One of the next milestones came in 1904, when Helge von Koch, extending ideas of Poincaré and dissatisfied with Weierstrass's abstract and analytic definition, gave a more geometric definition including hand drawn images of a similar function, which is now called the Koch curve ( see Figure 2 ).

:* Iterated function systems – use fixed geometric replacement rules ; may be stochastic or deterministic ; e. g., Koch snowflake, Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Harter-Heighway dragon curve, T-Square, Menger sponge

A Koch curve has an infinitely repeating self-similarity when it is magnified.

The Koch curve

The Koch snowflake ( also known as the Koch star and Koch island ) is a mathematical curve and one of the earliest fractal curves to have been described.

It is based on the Koch curve, which appeared in a 1904 paper titled " On a continuous curve without tangents, constructible from elementary geometry " ( original French title: Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire ) by the Swedish mathematician Helge von Koch.

The Koch curve has an infinite length because each time the steps above are performed on each line segment of the figure there are four times as many line segments, the length of each being one-third the length of the segments in the previous stage.

The Koch curve is continuous everywhere but differentiable nowhere.

the resulting curve converges to the Koch snowflake.

Following von Koch's concept, several variants of the Koch curve were designed, considering right angles ( quadratic ), other angles ( Césaro ) or circles and their extensions to higher dimensions ( Sphereflake ):

* Fractals derived from standard geometry by using iterative transformations on an initial common figure like a straight line ( the Cantor dust or the von Koch curve ), a triangle ( the Sierpinski triangle ), or a cube ( the Menger sponge ).

The image of simple plane curve can have Hausdorff dimension bigger than one ( see Koch snowflake ) and even positive Lebesgue measure ( the last example can be obtained by small variation of the Peano curve construction ).

He described the Koch curve in a 1904 paper entitled " On a continuous curve without tangents constructible from elementary geometry " ( original French title: " Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire ").

It has a topological dimension of 1, but it is by no means a rectifiable curve: the length of the curve between any two points on the Koch Snowflake is infinite.

John T. Koch has suggested that this Jovian epithet may originally have applied to Taranis, with allusion to the tendency of thunder near an observer to seem all-surrounding.

The screenplay by Howard Koch is based on the 1927 play of the same name by W. Somerset Maugham, originally filmed in 1929.

Flint Hill Resources LP, originally called Koch Petroleum Group, is a major refining and chemicals company based in Wichita, Kansas.

His recordings of the music of Stravinsky with the Orchestra of St. Luke's were originally available on eleven now out-of-print releases from MusicMasters and seven volumes from Koch.

* Koch people ( or Koche ), an ethnic group originally from the ancient Koch kingdom in north east India

" Although 100 Wayz was expected for release that year, it was postponed due to a dispute with Koch Records head Alan Grunblatt ; instead, they released the album That Was Then, This is Now, which included the singles originally intended for 100 Wayz, in late 2009.

Hobbes originally had a Heckler & Koch P7 pistol in the Pilot episode before moving onto the SIG Sauer P226 pistol and then onto the Walther P99.

They were originally reported as speaking their original Koch language, but on an examination of the specimens of the language, Dr. Grierson found that they have given up their original speech, and now only speak more or less corrupt variety of Northern Bengali.

Antibiosis was first described in 1877 in bacteria when Louis Pasteur and Robert Koch observed that an airborne bacillus could inhibit the growth of Bacillus anthracis.

It was first described by Robert Koch in 1890.

She was once described in the early 1990s by the New York Times as “ Ed Koch in a stretchy black dress ”.

Niels Fabian Helge von Koch ( Stockholm, January 25, 1870 – ibidem, March 11, 1924 ) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake, one of the earliest fractal curves to be described.

* Helge von Koch describes the " Koch snowflake ", one of the earliest fractal curves described.

In fact, Schneider's mixing of the medical and the moral has been described as the most noteworthy aspect of this work, which has been linked back to German reception of Cesare Lombroso's theory of the ' born criminal ', redefined by Emil Kraepelin and others ( see also Koch ) in to psychiatric terms as a ' moral defect '.

M. tuberculosis, then known as the " tubercle bacillus ", was first described on 24 March 1882 by Robert Koch, who subsequently received the Nobel Prize in physiology or medicine for this discovery in 1905 ; the bacterium is also known as " Koch's bacillus ".

Koch described poems “ Written by the men with their eyes on the myth / And the missus and the midterms …” He attacked the idea that poetry should be in any way stale.

In 1992, former Mayor Ed Koch, his previous opponent in 1963 and 1965, whom he now befriended and met with on occasions, described him with these observations:

It was first described by Robert Koch in 1890.

In mathematics, the Lévy C curve is a self-similar fractal that was first described and whose differentiability properties were analysed by Ernesto Cesàro in 1906 and G. Farber in 1910, but now bears the name of French mathematician Paul Pierre Lévy, who was the first to describe its self-similarity properties, as well as to provide a geometrical construction showing it as a representative curve in the same class as the Koch curve.

Koch, who had been mayor of New York while Ravitch ran the M. T. A., called that description " foolish " and described Ravitch as a " Renaissance man ".

Karl Koch described the song as being “ slow but huge, rocking .” " Who You Callin ' Bitch?

The TV series emphasizes the boisterous nature of the team, led by manager Billy Martin, catcher Thurman Munson and outfielder Reggie Jackson, as well as the malaise of the Bronx and New York City in general during that time, such as the blackout, the city's serious financial woes and near bankruptcy, the arson for insurance payments, and the election of Ed Koch as mayor.

Kits exist which will convert many pistols into carbines by the addition of a shoulder stock ; notable examples are the long barrelled Colt Buntline revolver stock, the Mauser C96 " Broomhandle " holster / stock, and various others for models such as the Browning Hi-Power, Luger, Colt M1911, and the Heckler & Koch VP70.

One critic states of psychologists that " Instead of replacing ' metaphysical ' terms such as ' desire ' and ' purpose ', they used it to legitimize them by giving them operational definitions ... the initial, quite radical operationalist ideas eventually came to serve as little more than a ' reassurance fetish ' ( Koch 1992 ) for mainstream methodological practice.

* A typeface created by Rudolf Koch

The concept of ' psychopathic inferiorities ' had been recently popularised in Germany by Julius Ludwig August Koch, who proposed congenital and acquired types.

They were assisted in some algorithmic work by John A. Koch.

The MP5 is actually designated as a " machine pistol " by Heckler & Koch ( MP5 stands for Maschinenpistole 5, or Machine Pistol 5 ), although some reserve this designation for even smaller submachine guns such as the MAC-10 and Glock 18, which are about the size and shape of pistols.

The Tartessian language from the southwest of the Iberian peninsula, written in a version of the Phoenician script in use around 825 BC, which John T. Koch has claimed to be able to readily translate, has been accepted by a number of philologists and other linguists as the first attested Celtic language, but the linguistic mainstream continues to treat Tartessian as an unclassified ( Pre-Indo-European?

A hagiographic account of Koch's career can be found in the 1939 Nazi propaganda film Robert Koch, der Bekämpfer des Todes ( The fighter against death ), directed by Hans Steinhoff and starring Emil Jannings as Koch.

Because the construction efforts on Veliki Brijun Island were jeopardized by malaria outbreaks which occurred during summer months, and even Austrian steel industrialist Paul Kupelweiser himself fell ill with the disease, at the turn of the century Kupelweiser invited in Koch, who at the time was studying different forms of malaria and quinine-based treatments.

* Musoptin. com, microscope objectives: as they were used by Robert Koch for his first photos of microorganisms ( 1877 – 1878 )

HK was founded by engineers Edmund Heckler, Theodor Koch, and Alex Seidel in 1949 from the remnants of the Mauser company ; the company was registered in 1950.

One way of proving that a given disease is " infectious ", is to satisfy Koch's postulates ( first proposed by Robert Koch ), which demands that the infectious agent be identified only in patients and not in healthy controls, and that patients who contract the agent also develop the disease.

* 1951 – Ilse Koch, " The Witch of Buchenwald ", wife of the commandant of the Buchenwald concentration camp, is sentenced to life imprisonment by a court in West Germany.

2002's Still Up In This Shit !, released by Hit-A-Lick / Koch Records, featured more Latin rap style and G-Funk tracks as well as a hidden bonus rock track titled " Cannabis ".

:* Guinea pig ( Cavia porcellus )-used by Robert Koch and other early bacteriologists as a host for bacterial infections, hence a byword for " laboratory animal " even though less commonly used today

* A typeface created by Rudolf Koch

The Heckler & Koch HK416 has been in use by Delta Force since 2004.

A 1970 HK VP70M 18-round Semi-automatic firearm | semi-automatic / three-round automatic burst-capable pistol manufactured by German arms firm Heckler & Koch

It is a 9 mm, 18-round, double action only, semi-automatic / three-round burst capable polymer frame pistol manufactured by German arms firm Heckler & Koch GmbH ; the VP designation stands for Volkspistole (" The people's pistol "), and the designation 70 was for the year of the first edition: 1970.

Koch found that he could transmit anthrax from one animal to another by taking a small sample of blood from the infected animal and injecting it into a healthy one, and this caused the healthy animal to become sick.

The Heckler & Koch G3 battle rifles used were considered by several experts to be inadequate for the distance at which the snipers were trying to shoot.

One type of broad usage would later be narrowed down by Koch in 1891 to the ' psychopathic inferiorities ' - later renamed abnormal personalities by Schneider.