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Peano's famous space-filling curve appeared in 1890 as a counterexample.WikiMatrix WikiMatrix
Because Giuseppe Peano (1858–1932) was the first to discover one, space-filling curves in the 2-dimensional plane are sometimes called Peano curves, but that phrase also refers to the Peano curve, the specific example of a space-filling curve found by Peano.WikiMatrix WikiMatrix
The designs are either generalized Peano curves, or based on a new space-filling construction technique.WikiMatrix WikiMatrix
The first modern and more precise definition of a vector space was introduced by Peano in 1888; by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged.WikiMatrix WikiMatrix
The second result was proved by Cantor in 1878, but only became intuitively apparent in 1890, when Giuseppe Peano introduced the space-filling curves, curved lines that twist and turn enough to fill the whole of any square, or cube, or hypercube, or finite-dimensional space.WikiMatrix WikiMatrix
Either the power-transmitting element (np) or the power-receiving element (ns) comprises a conductor that has the shape of a Peano curve, a space-filling curve, which covers a plane, said plane having breadth, by passing through, without intersecting itself, each region into which said plane is partitioned.patents-wipo patents-wipo
L-systems on the real line R: Prouhet-Thue-Morse system Well-known L-systems on a plane R2 are: space-filling curves (Hilbert curve, Peano's curves, Dekking's church, kolams), median space-filling curves (Lévy C curve, Harter-Heighway dragon curve, Davis-Knuth terdragon), tilings (sphinx tiling, Penrose tiling), trees, plants, and the like.WikiMatrix WikiMatrix
Mandelbrot shows how to calculate the Hausdorff dimension of each of these curves, each of which has a dimension D between 1 and 2 (he also mentions but does not give a construction for the space-filling Peano curve, which has a dimension exactly 2).WikiMatrix WikiMatrix
Peano was the first to give the modern definition of vector spaces and linear maps in 1888.WikiMatrix WikiMatrix
The modern, more abstract treatment, first formulated by Giuseppe Peano in 1888, encompasses more general objects than Euclidean space, but much of the theory can be seen as an extension of classical geometric ideas like lines, planes and their higher-dimensional analogs.WikiMatrix WikiMatrix
Peano's continuous space-filling curves cannot be 1-1 of course, otherwise Netto 's theorem would be contradicted.ParaCrawl Corpus ParaCrawl Corpus
Odd indeed they were, there were curves - one dimensional lines in effect - which filled two dimensional spaces, there were curves which were well behaved, that is nice and continuous but which had no slope at any point (Not just some points, ANY points) and they went by strange names, the Peano Space filling curve, the Sierpinski gasket, the Koch curve, the Cantor Ternary set.ParaCrawl Corpus ParaCrawl Corpus
The first modern and more precise definition of a vector space was introduced by Peano in 1888;[5] by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged.ParaCrawl Corpus ParaCrawl Corpus
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