Related to the geometry of tangrams: “The Haberdasher’s Puzzle” — a mathematical question, asked and answered by Henry Ernest Dudeney in 1907.
He produced a piece of cloth in the shape of a perfect equilateral triangle, as shown in the illustration, and said, “Be there any among ye full wise in the true cutting of cloth?… Show me, then, if ye can, in what manner this piece of cloth may be cut into four several pieces that may be put together to make a perfect square.”
The Canterbury Puzzles, by Henry Ernest Dudeney
I add an illustration showing the puzzle in a rather curious practical form, as it was made in polished mahogany with brass hinges for use by certain audiences. It will be seen that the four pieces form a sort of chain, and that when they are closed up in one direction they form the triangle, and when closed in the other direction they form the square.
These “hinged dissections” suggest other possibilities for the chained polyhedral portion packs we’ve looked at in the past, as well as suggesting a kind of transformative packaging in which containers can be designed to change shape. (See: Jessica Comin’s “laranja mecánica”)
(A patent that relates to this idea, after the fold…)
In Driscoll’s patent above, the chained polyhedrons are not simply extruded prisms, as we’ve seen in the past. They each bevel from a small triangle on one side to large triangle on the other. The portions appear to be identically shaped, but they alternate. Not clear on what this package was meant to contain. The patent was assigned to Thomas & Betts, “designer and manufacturer of connectors and components for electrical and communication markets.” (See also: Package of Containers)
Even more pertinent to our idea of using Dudeney’s Dissection in packaging design, is this promotional coin bank from ABN-AMRO.
Photo from Greg Frederickson’s book “Hinged Dissections: Swinging & Twisting”
Sadly, a photo does not appear to be available showing the bank in its square formation.