The Magnificent, Ever-Expanding Diminishing Stick


This PDF describes the technique of using a “diminishing stick” to lay out segments at a fixed proportion across multiple spans.



When “lining out” planking on a boat hull, boatbuilders often turned to an ancient geometric construction for quickly and accurately dividing spaces in constant proportions at a multitude of stations, each with a unique span. The output of the technique isn’t numerical–the results are the actual physical distances (called “magnitudes” by the Greeks) recorded on a stick.

Twentieth century carpenters might take a measurement at each station with their tape measure, then divide the number by three and use the resultant dimension to mark the mold at the two seams. But that’s way too much work; prone to error due to a misread or miscalculation; and its not as accurate as having the actual physical distance to record from. This PDF describes the technique of using a “diminishing stick” in detail.