Coda: 1989—The Axiomatization(s) of the Fold
Coda: 1989—The Axiomatization(s) of the Fold
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尾声：1989——折叠的公理化
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发表时间：
2018
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通讯作者：
M. Friedman
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作者：
M. Friedman
当然，最后一章并不是关于折纸数学的“成果”的最终结论：这个领域处于不断发展的过程中，它与计算机科学和计算机建模的交织变得越来越明显和突出。当然，这就提出了一个问题，即如何考虑物质性，它在早期部分地起着阻碍因素的作用;例如，人们可能想知道，21世纪世纪数学计算机模型和19世纪世纪数学物质折叠模型之间的认识论含义和差异，但这一讨论超出了本章的范围。本章试图描述的是，可以被称为数学和基于折叠的几何学的这一新的现代运动的第一步：这种几何学的完全公理化。虽然没有一个现代的观点与数学的折纸已经考虑，试图找到公理或基本运算的几何，开始于20世纪初的世纪，成果只接近80年代末。如果Beloch的兴趣在于证明基于折叠的几何至少与直尺和罗盘几何一样强大，从代数的角度以及构造方面来看，在20世纪80年代中期，人们感兴趣的是找到基本的，基本的操作，折叠的图形是由这些操作组成的，并通过这种方式，给这种几何一个合理的逻辑基础，就像直尺和指南针几何学几个世纪以来所拥有的一样。
The final chapter is, of course, not a final conclusion concerning the “fruition” of the mathematics of paper folding: this domain is in a process of continuous development, and its interweaving with computer sciences and computer modeling becomes more and more apparent and prominent. This, of course, raises the question as to how materiality, which earlier functioned partially as a hindering element, is considered; one may wonder, for example, as to the epistemological implications and differences between the twenty-first century mathematical computer models and the nineteenth century mathematical material folded models, but this discussion is beyond the scope of this chapter. What this chapter will attempt to describe is that which can be called the first step of this new, modern movement concerning mathematics and folding-based geometry: the complete axiomatization of this geometry. Though not the single modern point of view with which the mathematics of paper folding has been considered, the attempt to find axioms or basic operations for this geometry, started at the beginning of the twentieth century, bore fruit only towards the end of the 1980s. If Beloch’s interest lay in proving that folding-based geometry is at least as powerful as straightedge and compass geometry, from an algebraic point of view as well as construction-wise, during the mid-1980s, one was interested in finding the basic, fundamental operations from which a folded figure was composed, and by this means, giving this geometry a logical sound basis, the same that straightedge and compass geometry had for centuries.