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The Miura-Ori map

by Ian Bain

Folded maps are merciless to the user who makes the slightest error in returning them to their compact form. Pt the Tokyo ICA meeting Koryo Miura and Masamori Sakamaki from Tokyo University's Institute of Space and Aeronautical Science demonstrated an application, of space science, combined with a little Origami, which transforms the ergonomics of map folding.

Miura and Sakamaki normally work on the problems of packing large flat items, like satellite antennae and solar collectors, into the smallest, most compact shapes with a view to deploying them as rapidly and as simply as possible. They saw three problems with naps folded at right angles in the conventional manner. First, an orthagonally-folded map requires an unduly complicated series of movements to fold and unfold it. Secondly, once unfolded there is a strong possibility that the folds may be "unstable" and turn inside out. Finally, right-angled folds place a lot of stress on the paper inducing, almost without exception, tears which begin where two folds intersect.

The key to an alternative system of may folding lies in the ancient Japanese art of paper-folding, origami. One of the most common origami effects is to use a variant on concertina folding to produce a slightly ridged surface composed of a series of congruent parallelograms, by a variation on concertina folding.

Miura and Sakamaki looked at this kind of surface in terms of its geometry and elasticity and came to the conclusion that the most important point of difference from an orthogonally folded sheet is that the folds are interdependent. Thus a movement along one fold lire produces movement along the other. In other words, the user can open the map with just one pull at a corner. The new method also solves in part the other problems which Miura and Sakamaki cited. Interdependence of folds means that it is very difficult to reverse them and the amount of stress place or, the map sheet is also reduced because only one thickness of paper comes beneath the second fold, avoiding the need to fold several sheets. Will it catch on? That depends on commercial exploitation. and the automation of what is admittedly a complicated initial folding process. Miura and Sakamaki have devised a mechanical folder which they coyly term an "origami machine", but they did not reveal its details.

Professor Koryo Miura has since sent us a copy of the paper which was distributed at the International Cartographical Association's conference last August. This may now be borrowed from the library, and makes fascinating reading. The subject of map-folding is dealt with very fully and several of the topics discussed are worth a mention here. Professor Miura examines what he suggests is the oldest folded paper map in existence.

Now in a museum in (Milan, Italy, this comes from Egypt and describes the location of a gold mine in the Nubian district of that country. He looks at the problems of conventionally folded maps which are prone to stress and tearing at their right-angled folded corners. The Miura-on mop avoids this weakness. Diagrams showing the paths made by both right-hand and left-hand thumbs in unfolding the conventional and the Miura-Ori map are compared.

Professor Miura says that on his new map the angle made between the lengthwise-folds and the lines of geographical longitude can he calculated to N, equal to the westward inclination of the magnetic north in most parts of Japan! For those who would like to reconstruct the Miura Ori map, we reproduce a crease pattern diagram from Professor Miura's paper, together with precise dimensions required. For this size fold, the parallelogram angle should be about 84 degrees

This article by Ian Bain first appeared in the 23/10/80 issue of New Scientist, London, the weekly review of science & technology and was reproduced in an issue of British Origami in 1981

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