Paper cones serve the same function as wrappers or paper bags. It is difficult to ascertain the origin of such containers as they have been used in most European countries as well as the Middle East. Oddly, they appear to be unknown in China despite its early use of paper and tradition of ingenious packaging. During the period when goods were delivered to stores in bulk, individual portions of small items such as seeds, buttons or candy were often handed over to the customer by the merchant in cones. Being frequently used in their homelands, paper cones continued to be used by early Carpatho-Rusyns immigrants to the United States. Paper containers of this kind are called "kooljoks" in slavic languages.
At the beginning of the 21st century kooljoks are still in use in the Ukraine, Russia and other eastern countries although even there they are slowly being supplanted by plastic bags. They are still the totally predominant form of packaging for individual portions of such things as sunflower seeds when sold in open outdoor markets.
The picture to the left shows a young man and a woman selling sunflower seeds in Ukraine. In front of them are four bags of black shelled sunflower seeds. The boy is tearing out pages from a catalog and handing the pages to the more experienced woman who folds the paper into kooljoks. As she completes each kooljok she sticks it inside the ones made previously. Three stacks of finished kooljoks can be seen sticking out from under one of the bags of seeds in front of her.
When approached by a customer, the seller takes one of the kooljoks and fills it with seeds using a standard measure. One such standard measure (green) can be seen in the bag in front of the boy. These standard measures are always filled in front of the customer to their maximum extent (heaping) in order to demonstrate to customers that they are receiving the full amount. Usually, a few extra seeds are then added manually to the contents of the kooljok as kind of a good will bonus.
Among the Carpatho-Rusyn community in America, newspaper and brown wrapping paper were common construction materials for kooljoks. In Eastern Europe at the turn of the 21st century, the primary construction material consists of newspaper or pages torn from old books. Frequently, arks of such paper are torn carefully in half, across the paper's shortest dimension, to provide cones of smaller size. Advertising material or pages torn from magazines is also sometimes used.
There are two basic methods of constructing such cones. One is rather roughshod but quick, and is used when there is no particular need to prevent leakage or loss of contents. The primary purpose of such cones appears to be merely to maintain order in one's shopping bag. Such cones are made by simply rolling a cone from a rectangular sheet of paper and then hinder it from unraveling by inserting one hand into the cone to provide counterforce and then using the other hand to pinch the point of the cone, force it inward about one centimeter while at the same time twisting it a quarter or half turn. Kooljoks of this type are frequently made from half or whole sheets of newspaper.
There is a second basic method of making a kooljok that is quite ingenious and which can result in a sturdy enclosure so tight that even something as fine as salt can be carried about in it without leakage. It took a long time for this author to become aware of the fact that there were several basic types of kooljok and that there was often great skill and ingenuity involved in their construction. After this awareness, this author has examined and measured a large number of kooljoks and has even taken lessons in their construction from women in Ukrainian markets.
A basic procedure for making kooljoks, as described below, was first shown to this author by an old woman selling sunflower seeds at an outdoor market on the outskirts of the city of Volgograd, Russia. Her instructions were more along the lines of "like this..., and like this..., then like this..., and then... so there!" But with some quite enjoyable practice this author has been able to duplicate her technique.
This type of kooljok can be made out of paper of almost any size. Useful cones for small items can be made from sheets of paper as small as 10 x 16 centimeters (4 x 6 inches) with little difficulty. The instructions below apply when making a cone out of a sheet of paper of letter or A4 size. To make cones out of paper of other sizes, the measurements presented in the instructions below can be suitably scaled.
To make a cone out of a sheet of paper of letter or A4 size, begin by placing the paper horizontally in front of you. Fold the paper vertically about 8 centimeters (2 1/4 inches) from the left hand edge. It is of some importance that this fold is exactly vertical. This can be assured by making sure that the bottom edges coincide exactly when preparing the fold.
The next fold is made by folding the lower right hand corner of the paper upwards towards the top of the sheet. That this fold be made at the correct angle is probably the most important step in making a successful cone. Following the procedure below will help assure that this angle is made properly.
Begin this fold by pressing a finger- or thumbnail of the left hand down on the vertical crease at the very bottom of the paper as is indicated by the dot in the first diagram.
When pressure is being applied with a finger- or thumbnail of the left hand, it is possible to keep the edge of the paper at a slight tension while the rest of the fold is being made with the right hand. This will help assure that the fold radiates directly from the point where the vertical fold meets the bottom of the paper. As this fold is being made, try to make the angles "a" and "b" exactly equal. Origamist Kenneth Kawamura has pointed out that you can guarantee that angles a and b are equal if the corner that was initially the lower right corner of the paper comes to rest on a vertical midline (not indicated in the diagram), halfway between the first fold and the right edge of the paper. This is a geometrically exact construction procedure but it does not appear to be in common use.
The next fold is made by again bringing up the right folded edge. This time to a position on top of the first, vertical, crease. Making sure that these coincide exactly will, in effect, reduce by half any errors made when attempting to equalize the angles "a" and "b" as described above.
A similar procedure is followed twice more, using the triangular portion already made as a guide. First once...
And then a second time...
The next fold is made by folding the sharp point upwards and down, making the crease at the middle of the small tab that extends to the left of the point. The point should then lie on, or ever so slightly below the point where the upper part of the tab extends from out below the developing cone.
Now the cone is almost complete and only a few steps remain. Make the short fold indicated by the dotted line in the diagram to the left - then push the tab "d" into the little pocket formed by the point that has been previously folded over. This effectively keeps the cone from unrolling.
Naturally, this basic kooljok would function equally as well in its mirror-image form. This author has determined that kooljoks of the basic form as described above and its mirror-image form are about equally frequent. The mirror-image form, however, is more frequent when the maker is very skilled and highly practiced. The reason for this is that such women are so skilled that they do not need to actually make any of the creases. They merely roll a cone with the right hand so that the point of the cone is at the upper left hand corner of the paper, turn the point towards themselves and then flatten the point of the cone so accurately that the cone and locking tap are at the correct angles. This author has observed one woman who could judge the angle of the sides of the cone and the angle of rotation of the cone so exactly at the moment that the point was flattened that she could repeatedly construct kooljoks with both angles accurate to about 1 or 2 degrees of arc.
Sometimes a kooljok is left open when handed over to the purchaser. This is often the case when the contents are intended to be used immediately, such as candy or sunflower seeds. At other times the kooljok is sealed and there are two basic ways of doing this. If the cone is not to be filled too full and if the contents are something easily flattened like seeds or salt, then a flap can be constructed that will contain the contents. In the diagram above, a flap, "e", can be formed by folding the cone backwards along the line "f-f". This produces the flap which can be pushed down in between one of the layers of paper on the side of the cone to effectively seal it. With more bulky contents, the kooljok is closed by covering the contents using the paper of the cone opposite the flap and then folding the flap down at a sharp angle to prevent the first layer of paper from lifting.
There are optimal dimensions for the paper from which one makes a cone using the procedure above - there is a set of dimensions that reduces the occurrence of loose edges, that maximizes the size of the tab that holds the cone together while producing a flap that tightly seals the top so that even the very smallest items such as seeds or salt will not leak out.
The diagram below presents the paper dimensions and main folds for such a cone.
Here the width of the paper is about 73% greater than the height of the paper. The mathematically interested reader will recognize this as the height times the square root of 3. Measured from the right edge of the paper, the vertical crease is at a point 1.15 times the paper's height - two thirds of the paper's width. The first four folds are at 30-degree angles from one another.
When the cone is made from paper with these dimensions, the sides of the cone largely consists of three layers of paper and when sealing the cone with the flap one has the choice of placing it rather loosely between the shorter outer layer and the second layer or pushing it more securely down between the second and third layers. This cone has a minimum length of paper edge on the inside, reducing the possibility of leakage.
In the description above, all the main angles are at 30 degrees, both the angle of the cone itself as well as the locking tab. Variations from these 30-degree cone and tab angles may arise for a number of reasons. The available paper may not be of suitable dimensions. The maker of a kooljok may also wish to have the outer edges of the cone at an angle greater than 30 degrees in order to increase its volume. Often, too, the maker of a kooljok is forced to work quickly, resulting in inaccuracies in the angles of the folds. Still another reason for departure from 30-degree angles appears to be a desire to have a more symmetric closing flap. For these and other reasons there are often variations from the 30-degree angles described in the procedure above. Slight variations from these angles, however, can result in such large deviations in the relative size and position of the locking tab and pocket that it is not possible to securely hold the kooljok together. The tab near the point of the cone can be too small to prevent the cone from unraveling.
The diagram to the left illustrates this point. It shows the point area of a kooljok just prior to forming the locking tab. The "cone angle" (abc) is the flattened part of the cone itself while the "tab angle" (abd) is that part of the paper which is to become the locking tab.
This diagram demonstrates what can happen if the lower point of the kooljok, "b", is folded upward onto point "a" as in the procedure described for the idealized and carefully measured kooljok. When folded along the dotted line to form the locking tab, the tab "e" is too short to fit very deeply into the pocket "af." Such a kooljok would unroll easily. The author has found one example where this problem has been solved by folding the tab slightly within the cone itself so that a portion of the cone is used to lengthen the tab. This is a somewhat primitive solution and suitable only with rather thin paper.
A more generalized kooljok-making algorithm is described below. It is a rather ingenious generalization of the procedure already described and it is totally equivalent to it when the cone and tab tip angles are 30 degrees. It allows a sturdy container to be constructed even in cases where there is rather large deviations from the 30-degree angularity of the cone and tab tip. This generalized procedure begins by making a cone with a angle (flattened) from between 25 up to about 50 degrees. The folding is continued until there remains a flap of paper at something less than 90 degrees. Then a point, denoted by "x" in the diagram to the left, is found on the outer or right edge of the cone. Two red help lines have been drawn in the diagram to show how the position of point "x" is determined. Of course these two help lines are never drawn in actual practice but are shown here merely to show to the reader what a skilled kooljok maker is looking for when determining the position of point "x." The skilled kooljok maker attempts to estimate half the angle "cab," as for example, "cad" or "dab." This estimated angle is then translated along line "ab." Done successfully, the angles "cad," "dab" and "bax", are then all equal. This gives the position of point "x".
Point "b" is then folded up and oriented directly towards "a" and the edge segment "xb" is superimposed along the line "ax." The tab "adf" remains. This procedure guarantees that when this tab is folded across the cone along the line "af" there remains sufficient paper, "ade" to be pushed down behind a sometimes incomplete but deep pocket "afx." When the cone and tab angles are exactly 30 degrees this more generalized procedure in identical to the method first described.
The bottom of a kooljok has two corners. The angles of these two corners are uniquely determined by the "cone angle" and the "tab angle," that is the angle of the flattened cone and the angle made by the bottom edge of the tab of paper that extends away from the cone and from which the locking tab is constructed. If "a" is the "cone angle" and "b" is the "tab angle" then one corner at the bottom of the kooljok is 112.5+a/2-b/4 and the other corner is 67.5+a/2+b/4. If, as in the first kooljok-making procedure described above, a and b are both 30 degrees then the two bottom corners are 90 and 120 degree. Measurements taken from a number of kooljoks obtained in markets show that the cone angle is typically about 35 degrees while the tab tip angle averages close to 40 degrees and have bottom corner angles of 95 and 120 degrees. Another source of variation is the selection of the point on the edge of the paper which is to become the very tip of the cone. By varying the location of this point, the length of the pocket and locking tab can be made shorter or longer, in some cases extending the entire length of the kooljok.
As noted previously, the two bottom corners of the completed kooljok are normally unequal. This author has, however, come across a variant fold being used by someone in the Ukrainian city of Lviv which results in a more symmetrical kooljok, a kooljok having equal angles at the bottom.
The picture to the left describes this variant fold producing a kooljok having equal angles at the bottom. During the completion of the kooljok the bottom fold must first be identified. This bottom fold is to have equal angles with the sides of the completed kooljok. This bottom fold is indicated here by a dotted line and the final and the equal corners are indicated by thick yellow angles. Before actually making this fold, however, an additional fold is made (indicated here in green) extending downward from the point "x" to "c" at the bottom of the paper. In other words, the point "b" is lifted up and a fold made along the green line. This fold is made in such a way that the two angles "f" are equal and determined by the angle between the line "ax" and the desired bottom fold indicated by the dotted line. Thereafter, this variant kooljok is completed as before. The folded edge "cx" is superimposed along the red line produced the pocket and the extended tip is folded into the pocket. Although this extra fold may strengthen the pocket, the purpose of this variation appears to lie entirely in the esthetic qualities of the added symmetry.
With these sources of variation, and with the repeatability achieved from frequent repetition, market women create kooljoks with the individuality of written signatures.