additive group of real numbers, the classification of simple groups of order up to 200, and Hölder's theorem which implies that the Gamma function satisfies no algebraic differential equation.

Certainly, the meaning is clearer to one who is not familiar with Biblical teachings, in the New English Bible which reads: `` Then Jesus arrived at Jordan from Galilee, and he came to John to be baptized by him.

* 1952 – Hussein bin Talal is proclaimed King of Jordan.

* In episode 13, season 2 of 30 Rock entitled Succession Tracey Jordan says that he is Mozart and Frank is the guy who was always jealous of Mozart.

* 1987 – The London Agreement is secretly signed between Israeli Foreign Affairs Minister Shimon Peres and King Hussein of Jordan.

Other scholars, including C. C. Torrey, Kline and Jordan argue that the word is derived from the Hebrew moed (), meaning " assembly ".

Thus, " Armageddon " would mean " Mountain of Assembly ," which Jordan says is " a reference to the assembly at Mount Sinai, and to its replacement, Mount Zion.

The city is located northeast of Gaza and the Mediterranean Sea, west of Amman, Jordan, southeast of Tel Aviv, Israel and south of Jerusalem.

( God's speech foreshadows major themes of the book: the crossing of the Jordan and conquest of the land, its distribution, and the imperative need for obedience to the Law ; Joshua's own immediate obedience is seen in his speeches to the Israelite commanders and to the Transjordanian tribes, and the Transjordanians ' affirmation of Joshua's leadership echoes Yahweh's assurances of victory ).

The Israelites cross the Jordan through the miraculous intervention of God and his ark and are circumcised at Gibeath-Haaraloth ( translated as hill of foreskins ), renamed Gilgal in memory ( Gilgal sounds like Gallothi, I have removed, but is more likely to translate as circle of standing stones ).

The potential disunity of Israel is a constant theme, the greatest threat of disunity coming from the tribes east of the Jordan, and there is even a hint in chapter 22: 19 that the land across the Jordan is unclean and the tribes who live there are of secondary status.

The land east of the Jordan is divided among the tribes of Reuben, Gad, and the half-tribe of Manasseh.

" Writer June Jordan described Alston as " an American artist of first magnitude, and he is a Black American artist of undisturbed integrity.

In a few countries such as Jordan and Singapore ( see Singapore Civil Defence Force ), civil defense is essentially the same organisation as the fire brigade.

The Dead Sea (,,, " Sea of Salt ", also,, " The Sea of Death "), also called the Salt Sea, is a salt lake bordering Jordan to the east and Israel and the West Bank to the west.

It lies in the Jordan Rift Valley, and its main tributary is the Jordan River.

On " Alone Again, Natura-Diddily ", a Christian rock singer named Rachel Jordan ( played by singer-songwriter Shawn Colvin ) sings that she " was drinking like a Dartmouth boy.

Jordan is one of a small number of Arab countries to have named ambassadors to Iraq.

Brigham Young named a tributary of the Great Salt Lake the " Jordan River ".

While Ned Jordan is credited with changing the way advertising was written with his " Somewhere West of Laramie " ads for his Jordan Playboy, Reo's Flying Cloud — a name that provoked evocative images of speed and lightness — changed the way automobiles would be named in the future.

In April 1985, Nike introduced its own brand of basketball shoe which would become popular in its own right, the Air Jordan, named after the then-rookie Chicago Bulls basketball player, Michael Jordan.

In 2007, Friends of the Earth Middle East ( FoEME ) named the Jordan River as one of the world's 100 most endangered ecological sites, due in part to lack of cooperation between Israel and neighboring Arab states.

Route 90, part of which is named after Rehavam Zeevi, connects the northern and southern tips of Israel and parallels the Jordan River on the western side.

In the 1986 – 87 NBA season, Jordan continued his assault on the record books, leading the league in scoring with 37. 1 points per game and becoming the first Bull named to the All-NBA First Team.

However, for his efforts, Jordan was named NBA Most Valuable Player, an award he would win four more times over his career.

Michael Jordan would be named the league MVP for the fifth and final time, and the Bulls went into the playoffs as the number one seed in the Eastern Conference.

Jordan would be named the Finals MVP for the sixth time in his career.

Tim Duncan was named Finals MVP, becoming only the fourth player to win the MVP award three times ( joining Magic Johnson, Shaquille O ' Neal, and Michael Jordan ).

After Joe turns down several unsuitable " candidates ", Mr. Jordan takes him to see the body of a crooked, extremely wealthy banker-investor named Bruce Farnsworth.

Accompanied by Mr. Jordan, Joe finds that his replacement in the prizefight with the champ is a clean-cut, honest fighter named Murdoch, whom Joe knows and respects.

The novel is based on his experiences during the Spanish Civil War, with an American protagonist named Robert Jordan who fights with Spanish soldiers for the Republicans.

In 1619 Samuel Sharpe and Samuel Jordan from City Point, then named Charles City, were burgesses at the first meeting of the House of Burgesses.

" Marian Jordan portrayed both a lady named Marian and a little girl named Teeny, as well as playing musical accompaniment on piano.

This group included six brothers named Jordan.

Since 1956, Winn Parish has had three sheriffs named " Jordan.

It was named Alia ( or Aalya ) after King Hussein's eldest child, Princess Alia bint Al Hussein of Jordan ( born on 13 February 1956 ).

The city was named after Jordan Creek, a tributary of Owyhee River, which runs through the city ; the creek is named for a 19th century prospector, Michael M. Jordan.