A reprint from
American Scientist
the magazine of Sigma Xi, The Scientific Research Society
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Engineering
A Round Pie in a Square Box
Henry Petroski
W
hen 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 tabin-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
Henry Petroski is Aleksandar S. Vesic Professor
of Civil Engineering and a professor of history at
Duke University. Address: Box 90287, Durham,
NC 27708-0287
288
American Scientist, Volume 99
Mismatched pairs
of simple things can
inspire ingenious
solutions
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 congruently—along
with the round cans and bottles and
globular fruits and vegetables—into 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
Copyright © 2011 by Henry Petroski. Requests for permission to reprint or
reproduce this article should be directed to the author at [email protected].
A problem as seemingly simple as packaging a pizza can lead inventors to ingenious solutions. One key problem is the need to protect what
is nearly always a round pie, for which the current ubiquitous approach is the square corrugated-cardboard box. That solution led Carmela
Vitale to patent what is now widely known as a “pizza saver,” which prevents the top of the pizza box from touching and capturing the pie’s
cheese. Numerous variations on the original design have yet to appreciably improve on the original in functionality or aesthetics, with most
adaptations aimed at more compact storage.
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-so–minute 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 floppy—especially when they
are hot—and if there is anything bewww.americanscientist.org
tween 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 table—intact. 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
Copyright © 2011 by Henry Petroski. Requests for permission to reprint or
reproduce this article should be directed to the author at [email protected].
2011 July–August
289
somewhat similar to those of a doubleglazed 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
A “combined pizza box lid support and cutter” attempts to address two problems in one
device. Placed horizontally to the pizza, it supports the box top; once the box is opened, it
can be used as a rotary pizza slicer.
into triangular ones, we see triangles
dominating the structural pattern of so
many bridges and buildings—at 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
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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 problem—if it can be called even that—of
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
500°F.” The form that she preferred, and
the one that is illustrated in the patent, is
a utilitarian tripod, a minimalist threelegged 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
Copyright © 2011 by Henry Petroski. Requests for permission to reprint or
reproduce this article should be directed to the author at [email protected].
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 shortcoming—especially when the pizza
saver came in the form of a dollhousesize 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.
Although Mark A. Voves received a design patent for a “pizza cutting and eating tool,” the
device actually came to be known as and can be found on the Internet by searching for “pizza
fork.” For the pizza lover who prefers not to touch the gooey slices directly, this may be the
preferred tool for enjoying bite-sized pieces.
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 dualpurpose 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
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
www.americanscientist.org
The “combined food server and container lid support” is a plastic spatula whose handle holds
the box top up during transport and that can be used to serve slices when the box is opened.
For delivery, the blade of the device slides under several pieces of the pie, stablizing the
spatula against overturning forces.
Copyright © 2011 by Henry Petroski. Requests for permission to reprint or
reproduce this article should be directed to the author at [email protected].
2011 July–August
291
Another “lid support and serving aid” has
one of its legs inclined, elongated and covered
with serrations in order to cut slices apart. The
finger hole in the top is intended to facilitate
manipulating the tool.
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
One patent describes a method of scoring a
pizza box so its parts can be reused for serving the pie. The semicircular holes allow for
a better grip on the “plate” with the thumb.
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American Scientist, Volume 99
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 times—as is done in the process of
making a paper airplane—the 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.
Bibliography
Beck, Dilman A., and Susan E. Beck. 1989.
Combination food server and container lid
support. U.S. Patent No. 4,877,609.
Coomes, Steve. 2004. Thinking ‘round the box.
Pizza Marketplace. http://www.pizzamarketplace.com/article.php?id=3155.
Fisk, James, Jr. 1995. Pizza box with wedgeshaped break-down spatula-plates. U.S.
Patent No. 5,476,214.
Maultasch, Jonathan, and Bruce Maultasch.
1996. Combined pizza box lid support and
cutter. U.S. Patent No. 5,480,031.
Nelson, David C., and John J. Andrisin. 2007.
Pizza box lid support and serving aid. U.S.
Patent No. 7,191,902.
Vitale, Carmela. 1985. Package saver. U.S. Patent No. 4,498,586.
Voves, Mark A. 2000. Pizza cutting and eating
tool. U.S. Patent No. Des. 425,376.
Copyright © 2011 by Henry Petroski. Requests for permission to reprint or
reproduce this article should be directed to the author at [email protected].