Origami: Where Sculpture Meets Mathematics
Mathematical Origami: Defying the Impossible
Computational origami theorist Erik Demaine has pushed the boundaries of origami, creating sculptures that defy the traditional understanding of what’s possible with paper folding. By alternating mountain and valley folds in concentric squares, Demaine has achieved the previously impossible: hyperbolic paraboloids, a shape that was thought to be unattainable in origami.
The secret lies in the intricate crease patterns that Demaine creates, resulting in structures that “pop into a saddle shape” resembling a Pringle. Demaine’s sculptures are not only visually stunning but also raise fundamental questions about the mechanics of paper folding.
The History of Origami
The origins of origami can be traced back to 1797 Japan, with the publication of Akisato Rito’s book “Sembazuru Orikata.” In the 1800s, origami became a popular classroom activity in Europe, and in the 1950s, it emerged as a modern art form under the guidance of Japanese artist Akira Yoshizawa.
Contemporary origami artists like Eric Joisel and Robert Lang have pushed the envelope further, creating lifelike animal and human figures and complex compositions that have been showcased in prestigious institutions like the Louvre and the Museum of Modern Art.
Origami and Mathematics
Origami has a deep connection with mathematics, particularly geometry. The fold-and-cut problem, first posed in a Japanese book in 1721, asks how many different shapes can be created by folding a rectangular piece of paper and making a single cut. Demaine’s solution to this centuries-old problem demonstrated that any shape is possible, given the right geometric blueprint.
Computational Origami
Computer programs have revolutionized the field of origami. Software like TreeMaker and Origamizer allow users to design and explore complex crease patterns, enabling the creation of intricate and innovative shapes.
Origami in Practical Applications
Beyond its artistic value, origami has found practical applications in various fields. Car manufacturers use origami mathematics to design airbags that fold efficiently. Engineers are exploring the use of origami structures in nanomanufacture, creating flat objects that can transform into 3D shapes. Additionally, origami principles could aid in the design of synthetic virus-fighting proteins.
The Father-Son Duo
Erik Demaine and his father, Martin, have collaborated to create mesmerizing origami sculptures. Their work has been featured in the Smithsonian’s Renwick Gallery, showcasing the intersection of art and mathematics.
The Allure of Origami
Origami continues to captivate artists and mathematicians alike, offering a unique blend of creativity, precision, and problem-solving. As Demaine aptly puts it, “We’ve come up with a math problem that inspires new art—and an art problem that inspires new math.”
