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词汇 Menger sponge
分类 英语词汇 英语翻译词典
释义

Menger sponge

中文百科

门格海绵

门格海绵
An illustration of M4, the sponge after four iterations of the construction process.
A sculptural representation of iterations 0 (bottom) to 3 (top).

门格海绵是分形的一种。它是一个通用曲线，因为它的拓扑维数为一，且任何其它曲线或图都与门格海绵的某个子集同胚。它有时称为门格-谢尔宾斯基海绵或谢尔宾斯基海绵。它是康托尔集和谢尔宾斯基地毯在三维空间的推广。它首先由奥地利数学家卡尔·门格在1926年描述，当时他正在研究拓扑维数的概念。

英语百科

Menger sponge 门格海绵

An illustration of M4, the sponge after four iterations of the construction process.
A sculptural representation of iterations 0 (bottom) to 3 (top).
An illustration of the iterative construction of a Menger sponge up to M3, the third iteration.
Menger sponge animation through (4) recursion steps.

In mathematics, the Menger sponge (also known as the Menger universal curve) is a fractal curve. It is a three-dimensional generalization of the Cantor set and Sierpinski carpet, though it is slightly different from a Sierpinski sponge. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.
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