**N.B.**Different disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context.

It was an exciting event in the history of mathematics when in 1890, the Italian mathematician Peano constructed a continuous curve which passed through every point in the unit square.

Examples of such `space-filling' curves were later constructed by Hilbert (in 1891),

Moore (in 1900) , Lebesgue (in 1904), Sierpinski (in 1912) and Schoenberg (in 1938) . These have come to be known as Peano curves

Hilbert curve

An interesting question: Where would you be if you started at the lower right and traveled a third of the way along his recursively defined curve?

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