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第85行： − 单项式标度不变性的概念在高维时推广到齐次多项式，更一般地推广到齐次函数。齐次函数是射影空间的“土著”，齐次多项式在射影几何中作为射影簇进行研究。射影几何是数学中一个内容特别丰富的领域；在其最抽象的形式——概型的几何学中，它与弦理论中的各种主题都有联系。+ − + − + − 有时人们说分形是尺度不变的，尽管更准确地说，我们应该说它们是自相似的。一个分形通常只对一个离散的值集等于它自己，即使在这种情况下，平移和旋转也可能被用来匹配这个分形本身。+ + +
→Fractals 分形学
The idea of scale invariance of a monomial generalizes in higher dimensions to the idea of a homogeneous polynomial, and more generally to a homogeneous function. Homogeneous functions are the natural denizens of projective space, and homogeneous polynomials are studied as projective varieties in projective geometry. Projective geometry is a particularly rich field of mathematics; in its most abstract forms, the geometry of schemes, it has connections to various topics in string theory.
The idea of scale invariance of a monomial generalizes in higher dimensions to the idea of a homogeneous polynomial, and more generally to a homogeneous function. Homogeneous functions are the natural denizens of projective space, and homogeneous polynomials are studied as projective varieties in projective geometry. Projective geometry is a particularly rich field of mathematics; in its most abstract forms, the geometry of schemes, it has connections to various topics in string theory.
单项式标度不变性的概念在高维时推广到'''Homogeneous Polynomial 齐次多项式'''，更一般地推广到'''Homogeneous Function 齐次函数'''。齐次函数是射影空间的“土著”，齐次多项式在射影几何中作为'''Projective Varieties 射影簇'''进行研究。射影几何是数学中一个内容特别丰富的领域；在其最抽象的形式——'''Schemes 概型'''的几何学中，它与'''String Theory 弦理论'''中的各种主题都有联系。
===Fractals 分形学===
===Fractals 分形===
[[File:Kochsim.gif|thumb|right|250px|A [[Koch curve]] is [[self-similar]].|链接=Special:FilePath/Kochsim.gif]]
[[File:Kochsim.gif|thumb|right|250px|A [[Koch curve]] is [[self-similar]].|链接=Special:FilePath/Kochsim.gif]]
It is sometimes said that [[fractal]]s are scale-invariant, although more precisely, one should say that they are [[self-similar]]. A fractal is equal to itself typically for only a discrete set of values {{mvar|λ}}, and even then a translation and rotation may have to be applied to match the fractal up to itself.It is sometimes said that fractals are scale-invariant, although more precisely, one should say that they are self-similar. A fractal is equal to itself typically for only a discrete set of values , and even then a translation and rotation may have to be applied to match the fractal up to itself.
It is sometimes said that [[fractal]]s are scale-invariant, although more precisely, one should say that they are [[self-similar]]. A fractal is equal to itself typically for only a discrete set of values {{mvar|λ}}, and even then a translation and rotation may have to be applied to match the fractal up to itself.
It is sometimes said that fractals are scale-invariant, although more precisely, one should say that they are self-similar. A fractal is equal to itself typically for only a discrete set of values , and even then a translation and rotation may have to be applied to match the fractal up to itself.
有时人们认为分形是标度不变的，尽管更准确地来说，应该说分形是自相似的。一个分形通常是等于它自己的一个{{mvar|λ}}值离散集合，即使这样，一个平移和旋转可能不得不应用到匹配分形到它自己。
Thus, for example, the [[Koch curve]] scales with {{math|∆ {{=}} 1}}, but the scaling holds only for values of {{math|''λ'' {{=}} 1/3<sup>''n''</sup>}} for integer {{mvar|n}}. In addition, the Koch curve scales not only at the origin, but, in a certain sense, "everywhere": miniature copies of itself can be found all along the curve.
Thus, for example, the [[Koch curve]] scales with {{math|∆ {{=}} 1}}, but the scaling holds only for values of {{math|''λ'' {{=}} 1/3<sup>''n''</sup>}} for integer {{mvar|n}}. In addition, the Koch curve scales not only at the origin, but, in a certain sense, "everywhere": miniature copies of itself can be found all along the curve.