The all-corner fold, the blintz, is integral to origami. It is old: one of the first folds you learn, and new: an essential part of the origami techniques that took flight in the 20th century.
We will learn about the early history, the quest for pure origami and Gershon Legman, and the later history of the fold.
The Oldest Blintz Folds in Europe: Napkin Folds, 1629
The earliest use of the blintz fold can only be determined by studying sources that have come to light. The oldest evidence, so far, is an Italian booklet on napkin folding by Mattia Giegher published in Padova in 1629.1
Napkin folding was spread in other languages (in German, for example, by Georg Philipp Harsdörffer in 1640).3 See “Folded Beauty” by Joan Sallas4 for more on the fascinating history of napkin folding.
Baptismal Letters, 1700s
In Germany, in the 1700s, the use of baptismal letters, Taufbriefe, became common. They would often be printed with a beautiful decoration on the front in a pattern prepared for double-blintzing. The inside would contain printed scriptures and a handwritten name and date. The letter would be folded and given to the godfather with money inside.5
These baptismal letters are special in that the (double) blintz is the end result, employed to create a flat container. Thus they are the purest possible blintz model.
The widespread use of the double blintz was likely influenced by these common baptismal letters.
“Indeed, Fröbel’s own baptismal letter was folded in this shape.”7
The Oldest Evidence in Japan: ‘Ranma Zushiki,’ 1734
A Japanese woodblock print from the “Ranma Zushiki”8 (above), depicts a number of origami models.
Kunihiko Kasahara9 has analysed the print and concluded that the Yakko (E, a servant of a samurai) and the Ashitsuki-Sanpo (F, Japanese offering box with legs) are two of the models depicted, and those both utilize blintzes. The folding of the Yakko starts with no less than three blintzes from alternating sides, see the Yakko diagram in part 1 of this series.
The next time the blintz occurs is in “Kayaragusa” (aka “Kan no Mado”), from 1845, as a crease pattern for a wrapper for dried chestnuts (above). The diagram is incomplete, but if you make a blintzed preliminary base, outside reverse fold two of the blintzed flaps, and fold the bottom corner behind, you will get something similar to the drawing. I am, however, not aware of how it is supposed to be used as a wrapper.
Editor’s note: For more on the “Kan no Mado,” please see an article from issue 13 of The Fold reprising an email by David Lister.
Theodore Pomeroy11 has a different interpretation that explains the wrapper perfectly by suggesting the crease pattern is in error and should start with a diagonal fold. This leads to the following crease pattern, which at best is a “blintz” in a generalized sense, in that a square on the diagonal is still present.
Friedrich Fröbel (1782-1852) was a pedagogue who created the concept of the kindergarten. He formulated a number of activities to support the education of small children, including paper folding.12
Fröbel’s mathematical folds later became known as the folds of truth,13 one of his trinity of educational goals for the children:
“The first games that occupy a child pave a path for the child to attain, early on, a unified education in usefulness, beauty and truth.”14
In origami, these attributes become known as the folds of life, beauty and truth.
In 1850, Fröbel describes how to make the blintz as the first basic form, while elaborately pointing out elementary geometric properties,15 the folds of truth.
His description easily takes the prize as the most convoluted folding instructions ever, cast in 19th-century academic German without illustrations and intermixed with instructions to the children, mathematical truths and pedagogical observations. It is left as an exercise to the reader to try and follow his instructions.16
During the second half of the 1800s, Fröbel’s followers added models for his other two educational goals: folds of life and folds of beauty,17, 18, 19, 20, 21, 22 while mostly ignoring the geometric truths.
Most of the folds of life are double-blintz models. In 1869, Goldammer lists them as:
“A tablecloth, a bird, a sailboat, a double boat, a salt bowl, a flower, a shirt, a dragon, a windmill, a table, a cigar pocket, a flowerpot, a double box, a big box, a mirror, a boat, a boat with benches, etc.”24
Do you recognize the multiforms (of which Robert Harbin has a small set)?25 And the salt bowl, aka salt cellar, aka fortune teller?
The folds of beauty were all based on the blintz — or the windmill base derived from it — and they may best be described as the origami version of kaleidoscope patterns, as they obtain beauty via symmetrical repetition.
Michio Uchiyama organized origami into two broad systems of bases, the A system based, mostly on radial creases and the B system, based mostly on rectilinear creases,28 or rather, everything else. The system was maintained by his son Kochio, and the two theorists had quite an influence, particular in the Japanese origami community.
In the Uchiyama system, the blintz occurs as base number B10.29 The base is classified in the B-system because they used the medians (rectilinear) as landmarks. I wonder if it would have been in the A-system had they used the diagonals as landmarks.
Many of the models in Kayaragusa are rather complex, but typically, flaps are obtained by slitting the paper or cutting it into star shapes. This continued until fairly late in the 20th century. Origami master Isao Honda30 would use irregular shapes or cuts as required but also introduced compound figures to satisfy the need for more flaps:
“If you fold the front half of the body then the rear half, then join the two together, it is easy to make a number of animal folds including cats, dogs, elephants, rhinoceroses, etc.
“Though this method was not originally in common use, after we published our “Origami-shuko,” in 1940, in which we included a number of compound animal figures, this type of fold became very popular.”31
Even Honda’s pupil, the great master Akira Yoshizawa, used cuts and compound figures for all his complex models (examples above) for a long while. Yoshizawa also introduced the idea of gluing to attach two squares at overlapping corners, which essentially amounts to cutting the square into an irregular shape.33
However, Yoshizawa was not satisfied with those borderline techniques:
“Limit of origami: Beauty of origami exists in what is created from refraction of various surfaces and lines produced on a sheet of paper.
“Compound origami ... each separate piece should have its own individuality or personality. ... I don’t call any Origami a compound Origami, if it can only gain its individuality after being pasted or put together. It should be called a mosaic or paper craft.”34
Thus, a new understanding of what origami is emerges. The old origami (from before it is called origami) is seen as impure. Later on, Yoshizawa finds (non-blintz) techniques to make his now-famous models, such as the giraffe from 1987,35 with all the flaps from one square, and he becomes the father of modern origami.
The quest for the Holy Grail of origami — to fold anything from a single, uncut square, no matter how many flaps are needed — continued, leading to the bug wars of the 1990s, and ultimately resulting in box pleating, circle packing, Treemaker and mathematical models that proved the goal is theoretically possible.
The Sanpo and the Yakko of “Ranma Zushiki” are rather simple, the Yakko even crude and inefficient. Only the Lotus Flower (above) really utilizes the possibilities of the blintz: three or more blintzes to the same side, then invert the leaves to the other side, one by one.
However, we shall see how the blintz history writes itself into the quest for complex models from one uncut sheet.
In the early 1950s, Gershon Legman investigated folding all four corners to the center before folding an origami base, at which point the hidden-away corners could be retrieved again to form extra flaps, a standard technique in origami.
“An idea I had long cherished: namely, that one might construct all the usual bases — bird, frog, and fish — on the classic square paper, of which the four corners had first been “blintzed” to the center before constructing these bases. I felt, and I still feel, that this method of creating extra corners for use in the end-figure details makes unnecessary the excessive cutting into the paper seen in the “Kan-no-Mado” (Kayaragusa) and in the vulgar “koko” style foldings of Uchiyama senior. It even to a degree makes unnecessary the achieving of the same extra corners by the method of pasting together two square sheets at one overlapping corner, in the style made famous by Mr. Yoshizawa in all of his books, beginning with the figures he contributed to Mr. Isao Honda’s book “Origami Shuko” in 1944.”36
Legman goes on to write:
“The modern development of the blintz fold appears to be of Western origin. In Paris in 1953 and 1954, I showed the essentials of origami technique to the American origami artist, Mr. George Rhoads. ... I ... gave him [the idea to blintz the usual bases to make unnecessary the excessive cutting].”37
And indeed, Rhodes, a sculptor, later designed the now-famous elephant with four legs, trunk, tail, two tusks and two ears (above). This elephant is folded from the blintzed bird base. Diagrams are in Samuel Randlett’s “The Best of Origami.”38
That is one of the earliest examples of achieving naturalistic origami animals through the use of many flaps.
As early as the 1950s, farsighted origami designers made forays into these more complex bases. Yoshizawa, using a multiple-blintzed base, produced his remarkable Crab with 12 appendages, while Rhodes exploited the blintzed bird base for several distinctive animals, including his Elephant. But these were the exceptions.39
Countless children learn blintzing as one of the first folds in preschool when they meet the fortune teller, which is frequently used in commercial applications.
The blintzed bases are still used. An example is the blintzed lily designed designed a few years ago by Frederik Lenk.
Often, the multiforms, the fold of life, are learned, albeit outside the school system. Even Origametria,41 a system certified in Israel for teaching math through origami, seems to use neither the blintz nor the folds of truth.
The creative aspects of the folds of beauty have been rediscovered by origamists such as Kunihiko Kasahara.42 Leyla Torres demonstrates the creative aspects on her blog about windmill folds.43
In Germany, materials for Fröbelian folding are still in use and are sold through Labbé44 and Netzwerk Lernen,45 for example.
1. Mattia Giegher, Trattato delle Piegature (Padova: 1629), Universitätsbibliothek Basel. [back]
2. Giegher Trattato delle Piegature, plate 7. [back]
3. Georg Philipp Harsdörffer, Vollständiges TRINCIR-Büchleins — Der I. Theil. Von den Tafeldecken und desselben Zugehör (Germany: 1640). [back]
4. Joan Sallas, Gefaltete Schönheit (Freiburg: Joan Sallas, 2010). ISBN 978-3-00-032495-6. [back]
5. Andrea Kittel, “Taufbriefe,” Württembergische Kirchengeschichte Online, published 2014, accessed April 6, 2021, https://www.wkgo.de/cms/article/index/taufbriefe. [back]
6. Baptismal letter “Taufbrief” or “Patenbrief” (Germany: 1770). Owned by Hans Dybkjær. [back]
7. Michael Friedman, A History of Folding in Mathematics — Mathematizing the Margins (Cham, Switzerland: Birkhäuser, 2018). ISBN 978-3-319-72487-4 (ebook), 490, note 401. [back]
8. Ôoka Shunboku, Ranma Zushiki (Designs for Decorative Transoms), Woodblock-printed book. (Japan: Ônogi Ichibei. Japanese Edo period, about 1734). 19.4 x 26.3 cm. Downloaded Aug. 12, 2019 from the Museum of Fine Arts, Boston website: https://collections.mfa.org/objects/493254. The origami panel is about 45 pages to the right. [back]
‘Kayaragusa’, 1845
Fröbelian Folds, 1800s
Uchiyama, 1930s
The Quest for Pure Origami, 20th Century
Gershon Legman, 1950s
Modern times
Endnotes
10. Julia McLean Brossman and Martin W. Brossman, A Japanese Paper-folding Classic, (Pinecone Press, 1961). Library of Congress Catalog Card Number: 60.53693. An annotated facsimile of a precise copy of Kayaragusa’s Kan no Mado (Japan, originally handwritten around 1845), 6. [back]
11. Theodore “Ted” Pomeroy, comment on the original version of this article in an email communication to Jane Rosemarin, April 1, 2021. “The next wrapper [illustrated in the Ranma Zushiki], for Araiyone [Brossman and Brossman A Japanese Paper-folding Classic, 6], is similar to the paper cup of Western tradition, and the crease pattern is closer to being accurate. It is imprecise at the corners, which are sharp in the illustrated fold, but the diagonal is not drawn precisely through the corners. Perhaps the crease pattern diagrams in this book reproduce errors in these two cases. To make a wrapper for kachikuri: 1) Fold your paper into a triangle (diaper fold), 2) Fold the acute points up to the right-angle point (as in a samuri helmet), 3) Fold each of the acute point out so that a right angle is made where the folded edge meets the edge of the paper underneath, 4) Fold the base back to the rear (mountain fold) at the bottom point, 5) Open the two points at the top as your container.
“This does become an interesting and simply ornamented container for small items. Sometimes the diagrams are difficult [to follow], in this case I think there is an error, at least for the wrapper of the ‘dried chestnut’.” [back]
12. Friedman, A History of Folding, section 4.2.1. [back]
13. Wichard Lange, Friedrich Fröbels gesammelte pädagogische Schriften — Zweite Abtheilung: Friedrich Fröbel als Begründer der Kindergärten. (Berlin: Verlag von Th. Chr. Fr. Enslin, 1874). [back]
14. “der durch das erste Kinderspiel angebahnte Weg der Kinderbeschäftigung ... das Kind früh zu einstimmender Bildung für Nützlichkeit, Schönheit und Wahrheit erfaßt;” Lange, Friedrich Fröbels gesammelte pädagogische Schriften, 44. Translated by Jane Rosemarin. [back]
15. Friedrich Fröbel, Kinderbeschäftigung. Anleitung zum Papierfalten — Ein Bruchstück. Eine entwickelnd-erziehende und unterhaltend belehrende Kinderbeschäftigung für Kinder von 5 bis 7 Jahren und darüber, unter eingehender Mitwirkung von leitenden Erwachsenen (Germany, Friedrich Fröbels Wochenschrift, 1850). Reprinted in Lange, 1874, 371-388. [back]
16. Folding instructions for the blintz extracted from Fröbel, Kinderbeschäftigung (1850). Translated from the German by Hans Dybkjær with the aid of Laila Dybkjær.
Prior to the start of these excerpts, Fröbel described constructing a square through which a diagonal line is present. The omitted parts “...” represent pages of pedagogical remarks and mathematical truths.
“Then I place the square between the fingers so they are in the center of the square. Now from two opposite edges (last time it was from two opposite corners), and say: ‘proceeding as last time, while I place edge on edge and corner on corner, I divide my square with a cross-line in two equal parts or halves, that is, in two equal rectangles (according to the position)’.” [...]
“[We got] a rectangle where one long edge was closed and the other three edges open. From here we proceed and bend it together in the short cross-line so one half of the closed edge is folded onto the other half of that edge so that the two short edges are put together. This creates a square with a fully closed and a half-closed edge; the two other edges are fully open, in four parts.”
[… Meanwhile, Fröbel has unfolded everything to explain mathematical truths, and he has now returned to the rectangle, the book fold.]
“Place the paper folded like this with the closed side to the left, and you say: ‘I divide the square with a diagonal line in two equal parts; that is, in two right-angled, equal-angled triangles [rechtwinklig-gleichwinkliges Dreieck]’.
“As you now rotate the thus divided square downward and the opposite upward, you proceed as before and say: ‘I divide the square in two equally large parts, that is in two right-angled, equal-angled triangles’.
“‘I now open the rectangle, whereby that and a greater, right-angled, equal-angled triangle is in front of me’.”
[... After several remarks Fröbel somehow assumes we are now looking at the other side of the model.]
“For the children, the rectangle, with the divided squares next to each other, will be further divided in the two square areas with the well-known words: ‘I divide etc.’ Thus again, each of the two squares is divided by a diagonal line into two isosceles triangles with the well-known words, whereby you, as you see, get a single isosceles triangle, which, however, as you see by unfolding, is a square, which is two squares on top of or behind each other, of which one with two separating cross-lines is divided into four equally large parts, that is, four isosceles triangles, and the other, when turning it to the front, is also divided into four equally large parts, but divided into four squares with two cross-lines or cross-breaks.” [...]
“If you now fold the divided triangles outward, you end up with the main square again, and inside that the previous double square, now only indicated with crease lines, which are in the opposite position to the main square, and thus called the opposite square as it has its corners or angles where the main square has its edges or lines, and has its edges in the direction where the corners and angles of the main square are.” [...]
“With these four, with which, in addition to their comparison with the triangles, all previous observations are repeated for increasing clarity, the first basic form is now given, from which the first main forms necessarily develop.” [back]
17. J.-F. Jacobs, Manuel Practique de Jardin d’Enfants de Frédéric Froebel — a l’Usage des Institutrices et de Méres de Famille (Paris: C. Borrani, 1859). Google Books ebook. https://books.google.com/books/about/Manuel_pratique_des_jardins_d_enfants_de.html?id=fEJAAAAAcAAJ [back]
18. Elise van Calcar, Kleine Papierwerkers — Wat men van een stukje papier al maken kan. Het Vouwen. (Amsterdam: K. H. Schadd, 1864). [back]
19. H. Goldammer, Das Kindergarten. Handbuch der fröbel'schen Erziehungsmethode, Spielgaben und Beschäftigungen — Nach Fröbels Schriften und den Schriften der Frau (Berlin: B. v. Marenholz-Bülow, Carl Habel, 1869). [back]
20. Bertha von Marenholtz-Bülow, Theoretisches und praktisches Handbuch der Fröbelschen Erziehungslehre — Zweiter Teil: Die Praxis der Fröbelschen Erziehungslehre (Kassel: Georg H. Wigand, 1887). [back]
21. Eleonore Heerwart, “Course for Paper Folding — One of Froebel’s Occupations for Children” (England, 1895). Reprinted in John Smith (ed.), Conference of Origami in Education and Therapy (England: British Origami Society,1991), 101-153. [back]
22. Marie Müller-Wunderlich, Die Fröbelschen Beschäftigungen. 2 Heft: Das Falten, Friedrich Brandstetter (Leipzig: ca. 1900). [back]
23. Marenholtz-Bülow, Theoretisches und praktisches Handbuch, das Falten Tafel III.[back]
24. “Ein mit den vier Zipfeln herunter hängendes Tischtuch, einen Vogel, ein Seegelboot, einen Doppel-kahn, ein Salz-näpfchen, eine Blume, ein Hemdchen, einen Drachen, eine Windmühle, einen Tisch, eine Cigarrentasche, einen Blumentopf, einen Doppel-kasten, einen großen Kasten, einen Spiegel, ein Boot, ein Boot mit Bänken u. s. w.” Goldammer, Das Kindergarten, 109. [back]
25. Robert Harbin, Origami — the Art of Paper Folding (London: Barnes & Nobles Books, 1979). ISBN 0-06-463496-5. [back]
26. Jacobs, Manuel Practique de Jardin d’Enfants de Frédéric Froebel. [back]
27. Marenholtz-Bülow, Theoretisches und praktisches Handbuch, figures 36 and 41 in das Falten Tafel III. [back]
28. Robert J. Lang, Origami Design Secrets — Mathematical Methods for an Ancient Art. (Boca Raton, Fla.: CRC Press, 2012). ISBN 978-1-4398-6774-7, 58-60, ebook. [back]
29. Robert J. Lang, Origami Design Secrets (2012), Figure 4.5. [back]
30. Isao Honda, The World of Origami, (Tokyo: Japan Publications, second edition 1966. First edition 1965). [back]
31. Honda, The World of Origami, 40. [back]
32. Akira Yoshizawa, Sosaku Origami (Creative Origami), (Tokyo: Kamakura Shobo, 1973). ISBN 1072-0030-0952. Translation leaflet by Itsu Suzaki, courtesy of Friends of the Origami Center of America, New York. [back]
33. Gershon Legman, “Secrets of the Blintz: Historical and Technical.” In The Origami Companion, a newsletter created by Dokuohtei Nakano. Part 1 was published in newsletter number 4 (1972); Part 2 in newsletter number 5 (1973); Part 3 in newsletter number 6 (1973); Part 4 in newsletter number 7 (1973). Courtesy The Gershon Legman Archives, Laura Rozenberg, Museo del Origami, Uruguay. [back]
34. Akira Yoshizawa, Sosaku Origami, 40. [back]
35. Akira Yoshizawa, Origami Museum I: Animals (Creative Origami), (Tokyo: Kamakura Shobo, 1987). ISBN 0-87040-737-6. [back]
36. Gershon Legman, The Origami Companion, 1972. [back]
37. Gershon Legman, The Origami Companion, 1972. [back]
38. Samuel Randlett, The Art of Origami. Paper Folding, Traditional and Modern (New York: E. P. Dutton, 1961). [back]
39. Robert J. Lang, Origami Design Secrets: Mathematical Methods for an Ancient Art, (Natick, Mass.: A. K. Peters, 2003), 64. ISBN 1-56881-194-2. [back]
40. Hans Dybkjær, Roskilde Festivalavisen 2009, accessed April 11, 2021 from https://papirfoldning.dk/da/ugensfold/2009-27.html. [back]
41. Miri Golan, Origametria, 2017, accessed April, 11, 2021. https://origametria.com. [back]
42. Kunihiko Kasahara, The Art and Wonder of Origami (England, Apple Press, 2004). ISBN 1-84543-061-1. [back]
43. Leyla Torres, Windmill base variations, 2011, accessed April 11, 2021. https://www.origamispirit.com/2011/05/windmill-base-variations-video/. [back]
44. Labbé: Search results for “Fröbel”: Edition Fröbel: Das Falten. https://shop.labbe.de/catalogsearch/result/?q=fröbel, accessed April 6, 2021. [back]
45. Netzwerk Lernen “Unterrichtsmaterialien” (Learning Network “Teaching Materials”), accessed April 6, 2021, https://www.netzwerk-lernen.de/advanced_search_result.php?keywords=origami. [back]
Other Articles in This Series
“The Complete Blintz Part 1: The Yakko”
“The Complete Blintz Part 3: Blintz Story Telling”
“The Complete Blintz Part 4: The Dragon and the Might of the Blintz”
“The Complete Blintz Part 5: Creating via Blintzing”
“The Complete Blintz Part 6: The Cushion Fold”
“The Complete Blintz Part 7: Deconstructing the Corner Fold”
“The Complete Blintz Part 8: A Longer Masu Box by Grafting”
Comments
Although is not paperfolding, this is an early picture of the Blintz base in the ancient Babilony (circe 1700 BC) . https://public.csusm.edu/aitken_html/m330/Meso/BabGeom.JPG
Hi Jose, thanks for the reference. Interesting. The geometry is indeed old. I guess they didn't fold the clay tablets :-)
As you indicate, it sure is the oldest drawing resembling the blintz crease pattern. Even if the intent to fold isn't there, the idea of the four triangles equaling the internal square is present.
Best regards,
Hans