If You Lift the Corner of the Carpet

Ali Bahmani on Origami, Mathematics, and What Happens When You Pick Up a Sheet of Paper — Cozy Corner with Hossein Nasiri, Episode 88

There are no shortcuts. You have to go through all those paths. You have to try all the different combinations as much as you possibly can, until you reach a point where you say: okay, this one is left. Now I will push this one a bit further and something new will appear.

That is how Ali Bahmani describes the discipline behind origami design — and it serves equally well as a description of the conversation itself. In this episode of Cozy Corner with Hossein Nasiri, Bahmani, an origami artist based in Canada and one of roughly 300 to 500 artists worldwide who have their own original designs, published works, and exhibition history, takes Hossein — and anyone watching — on a long, wide-ranging journey through what origami actually is, why it matters well beyond paper cranes, and how a single fold line, correctly placed, becomes the boundary between mathematics and something closer to poetry.

Sadako and the Thousand Cranes

The episode opens with a story that has spread far beyond origami: Sadako Sasaki, a child survivor of Hiroshima who, hospitalized from radiation exposure years after the bomb, was told by a nurse that folding a thousand paper cranes would grant any wish she made. She started. She reached around six hundred before she died. Her classmates folded the remaining four hundred to complete the count. Today there is a memorial in Hiroshima, and every August, thousands of cranes — sometimes tens of thousands strung on threads — are brought as a tribute.

The crane, Bahmani notes, is not just Japan’s most recognized origami design. It is globally understood as a symbol of peace. And its story has become one of the most widely referenced in fiction, film, and music — including, Hossein adds, a music video by Iranian filmmaker Amirhossein Darafsheh that fully recreated the narrative.

“Ori” Means Folding. “Gami” Means Paper.

Origami as a word is Japanese, and the Japanese were largely responsible for building its global brand — partly through the name itself, which has no equivalent shorthand in other languages even though the concept (paper folding) translates literally into German, English, Persian, and elsewhere. As for its origins: written documentation exists from four or five hundred years ago in Japan, though Bahmani is skeptical of claims that stretch the history all the way back to the invention of paper itself. What is certain is that for most of its recorded history, origami was an oral tradition — a pastime passed person to person, with fewer than fifty designs in circulation. It remained that way until, roughly, a hundred years ago.

The Man Who Invented a Tradition

The hinge of origami’s modern existence is one man: Akira Yoshizawa, a Japanese artist who — almost single-handedly, and across a lifetime of ninety-five years — took the small, limited repertoire of traditional origami and turned it into a full technical discipline with dozens of distinct methods. His Wikipedia page credits him with designing fifty thousand origami models. Bahmani simply says: it is truly unbelievable.

Yoshizawa worked intuitively. He did not write equations. He folded. He discovered. And the tradition he created was already spreading internationally before he died — in parallel, similar explorations had been happening in Spain, Germany, and China, though without a figure of his stature or documentation.

Alongside Yoshizawa, Bahmani describes the Bauhaus connection: Josef Albers, teacher and theorist of color, who brought a pack of paper into his classroom at Bauhaus and told students they had a cheap material and had to invent something with it. Some of the geometric origami techniques that emerged from that era still have applications in aerospace today.

Every Fold Creates a Line. Every Line Has Geometry.

The most intellectually rich section of the episode is Bahmani’s explanation of what origami’s relationship to mathematics actually looks like in practice. Every fold creates a crease line on the paper. That line has geometry. That geometry can be studied, simulated, and designed. It is not merely decorative — it is Euclidean geometry, angles, points, divisions — and many geometric constructions that students learn with ruler and compass can be reproduced through folding alone.

In 2014, Bahmani and his friend Kyumars Sharif Moghaddam (then a mathematics student at the University of Tehran) wrote a paper presenting a method for teaching fractal geometry to middle school students using origami. Rather than explaining self-similar patterns abstractly, they gave students a physical model — a series of small cubes that locked together, each iteration larger than the last, based on the Sierpinski triangle pattern, but volumetric. They presented the paper at the University of Tokyo at the Origami Science Mathematics Engineering conference, held every four years in a different country. It was published in the sixth volume of OSME, by the American Mathematical Society.

“If you actually build that fractal with your own hands,” Bahmani says, “you are physically touching that geometry and seeing the result. That gives you another level of connection with the concept.”

Categories: From Crane to Miura Fold

Bahmani walks through the main categories of origami with examples at hand throughout the conversation. Representational origami depicts a recognizable object — a peacock, a frog, a scorpion — and ranges from simple to so detailed it seems impossible from a single sheet. Tessellation is a repeating geometric pattern that, in principle, could be continued indefinitely: the only limits are time, skill, and materials. Bahmani describes a piece by his German friend Robin Schulz, sent in 2019 and now framed on his wall — a single sheet of paper, no cuts, with individual folds spaced roughly one millimeter apart across the entire surface, hand-done.

Modular origami assembles multiple sheets locked into each other without glue, the locking mechanism being part of the design itself — a technique that has been used in architectural installations. And then there is the Miura fold: named after both Josef Albers (who used a similar structure) and Japanese engineer Miura, it is the origami principle behind folding solar panels for satellites and spacecraft, where the entire surface collapses and expands with a single motion.

Curve origami, which Bahmani describes without a physical demonstration, uses curved fold lines rather than straight ones, opening a completely different category of forms and applications. Kirigami (cutting plus folding) and pop-up techniques — both ninety-degree and the rarer one-hundred-and-eighty-degree format seen in children’s books — round out the main categories.

Airbags, Tetra Pak, and Toyota

One of the episode’s most surprising threads is the range of industries where origami thinking has genuinely been applied. Bahmani mentions packaging design (reducing material waste by starting from a single sheet and folding it into the final form), furniture (IKEA logic, but more so), architectural envelope design, the pleating techniques in fashion that have been used for generations, and solar panels. He adds a specific example: Tetra Pak at some point ran an open call to the origami community asking for help solving a design problem. The packaging visible in Tetra Pak products today, he suggests, reflects that collaboration.

He describes a collaboration with a Toyota subsidiary at an origami conference — the company approached him, offered to prototype his designs in metal, and produced a steel version of one of his tessellations using their high-level automotive manufacturing expertise. The reason origami applies to airbag engineering, he explains, is simulation: you cannot crash four hundred cars to observe every possible airbag folding behavior. You have to simulate it. Simulating a folded sheet requires mathematics — specifically the mathematics of how that sheet collapses and expands under various conditions. Origami provides that mathematical framework.

MirOrigami — Folding Metal, Thinking in Reflection

Bahmani’s most personal technical development is a body of work he calls MirOrigami — a name combining mirror and origami. He began experimenting with folding steel sheets: mirror-finished, laser-cut to allow folding (metal’s thickness requires that the fold lines be cut open, otherwise the material is too rigid), and assembled by hand into installations. The surface reflects light and surroundings the way Iranian mirror work does, but the underlying structure is entirely origami.

He describes prototyping these designs first in paper, then translating to metal — same pattern, same geometry, different material and scale. A prototype from the Toyota collaboration sits on the table during the conversation: a steel tessellation, single sheet, foldable by hand. He presses it flat and reopens it to demonstrate.

The Exhibition at Bauhaus Was Forty Years Before Your Model

One of origami’s persistent and genuinely fascinating problems, Bahmani notes, is convergent design: two artists, working independently without knowledge of each other, arriving at the same or similar folding. He has a model whose tutorial has two or three hundred thousand views on YouTube — and only later discovered that something nearly identical had been made by a Japanese artist forty years earlier. The origami community, he says, treats this with a relaxed acknowledgement: it happens. It is almost expected, given how constrained the mathematical space of possible folds actually is.

The Book That Arrived From the United States

The most personally charged moment in the conversation is Bahmani’s account of how his serious engagement with origami began. He was a university student, had known origami only as simple shapes from childhood in Japan and then school. Around 2009 or 2010, he visited an exhibition at Amir Kabir University with friends and saw complex, unusual designs he had never imagined possible from paper. He was around twenty or twenty-one.

He started following the international community through an email-based forum, which was then the active center of global origami discussion. He emailed Peter Engel, an architect and author of Origami from Angelfish to Zen — a book he had found and loved. He didn’t expect a reply. Engel replied. They exchanged emails. Then, from the United States, Engel mailed him the book — already out of print — along with two newer books, spending approximately a hundred and fifty dollars of his own money, and signed them.

The inscription reads: “To Ali. Wishing you a fabulous and fantastic folding fan. Best wishes. Peter Engel.” October 18, 2012.

That package, Bahmani says, changed his life. It showed him the community was real, generous, and worth joining. By 2012 he and Kyumars had already decided they wanted to present at the Tokyo OSME conference in 2014. They hadn’t yet imagined writing a paper.

The Cozy Corner — When the Problem Becomes Interesting

Asked where his own cozy corner is, Bahmani’s answer is not a place: it’s a state. The moment a problem appears and he can see, somewhere in his mind, the beginning of a path toward solving it — that is when everything else falls away. He doesn’t necessarily start with a clear goal. It might begin from conversation, or from noticing something, or from play: what happens if we do it this way? Then suddenly something clicks and he follows it all the way through. He describes this as the environment in which he produces — problem becomes exciting, creativity follows.

A Dedication

Bahmani dedicates the conversation to the people who brought him into origami — Peter Engel and dozens of others like him across the global community — who reached out to a young artist starting from almost nothing, answered emails, sent books across oceans, and held workshops with him despite having forty or fifty years more experience. He adds that he hopes this conversation itself becomes that same kind of window for someone watching: that if they lift the corner of the carpet, they might find something extraordinary underneath.