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第58行：
第58行： − 标度不变函数的实例是单项式：+ − + − :<math>f(\lambda x) = (\lambda x)^n = \lambda^n f(x)~.</math>+ − :f(\lambda x) = (\lambda x)^n = \lambda^n f(x)~.+ − − : f (lambda x) = (lambda x) ^ n = lambda ^ n f (x) ~ . 第72行：
第70行： − 比例不变曲线的一个例子是等角螺线，这是一种在自然界中经常出现的曲线。在极坐标系中，螺旋线可以写成+ − − :\theta = \frac{1}{b} \ln(r/a)~. − − 1}{ b } ln (r/a) ~ . 第84行：
第78行： − 允许旋转的曲线，它是不变的所有重新标度; 也就是说，是相同的旋转版本的。+
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Examples of scale-invariant functions are the monomials f(x)=x^n, for which , in that clearly
Examples of scale-invariant functions are the monomials f(x)=x^n, for which , in that clearly
许多标变函数的实例是单项式：
<math>f(x)=x^n</math>，对于这个单项式
<math>f(x)=x^n</math>，
其中 {{math|Δ {{=}} ''n''}}，且有：
<math>f(\lambda x) = (\lambda x)^n = \lambda^n f(x)~.</math>
An example of a scale-invariant curve is the [[logarithmic spiral]], a kind of curve that often appears in nature. In [[polar coordinates]] {{math|(''r'', ''θ'')}}, the spiral can be written as
An example of a scale-invariant curve is the [[logarithmic spiral]], a kind of curve that often appears in nature. In [[polar coordinates]] {{math|(''r'', ''θ'')}}, the spiral can be written as
An example of a scale-invariant curve is the logarithmic spiral, a kind of curve that often appears in nature. In polar coordinates , the spiral can be written as
An example of a scale-invariant curve is the logarithmic spiral, a kind of curve that often appears in nature. In polar coordinates , the spiral can be written as
一个标度不变曲线的例子是'''Logarithmic Spiral 对数螺线（等角螺线）'''，这是一种在自然界中经常出现的曲线。在极坐标系中，螺旋线可以写成
:<math>\theta = \frac{1}{b} \ln(r/a)~.</math>
:<math>\theta = \frac{1}{b} \ln(r/a)~.</math>
Allowing for rotations of the curve, it is invariant under all rescalings {{mvar|λ}}; that is, {{math|''θ''(''λr'')}} is identical to a rotated version of {{math|''θ''(''r'')}}.
Allowing for rotations of the curve, it is invariant under all rescalings {{mvar|λ}}; that is, {{math|''θ''(''λr'')}} is identical to a rotated version of {{math|''θ''(''r'')}}.
Allowing for rotations of the curve, it is invariant under all rescalings ; that is, is identical to a rotated version of .
Allowing for rotations of the curve, it is invariant under all rescalings ; that is, is identical to a rotated version of .
在任意重新标度{{mvar|λ}}下，标度不变也允许曲线进行旋转；换句话说，{{math|''θ''(''λr'')}}与其旋转后的{{math|''θ''(''r'')}}一模一样。
===Projective geometry===
===Projective geometry===