Hence, the total length increases by one third and thus the length at step n will be ( 4 / 3 )< sup > n </ sup > of the original triangle perimeter: the fractal dimension is log 4 / log 3 ≈ 1. 26, greater than the dimension of a line ( 1 ) but less than Peano's space-filling curve ( 2 ).

Therefore, Peano's space-filling curve was found to be highly counterintuitive.

The analytic form of the Hilbert curve, however, is more complicated than Peano's.

In this, Hilbert was anticipated by Peano's work from 1889.

The general first-order theory of the natural numbers expressed in Peano's axioms cannot be decided with such an algorithm, however.

This became one of Peano's main philosophical interests for the rest of his life.

Russell was so struck by Peano's innovative logical symbols that he left the conference and returned home to study Peano's text.

Peano's students Mario Pieri and Alessandro Padoa had a papers presented at the philosophy congress also.

Having previously created Idiom Neutral, the Academy effectively chose to abandon it in favor of Peano's Latino sine flexione.

* Euclidean geometry, under Peano's axiom system the primitive notions are point, segment and motion.

Peano's original formulation of the axioms used 1 instead of 0 as the " first " natural number.

Peano's ground-breaking paper contained no illustrations of his construction, which is defined in terms of ternary expansions and a mirroring operator.

Peano's paper also ends by observing that the technique can be obviously extended to other odd bases besides base 3.

A year later, David Hilbert published in the same journal a variation of Peano's construction.

The Academia pro Interlingua was an organization dedicated to the promotion of international auxiliary languages, and is associated in particular with Prof. Giuseppe Peano's language Latino sine flexione ( Latin without inflections ).

When the Akademi effectively chose to abandon Idiom Neutral in favor of Latino sine flexione in 1908, it elected Peano as its director, and the name of the group was changed to Academia pro Interlingua since Interlingua was an alternative name for Peano's language.

By advocating an artificial international language, constructed along logical principles and with a vocabulary taken from existing European languages, Couturat was paralleling Peano's advocacy of Interlingua.

This sense of definition allowed Poincaré to argue with Bertrand Russell over Giuseppe Peano's axiomatic theory of natural numbers.

Since Peano's axiom is as infinite as the natural numbers, it is difficult to prove that the property of P does belong to any x and also x + 1.

From this Poincaré argues that if we fail to establish the consistency of Peano's axioms for natural numbers without falling into circularity, then the principle of complete induction is not provable by general logic.

To an intuitionist this seems to rank the law of excluded middle as just as unrigorous as Peano's vicious circle.

* Peano's dismissal of Veronese ' work.

Moreover, the title and language varied: the first three, titled Formulaire de Mathématiques, and the fourth, titled, Formulaire Mathématique, were written in French, while Latino sine flexione, Peano's own invention, was used for the fifth edition, titled Formulario Mathematico.

First, arguably his most famous finding, the forgetting curve.

Henri Léon Lebesgue ForMemRS (; June 28, 1875 – July 26, 1941 ) was a French mathematician most famous for his theory of integration, which was a generalization of the 17th century concept of integration — summing the area between an axis and the curve of a function defined for that axis.

The curva Bulgarelli ( in English, Bulgarelli curve ), the curve of Bologna's ultras, is dedicated to the famous football player Giacomo Bulgarelli, recently deceased ( 21 February 2009 ).

Wanniski was instrumental in popularizing the ideas of lower tax rates embodied in the " Laffer Curve ," and was present in 1974 when Arthur Laffer drew the curve on the famous napkin for Dick Cheney and Donald Rumsfeld.

In 1748, Maria Agnesi published her famous summation treatise Instituzioni analitiche ad uso della gioventù italiana, in which the curve was named according to Grandi, ' versiera '.

In the same preface is included ( a ) the famous problem known by Pappus's name, often enunciated thus: Having given a number of straight lines, to find the geometric locus of a point such that the lengths of the perpendiculars upon, or ( more generally ) the lines drawn from it obliquely at given inclinations to, the given lines satisfy the condition that the product of certain of them may bear a constant ratio to the product of the remaining ones ; ( Pappus does not express it in this form but by means of composition of ratios, saying that if the ratio is given which is compounded of the ratios of pairs one of one set and one of another of the lines so drawn, and of the ratio of the odd one, if any, to a given straight line, the point will lie on a curve given in position ); ( b ) the theorems which were rediscovered by and named after Paul Guldin, but appear to have been discovered by Pappus himself.

He developed utility theory, introducing the indifference curve and the famous Edgeworth box, which is now familiar to undergraduate students of microeconomics.

T. P. Wright is famous for the discussion of the learning curve in aircraft industry.

The most famous practitioners of this type of knuckle curve are Burt ' Happy ' Hooton, who pitched for the Chicago Cubs and the Los Angeles Dodgers from the mid 1970s to mid 1980s, and current Los Angeles Angels of Anaheim reliever Jason Isringhausen.

Ernst Engel ( March 26, 1821 – December 8, 1896 ) was a German statistician and economist, famous for the Engel curve and the Engel's law.

He is most famous for his legendary ability to score from corner kicks and his ability to curve the ball and place it wherever he pleased ; his immense fame gained from this led him to take over as a coach for Dynamo Kiev.

Well known to many now is the famous Growth-Share Matrix (' cash cow ') and the ' Experience curve '.

In symmetric unimodal distributions, such as the normal ( or Gaussian ) distribution ( the distribution whose density function, when graphed, gives the famous " bell curve "), the mean ( if defined ), median and mode all coincide.

The Chain of Rocks Bridge was famous for having a curve in the middle.

Bet Lynch ( Julie Goodyear ) first appeared in 1966, before becoming a regular in 1970, and went on to become one of the most famous Corrie characters.

White's dachshund, appeared in many of his famous essays.

One of his own famous contributions to this journal also appeared in the form of a monograph ( 105 p .) entitled Über Sprachstörungen im Traume ( on language disturbances in dreams ).

Ekman's most famous work revolved around the finding that certain emotions appeared to be universally recognized, even in cultures that were preliterate and could not have learned associations for facial expressions through media.

That same year, Hackman appeared in what became one of his most famous comedic roles as the blind hermit in Young Frankenstein.

Aasen's famous Dictionary of the Norwegian Dialects appeared in its original form in 1850, and from this publication dates all the wide cultivation of the popular language in Norwegian, since Aasen really did no less than construct, out of the different materials at his disposal, a popular language or definite folke-maal ( people's language ) for Norway.

It was not until 1567 that the first portrait of Gutenberg, almost certainly an imaginary reconstruction, appeared in Heinrich Pantaleon's biography of famous Germans.

Modern ideas in art appeared in commercials and logos, the famous London Underground logo, designed by Edward Johnston in 1919, being an early example of the need for clear, easily recognizable and memorable visual symbols.

Palin appeared in some of the most famous Python sketches, including " Argument Clinic ," " Dead Parrot ," " The Lumberjack Song ," " The Spanish Inquisition ," and " The Fish-Slapping Dance.

Hare's famous original work Machinery of Representation appeared in 1857 ( in two editions ) and many editions of his equally famous Treatise on the Election of Representatives: Parliamentary and Municipal appeared between 1859 and 1873.

An oft-repeated story about Grace is that, in 1896, the Australian pace bowler Ernie Jones bowled a short-pitched delivery so close to his face that it appeared to go through the famous beard which made him so instantly recognisable.

They also appeared in a cameo as firemen ( the role that helped make them famous in Soup to Nuts ) in the film It's a Mad, Mad, Mad, Mad World.

The following year, he appeared in arguably his most famous and acclaimed role as the eccentric, violent, yet sympathetic anti-hero replicant Roy Batty in Ridley Scott's 1982 science fiction thriller, Blade Runner — in which role Hauer improvised the oft-quoted tears in rain soliloquy.

Enfield appeared in some television commercials before becoming famous, including one made in 1987 for Heineken.

In Britain, Jade Goody became famous after appearing on Big Brother 3 in 2002 ; she later appeared on other reality programs, wrote a bestselling autobiography and launched a top-selling perfume line.

Several socialites, or children of famous parents, who were somewhat well-known before they appeared on reality television shows have become much more famous as a result, including Paris Hilton, Nicole Richie, Kelly Osbourne, Kim Kardashian, and many of the rest of the Kardashian family.

This is his most famous work, and was the ablest statement and defense of the principle of absolute liberty of conscience that had appeared in any language.

He is famous for playing mobsters, including Michael Corleone in The Godfather trilogy and Tony Montana in Scarface, though he has also appeared several times on the other side of the law — as a police officer, a detective and a lawyer.

In the 20th century, in the last apparition of the Blessed Virgin Mary in Fátima, Portugal, Sister Lúcia, one of the most famous visionaries of Our Lady, said that the Virgin appeared to her as Our Lady of Mount Carmel ( holding the Brown Scapular ).

His most famous phrase was used as the title for the sports quiz programme They Think It's All Over, on which he once appeared as a guest.