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* 一般来说，无量纲量是标度不变量。统计学中的类似概念是'''Standardized Moments 标准化矩'''，它是变量的标度不变统计量，而非标准化矩不是。

* 一般来说，无量纲量是标度不变量。统计学中的类似概念是'''Standardized Moments 标准化矩'''，它是变量的标度不变统计量，而非标准化矩不是。

==Scale-invariant curves and self-similarity==

==Scale-invariant curves and self-similarity 标度不变曲线与自相似性==

In mathematics, one can consider the scaling properties of a [[function (mathematics)|function]] or [[curve]] {{math|''f'' (''x'')}} under rescalings of the variable {{mvar|x}}.  That is, one is interested in the shape of {{math|''f'' (''λx'')}} for some scale factor {{mvar|λ}}, which can be taken to be a length or size rescaling. The requirement for  {{math|''f'' (''x'')}} to be invariant under all rescalings is usually taken to be

In mathematics, one can consider the scaling properties of a [[function (mathematics)|function]] or [[curve]] {{math|''f'' (''x'')}} under rescalings of the variable {{mvar|x}}.  That is, one is interested in the shape of {{math|''f'' (''λx'')}} for some scale factor {{mvar|λ}}, which can be taken to be a length or size rescaling. The requirement for  {{math|''f'' (''x'')}} to be invariant under all rescalings is usually taken to be

:<math>f(\lambda x)=\lambda^{\Delta}f(x)</math>

:<math>f(\lambda x)=\lambda^{\Delta}f(x)</math>

for some choice of exponent , and for all dilations . This is equivalent to     being a homogeneous function of degree .

for some choice of exponent , and for all dilations . This is equivalent to     being a homogeneous function of degree .

在数学中，我们可以考虑函数或曲线在变量重新标度下的标度性质。也就是说，人们对某些比例因子的形状感兴趣，这些比例因子可以被视为长度或大小的重新标度。对于指数的某种选择和所有的膨胀，在所有重新调整下保持不变的要求通常被认为是: f (lambda x) = lambda ^ { Delta } f (x)。这相当于一个齐次函数的学位。

在数学中，我们会考虑函数或曲线在变量{{mvar|x}}重新标度下的标度性质。也就是说，人们对某些标度因子{{mvar|λ}} 对应下{{math|''f'' (''λx'')}}的形状感兴趣，这些比例因子可以被视为长度或大小的重新标度。对于指数的某种选择和所有的膨胀，在所有重新调整下保持不变的要求通常被认为是: f (lambda x) = lambda ^ { Delta } f (x)。这相当于一个齐次函数的学位。

Examples of scale-invariant functions are the [[monomial]]s <math>f(x)=x^n</math>, for which {{math|Δ {{=}} ''n''}}, in that clearly

Examples of scale-invariant functions are the [[monomial]]s <math>f(x)=x^n</math>, for which {{math|Δ {{=}} ''n''}}, in that clearly