纸张尺寸的国际标准 ISO 216(如 A4、A3)是以 2 的平方根为基础的,每张纸的长宽比为 [latex]1:\sqrt{2}[/latex]。这一独特的特性意味着,当一张纸平行于其较短的两边被剪开或折成两半时,所产生的两张较小的纸的长宽比与原来的完全相同,即 [latex]1:\sqrt{2}[/latex]。.

(图片仅供参考)
纸张尺寸的国际标准 ISO 216(如 A4、A3)是以 2 的平方根为基础的,每张纸的长宽比为 [latex]1:\sqrt{2}[/latex]。这一独特的特性意味着,当一张纸平行于其较短的两边被剪开或折成两半时,所产生的两张较小的纸的长宽比与原来的完全相同,即 [latex]1:\sqrt{2}[/latex]。.
该系统最初由格奥尔格·克里斯托夫·利希滕贝格于1786年提出,后由沃尔特·波斯特曼于1922年在德国标准化为DIN 476标准,其建立在两个原则之上:基准尺寸(A0)的总面积为一平方米,且边长比例为[latex]1:√2[/latex]。 设A0纸张的边长为[latex]×[/latex]和[latex]×[/latex],则形成如下方程组:[latex]/x = √2×[/latex],[latex]×y = 1[/latex]。解此方程组可得A0纸张尺寸约为841毫米×1189毫米。.
Each subsequent size in the A series (A1, A2, A3, A4, etc.) is created by halving the previous size along its longer dimension. For example, cutting an A3 sheet in half produces two A4 sheets. Because of the [latex]\sqrt{2}[/latex] aspect ratio, these new A4 sheets have the same proportions as the original A3 sheet. This elegant mathematical property is incredibly practical. It allows for easy scaling of documents on photocopiers and printers (e.g., enlarging from A4 to A3 is a simple 141% or [latex]\sqrt{2}[/latex] magnification) without cropping or leaving empty margins. This efficiency and simplicity have led to its near-universal adoption worldwide, with the notable exceptions of the United States and Canada.
纸张尺寸中的 2 的平方根
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