Kidjel Ratio Cali-Pro Proportional Dividers

This metal instrument has two long arms and two short arms, all colored gold and arranged as in a pantograph. Needle points are bolted to both ends of the long arms. The arms are fixed at a desired distance with a thumbscrew on a central rod. Unlike a pantograph or standard proportional dividers, the instrument is not marked so that it may be set for a variety of proportional relationships and thus be used to create scale drawings at a variety of sizes. Instead, the inventor, Honolulu portrait artist Maurice Kidjel (1888–1976), designed the instrument so that it always preserved a ratio of 5.333 : 1. To create drawings in this "universal ratio," the user set the long needles at the width of the large part of the drawing and then turned the dividers over to use the short needles to make a small part of the drawing in proportion to the large part of the drawing.

A large white cardboard box is marked in maroon on the top and both ends: THE KIDJEL RATIO (/) CALI-PRO. According to a mark on the bottom, the box was manufactured by Christian & Co., Inc., of North Hollywood, Calif. Cardboard and yellow foam inside the box provided support and cushioning to the dividers and related documentation.

Russian-born Kidjel and his business partner, Kenneth W. K. Young, began selling this device for $25.00 around 1960. According to the advertising flyer received with the object (MA.304213.04), the dividers were used only to lay out designs in the "universal ratio." However, Kidjel also believed that this ratio was the key to solving the three classic construction problems of Greek antiquity. His solutions, constructed with a compass and straight edge, appeared in the textbook distributed with the Cali-Pro (MA.304213.03). His work depended on a false definition of pi and thus is not mathematically valid. Nonetheless, Daniel Inouye read a tribute to Kidjel's ratio system into the U.S. Congressional Record on June 3, 1960. Although Kidjel's foray into mathematical proof was not successful, the dividers were relatively popular with draftsmen in the 1960s and 1970s. Kidjel was also widely respected as an artist, and his artwork was exhibited at the Smithsonian in June 1947.

References: Maurice Kidjel, The Two Hours that Shook the Mathematical World (Hawaii Art Publishing Co., 1958); Maurice Kidjel and Kenneth W. K. Young, Challenging and Solving the "3 Impossibles" (Honolulu: Kidjel-Young Associates, [1961]); Advertisement for Kidjel Cali-Pro, Art Education 15, no. 4 (1962): 2; Maurice Kidjel, "Proportional Calipers" (U.S. Patent 3,226,835 issued January 4, 1966; UK Patent 1,039,636 issued August 17, 1966); Martin Gardner, "Mathematical Games," Scientific American 214 (June 1966): 116–122.

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