Last Updated：2025/11/24

(mathematical analysis) a curve whose range contains the entire 2-dimensional unit square (or the 3-dimensional unit cube)

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space-filling curve

Source Word

space-filling curve

(mathematical analysis) a curve whose range contains the entire 2-dimensional unit square (or the 3-dimensional unit cube)

Japanese Meaning

数学解析の分野で用いられる概念。1次元の区間から定義された曲線が、その値域として2次元の単位正方形や3次元の単位立方体全体を埋め尽くすものを指す。

The mathematician demonstrated how a space-filling curve can pass arbitrarily close to every point in the unit square.

数学者は、像が単位正方形全体を含む充填曲線が、その正方形内のすべての点に任意に近づけることを示した。

Sense（1）

(mathematical analysis) a curve whose range contains the entire 2-dimensional unit square (or the 3-dimensional unit cube)

From space-filling curves it can be deduced that ℝ² and ℝ³ have the same cardinality as ℝ.

space-filling curves

（ plural ）