When I reproduce a sheet full of logotypes on a copy camera I usually start with the largest size original I will need and make copies at 61.8 percent of the original. I add the new 61.8 percent copy next to the original and make a second copy. The second copy is added to the original and a third copy is made. In electronics we would call this a feedback loop because the output is fed back into the input.
You end up with a smoothly varied selection of copies. The quanitity of each size logos follows a binomial distribution
and has a striking resemblance to the coefficients in Pascal's triangle.
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Size of logo |
Quantity of each size logo per Reduction Shot |
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|
1st |
2nd |
3rd |
4th |
5th |
6th |
7th |
|
|
100 % |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
61.8 % |
1 |
2 |
3 |
4 |
5 |
6 |
|
|
38.2 % |
1 |
3 |
6 |
10 |
15 |
||
|
23.6 % |
1 |
4 |
10 |
20 |
|||
|
14.6 % |
1 |
5 |
15 |
||||
|
9 % |
1 |
6 |
|||||
|
5.6 % |
1 |
||||||
1.61803398874989484820458683436564 X
0.61803398874989484820458683436588 X
Somewhere between the invention of moveable type and the introduction of Aldus Pagemaker there were a few years when graphic artists used photographic materials to create original artwork for offset printing. The sixties were probably the central decade of the offset printing-photographic reproduction era. Wood and metal type was fading away and laser printers weren't invented yet (heck in the early 60's a lot of people didn't have copy machines and those that were around usually only copied at 100%). During those few short years when photography was king, an artists proportional calculator was his or her number one tool.
The copy camera or stat camera was the central tool in graphic arts. The stat camera made photographic copies of type, line art, and layouts at one to one proportions or at some percentage of reduction or enlargement. The other neat thing the copy camera was used for was to convert a continuous tone (grey scale or color) photograph into a piece of pure black or white line art. A halftone screen laid over a piece of photographic emulsion would magically convert endless shades of grey into endless sizes of black dots.
Proportional calculators usually consisted of two cardboard disks grommeted together with inch and fraction markings. You would dial in a percentage increase or decrease and then you could read off other pairs of dimensions that were the same proportion. Lots of times artwork was done oversized and then, late in the process, when the printer was making negatives of the artwork he would reduce the black on white paper artwork to the final reduced size. This tended to minimize dust and dirt problems and increase sharpness and crispness in the final negatives that were used to "burn" the aluminum offset plates.
Photographs used in the printing and publishing trade were a standard 8 by 10 inches size. The photos themselves weren't part of the layouts and "camera-ready" pasted-up artwork. Instead there would be black rectangles or outlines showing the desired size and placement of photos. If you decided that you were going to produce your artwork on 8 1/2 inch by 11 inch paper and then reduce it to fit on a 7 by 9 inch page size you would use the proportional calculator to get your sizes right. The first thing you would calculate would be the overall reduction ratio. Other questions that would follow included:
This program automates proportional calculations for graphic artists. An "app" or "applet"
for the
Texas Instruments Avigo personal organizer. The 2010 Apple iPad is patterned on the 1997 TI Avigo
and the Palm Pilots.
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First enter the horizontal and vertical measurements of an original piece of artwork when prompted. |
Orig. A: 640 Orig. B: 480 |
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Next enter a horizontal measure that you want to fit the original piece of artwork into. |
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And the reproduction calculator will supply you with the missing dimension, in this case vertical. |
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The calculator will also display the X factor |
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Tap to continue |
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And the reproduction calculator will supply you with the missing dimension, in this case vertical. |
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When you are done enter a zero at any prompt to exit |
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