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mckenzeeAfter much scribbling on envelopes and doing geometry in my head, I realized that my future comic projects will be based on the Square Root of 2. The math was simple, really. 1 divided by the square root of 2 equals the square root of 2 divided by 2. Hence, as the panel/page/spread doubles in size, the proportions stay the same. Fortunately, Europe is once again more logical that the United States, as this system is the same as the ISO 216 paper size system (A3, A4, A5, &c...)
The ISO 216 paper size system is an international standard that is used in many places in the world in copy and print devices that defines paper sizes. Based on the metric system, the ISO paper size system uses a height-to-width ratio with an aspect ratio of 1 to 1.414 (The square root of 2). If a sheet is cut into two, the resulting halves are the same proportions as the original.
This standard defines three series of paper sizes; A, B and C. All successive paper sizes are derived from the base standard A0, which is a sheet of paper measuring 1 square meter or 841 x 1189mm. The most common size of paper is A4 (210x297mm), which is standard letterhead paper size. The C series of sizes is for envelopes, where the C4 (229 x 324mm) is defined under ISO 269 and is most often used with A4 size paper. The B series contains intermediate sizes for the A series but are sizes that are not frequently used.
The simplicity of the derivation (square root of 2 is the diagonal through a square of side length 1) is paralleled by the ease of maintaining the proportion through division or multiplication of the proportioned rectangles. The sum of two rectangles of proportion (Square root of 2) : 1 long side by long side is (Square root of 2) : 2. Divided by the square root of two we arrive at 1 : (Square root of 2), the same ratio as the two rectangles that were added together, only with a change of orientation.
The ISO 216 paper size system is an international standard that is used in many places in the world in copy and print devices that defines paper sizes. Based on the metric system, the ISO paper size system uses a height-to-width ratio with an aspect ratio of 1 to 1.414 (The square root of 2). If a sheet is cut into two, the resulting halves are the same proportions as the original.
This standard defines three series of paper sizes; A, B and C. All successive paper sizes are derived from the base standard A0, which is a sheet of paper measuring 1 square meter or 841 x 1189mm. The most common size of paper is A4 (210x297mm), which is standard letterhead paper size. The C series of sizes is for envelopes, where the C4 (229 x 324mm) is defined under ISO 269 and is most often used with A4 size paper. The B series contains intermediate sizes for the A series but are sizes that are not frequently used.
The simplicity of the derivation (square root of 2 is the diagonal through a square of side length 1) is paralleled by the ease of maintaining the proportion through division or multiplication of the proportioned rectangles. The sum of two rectangles of proportion (Square root of 2) : 1 long side by long side is (Square root of 2) : 2. Divided by the square root of two we arrive at 1 : (Square root of 2), the same ratio as the two rectangles that were added together, only with a change of orientation.