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A Round Pie in a Square Box American Scientist


A Round Pie in a Square Box

Mismatched pairs of simple things can inspire ingenious solutions

Henry Petroski

When I was a child, I enjoyed accompanying my father to the bakery, where I could observe things that I found to be as sweet intellectually as the confections on the shelves were sensually. My appetite for the mechanical devices and gadgets in the place was insatiable. I was fascinated by the slicing machine into which the woman behind the counter placed a full loaf of bread and received a neatly sliced one in return. After lifting the segmented loaf from the machine with two hands, imperceptibly compressing it the way a juggler does a set of cigar boxes that looks to be defying gravity, the bakery woman upended the loaf of precisely aligned slices and balanced it in a vertical position in the palm of one hand while reaching with the other and snapping open the white paper bag into which she would slide the sliced loaf and in which the customer would carry the bread home. To me, indeed, the whole process was the greatest thing since sliced bread itself.

Another operation that captured my attention was the action of placing a pie or cake in a box, which itself first had to be formed from one of the flat sheets of irregularly but deliberately shaped white cardboard that were stacked neatly on a shelf under the counter. First, in plain view of a father and his child, three sides of the latent box were folded up and joined together by a tab-in-slot sleight of hand. Into this partially formed box the pie or cake was partly lowered from the top and partly slid from the front, thereby displacing neither a crumb of crust nor a swirl of icing. With the dessert in place, the last of the box’s sides was raised like the tailgate of a delivery truck and made secure by another tab-in-slot maneuver. As the shopwoman brought the top of the box down to close it, her deft hands kept the flaps from invading the space between the insides of the box and its contents. The flaps were left outside flapping like wings.

The box still had to be secured with cotton string, sometimes plain white and sometimes candy striped. The supply of string was kept on large spools that had the shape of truncated cones and turned on strategically located spindles. I know this because the spools were often kept in plain sight, either right on the work counter or high above it. But no matter from where it was deployed, the string could be played out easily, if noisily, and it was wrapped around the box seemingly with the speed that Superman could circle the Earth. First three or four turns secured the front flap, and then three or four did the same for the side flaps. In preparation for tying the concluding knots, the string was cut with the flick of a finger, which wore a pragmatic steel ring set not with a stone but with a small knife blade shaped like a miniature sickle. When two or more boxes were to be taken home, they were stacked in a tower formation and tied together for the carrying. The only thing that bothered me about the uniting of pies and cakes with boxes and string was that the pies were round and the boxes square.

Out of Shape

The world of things is full of mismatched objects. Like round pegs in square holes, they do not fit neatly together. But when they are joined, neither do they easily fall apart. The world of things can be a world of awkward pairings, marked by misfit, imperfection and compromise, but even in these there can be lessons to be learned about why and how they came to be. And their stories can reveal the secrets of how so many things do fit together, albeit imperfectly.

The white-boxes-and-string world of the old-time bakeshop is alien to the baked-goods department of today’s supermarket. Here, most things are prepackaged in transparent plastic cases formed to conform to the shape of their contents. Round pies tempt us from beneath round transparent domes. Tops snap onto bottoms and lock in place without the use of string. The packages are neither biodegradable nor easily carried with one hand, but they do fit, if not geometrically congruentlyalong with the round cans and bottles and globular fruits and vegetablesinto the ample trapezoidal hold of a shopping cart. The incongruity of things made and things found is a fact of life, and like most facts of life it is accepted as the way things are, if not embraced as welcome variety. Maybe it would be a more efficient use of resources and space if all things, including pegs and holes, were square, but who would want to slice a squarish pie or catch a cubic ball?

So, we not only accept the shapes of the world as we find them, but we also adapt to the idiosyncrasies of their interaction. And one of the most common surviving examples of this is the round pizza delivered in the squat square box. As my father accepted without comment his chocolate cake and apple pie in white boxes bound in candy-cane string, so most of us accept our pizzas in corrugated-cardboard containers that come in a wide but limited range of styles and colors. The basic container comes in the neutral earthen color of corrugated-cardboard boxes, but some restaurants think it to their advantage to use white cardboard and imprint the boxes they use with the name of the business, often in the green, white and red colors of the Italian flag. However dressed up, the corrugated-cardboard box is near-ideal packaging for a hot pizza that must endure a 15-or-sominute journey from commercial oven to domestic table.

Relatively thin and unreinforced cardboard, the stuff of which cake and cereal boxes are made, is a rather flimsy material and hardly suitable for bearing the weight of a pizza pie distributed over the reach of a 16- or 18-inch circle. That box material worked for pies and cakes not only because their diameter is typically only about eight inches, but also because they were usually supported by a pie tin or cake base that enforced their burden’s flat shape. Pizza pies, on the other hand, are notoriously soft and floppyespecially when they are hotand if there is anything between them and the box they are placed in, it tends to be a flimsy sheet of waxed paper, whose purpose is to provide not structural stiffness but a modicum of gentility. Where the pizza is especially oily, the paper also may help keep the box bottom dry.

Like the old bakery-cake container, every pizza box begins as a flat sheet, which is die cut into an irregular shape that can be folded into a (usually prismatic) box. Like the cake container, the box gains stiffness by being closed, but with the flaps tucked inside rather than being tied down outside. Some of us have experienced the transformation from flat to full first-hand by assembling gift boxes out of the unassembled parts we have been provided by a department store. For those of us who have not, we can reverse engineer any cardboard box to gain a tactile appreciation for the advantages of the closed structure. We know from shopping at the supermarket that full and sealed boxes of corn flakes hold their shape and protect their fragile contents through the successive processes of being filled at the plant, packed into cartons there, shipped to the store, stocked on the shelf, taken down from the shelf, placed in the cart, slid past the scanner, thrown in the bag, stuffed in the car, jostled on the road, dropped on the drive, squeezed into the pantry and brought to the tableintact. Soon as the box is opened, however, we can feel its rigidity drop. That is because the sealed top had prevented the sides from altering their geometry.

Reverse engineering the cereal box begins with emptying it of its contents and unsealing the bottom. This leaves an open-box structure, which is readily felt to be much less rigid than its closed counterpart. The doubly-opened box can be sighted through, as if it were a tube. However, unlike a circular tube, whose shape cannot be changed without some crushing, the rectangular tube of the cereal box can be transformed into a parallelogram without altering the flatness of any of its sides. It is this nature of the rectangle that requires it to be braced with diagonals if it is to be used as a basic structural shape for, say, a building or a bridge. Since diagonals bisect a quadrilateral shape into triangular ones, we see triangles dominating the structural pattern of so many bridges and buildingsat least before they are clad in an architectural facade. Without diagonals, the open cereal box is more a mechanism than a structure, and its interior shape can be transformed from rectangle to parallelogram and even to a flattened box with ease. Locating the seam that usually runs down one corner of the box and separating its glued surfaces allows us to open the box fully and lay its insides flat out. This is how the cake box in the bakery and the pie box in the pizzeria are delivered from the box factory.

The corrugated cardboard box is remarkably well-suited for transporting a hot pizza, and this is no doubt why for decades it has remained generally unchanged in design and use. Starting out flat as it does, it takes up relatively little storage space, which is often at a premium in mom-and-pop pizza shops. A basic pizza box is relatively inexpensive, costing perhaps 25 cents when bought off the Internet in lots of 50 and considerably less when purchased wholesale in chain-store quantities. Corrugated cardboard is a relatively stiff material and so, especially when closed, a box made of it is good at holding its shape and so at preserving the shape of its contents. In addition, the nature of the corrugation process is to include channels of air in the sandwich structure, thus providing insulating properties somewhat similar to those of a double-glazed window pane. This, of course, helps the pizza retain its heat while in transit. Finally, cardboard is absorbent, and so to a degree keeps olive oil or other pizza juices from dripping out.

Building Better Pizza Packaging

But nothing is perfect in design or use, and so the common pizza box also has its limitations, shortcomings and downright failures, which tend to be accepted and adjusted to by proprietors and customers alike. But few flaws escape the eyes of inventors, designers and engineers, who are always looking to improve on things. Yet even among these groups, the fact that a square box is used for a round pie is hardly worth further comment, other than to mention that there have been evolutionary changes that have addressed the problemif it can be called even thatof the mismatch in geometry. Domino’s Pizza developed its polygonal box that better approximates the circular geometry of its contents, and there are circular pizza containers made of Styrofoam and other moldable materials. Such extravagances might be justified by branding, marketing and targeted advertising objectives, but they are seldom affordable to the small, independently owned pizza parlor.

There are nongeometrical problems with the pie-in-a-box concept that do lend themselves to simple and inexpensive solutions. But these kinds of problems tend to be invisible to or ignored by all but the most persnickety of inventors. One such problem manifests itself when the top of the box in which a hot pizza resides sags excessively because of the softening effect of the steamy environment inside or because something heavy is placed atop the box. The problem can also arise when the boxed pizza is transported in a car that rattles over railroad tracks or bounces in and out of potholes. When the box is opened after such a ride, more cheese can be found stuck to the underside of the box top than remains on the pizza itself. Tolerant customers might scrape the cheese off the cardboard and redistribute it on the pie, but inventors can be intolerant of everything but their own inventions.

The inventor Carmela Vitale was evidently bothered enough by the problem of the box top eating the cheese off the pie to devise a solution. As she explained in her patent, which was issued in 1985, cheaply made and disposable containers, “particularly those used to deliver pizza pies or large cakes or pies, comprise boxes with relatively large covers formed of inexpensive board material” that have a tendency “to sag or to be easily depressed at their center portions so that they may damage or mark the pies or cakes during storage or delivery.” Her solution was “to provide a lightweight and inexpensive device,” which would be molded “from one of the plastics which is heat resistant such as the thermo set plastics and which will resist temperatures of as high as about 500F.” The form that she preferred, and the one that is illustrated in the patent, is a utilitarian tripod, a minimalist three-legged stool. In her description of the so-called “preferred embodiment,” she explained that the legs should have “a minimal cross section to minimize any marking of the protected article” and also “to minimize the volume of plastic required” and thereby keep the cost low.

Curiously, Vitale called her little device a “package saver” and used that term also as the title of her patent. In fact, as she herself recognized in the claims of her patent, the benefit of the tripod is in “preventing damage to the packaged food article by the cover.” Thus it is not the disposable package that is being saved, but its contents. The device has since been appropriately renamed a “pizza saver,” though few people who admire the thing for so effectively saving their pizza from being scalped of its cheese know it by that name. In fact, it is most popularly referred to as an all-purpose “little thingy,” which in context everyone understands. People also appreciate that with its thin, spindly legs it has a very small footprint on the pizza and consumes very little of the pie itself.

Although possessing no grace or elegance of form, Vitale’s answer to the problem of the cheese-eating box top is considered an elegant solution. It has no unnecessary embellishments. Clearly, the small and inexpensive device was meant to be as disposable as the pizza box, but not everyone who saw the pizza saver could throw it away. Especially people engaged in arts and crafts tended to wash it off and put it away for some future use that they were sure it would someday have. One woman whose hobby was decorating eggs found that turning it upside down made it serve as an ideal egg easel. She did have one complaint, however, and that was that the little thingy was rather expensive, a fault that she attributed to having to pay for its elaborate packaging, namely, a large pizza in a larger box.

As elegant a solution as the pizza saver might be, not everyone saw it to be without structural flaws of its own. One inventor identified a critical shortcomingespecially when the pizza saver came in the form of a dollhouse-size three-legged table with a solid round top. How was it to be packaged when purchased not one at a time but in bulk, for the pizzeria that wanted to secure a supply of pizza savers had to buy them in quantities of a thousand. The way the savers typically came was loose in a large corrugated-cardboard box, and, as with a box of cornflakes, the contents tended to settle during shipping. Still, the large box could take up an inordinate amount of space in a cramped pizza shop. The inventor’s solution to packing pizza savers with flat table tops more compactly was to incorporate into the top holes into which the legs of a second saver could be inserted. A series of savers nested in such a way would naturally take up less space than a random jumble of them. What the inventor seemed to ignore, however, was the labor that would be involved in nesting the tripods, thereby adding to the cost of something whose price was supposed to be kept as low as possible. Inventors sometimes lose sight of the bigger picture.

Getting a Handle on a Slice

Keeping the cheese on the pie is only one problem with hot pizza. Another is getting the first slice out of the box. It is here that the square box actually works to advantage. While a round container would certainly be more geometrically matched to its contents, getting the pizza out of it could lead to considerable frustration, for if the fit were too snug fingers could not easily get under the crust to lift out a slice. With the box square, however, there is ample open space in the corners to get a full hand of fingers underneath the pie. Unfortunately, there can still be another hurdle to overcome before the slice is fully free, for the hot melted cheese tends to flow across the cuts defining the slices, effectively fusing them together in transit to the table. In this case, it can be virtually impossible to lift a slice apart from the rest of the pie without having some undesirable redistribution of cheese between adjacent slices or experiencing the stretching out of long strings of cheese that tie the adjacent slices together. When this happens, it is convenient to have a knife or wheeled cutter handy to sever the connections.

Some inventors, like still-life painters who crowd as much onto their canvas as possible, try to solve multiple problems with multipurpose devices crowded with features. Sometimes their inventions succeed; sometimes they do not. One pair of inventors looked to solve the sagging box top and stringy cheese problems with a single device, which they called a “combined pizza box lid support and cutter.” Made of plastic to keep its cost down, the dual-purpose device resembles a rotary cutter but with the wheel’s axle extending to about the height of a delivery box. Another team of inventors received a patent for a “combination food server and container lid support,” which consisted of a pie-slice shaped spatula with its handle offset like that of a mason’s trowel, the amount of the offset being roughly that of the height of the pizza box. (The patent even explained how the device could be inserted into a sliced pizza, so that the blade was under the pie and the handle above it, supporting the top.) Another inventor received a design patent for a combination fork and wheeled cutter, thereby enabling the fastidious pizza eater to cut and spear pieces of pizza without needing two hands free to manipulate a separate knife and fork.

Another team of inventors received a patent in 2007 for what they described as a “lid support and serving aid,” which was embodied in a plastic tripod with one of its legs inclined, elongated and serrated so that it could be used to cut through cheese and crust to produce individual slices. The top platform of the tripod contained a hole large enough for an index finger so that a good grip could be had for executing the cutting process. The platform was also shaped so that individual tripods could be nested like function-room chairs, thus saving shipping and stocking space.

No matter how a slice of pizza is gotten free from its neighbors and from the box they all came in, there can still remain obstacles to neat and comfortable eating. Especially when they are hot, slices of pizza tend to be floppy and so extra care is required in lifting them to the mouth in a configuration that will not encourage cheese to slough off and oil to drip onto the eater’s clothes. A number of inventors have patented pizza boxes with perforated tops and bottoms that allow wedge-shaped pieces of cardboard to be separated from the delivery box to be used as “plates” on which to serve individual slices of pizza. (Some come complete with thumb holes that can be punched out for easier holding.) This reuse of the box not only helps support saggy slices but also encourages the reuse at least of parts of otherwise throwaway boxes.

One traditional way of handling the sagging slice is to bend it along a radial line from tip to crust, effectively creating a trough that gives structural stiffness to the otherwise limp wedge. Interestingly, it is the same structural principle of folding that gives stiffness to the corrugated cardboard box that the pizza comes in and the dimpled paper plate that it is often served on. The principle can easily be demonstrated with a single sheet of paper. Unfolded, it will sag easily when lifted off a pile; folded one or more timesas is done in the process of making a paper airplanethe sheet has considerable stiffness to hold its shape. Achieving stiffness by folding is a ubiquitous technique in structural engineering, being exhibited in everything from corrugated tin roofs to sculpted concrete shells to molded automobile bodies.

The everyday actions of boxing, transporting and delivering a warm pizza, as well as those of separating, serving and eating a slice of the pie, provide familiar examples of how problems are perceived and solutions offered for the engineering and design of complex systems of all kinds. Indeed, anything made and used can serve to illustrate the processes of engineering, invention and design, and the more simple and familiar the thing employed, the more illuminating the example may be.

Henry Petroski



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