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Learn Origami Mathematics and Geometry with The Greatest Dream Origami Toshi



The Greatest Dream Origami Toshi




Origami is the art of folding paper into various shapes and forms, such as animals, flowers, stars, and more. Origami is popular around the world for its beauty, simplicity, creativity, and fun. But origami is more than just a hobby or a craft. It is also a science, a mathematics, a philosophy, and a dream. And no one knows this better than Toshikazu Kawasaki, the greatest dream origami toshi.




The Greatest Dream Origami Toshi


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Toshikazu Kawasaki is a Japanese mathematician and origamist who has created hundreds of original origami models, including the famous Kawasaki rose and the Kawasaki snowflake. He is also known for his dream of creating a perfect origami model that can be folded from any shape of paper, with any number of sides, without any cuts or glue. In this article, we will explore the fascinating world of origami and Toshikazu Kawasaki, and learn how to make some of his amazing origami models.


What is origami and why is it popular?




Origami is derived from the Japanese words "ori" meaning folding and "kami" meaning paper. It is believed that origami originated in China around the first or second century AD, when paper was invented. Paper was then brought to Japan by Buddhist monks in the sixth century AD, where it was used for religious ceremonies and rituals. Origami became a popular art form in Japan during the Edo period (1603-1868), when paper was more widely available and affordable.


Origami is popular for many reasons. Some people enjoy origami as a relaxing and meditative activity that helps them focus and calm their minds. Some people like origami as a creative and expressive outlet that allows them to make beautiful and unique artworks. Some people appreciate origami as a scientific and mathematical challenge that involves geometry, symmetry, angles, fractions, and patterns. Some people love origami as a cultural and educational tool that teaches them about different countries, animals, plants, legends, and stories.


The history and evolution of origami




Origami has a long and rich history that spans across different cultures and eras. Some of the earliest examples of origami are found in ancient China, where paper was used to make ceremonial objects such as boats, lanterns, boxes, and envelopes. In Japan, origami was used to make sacred offerings such as cranes, frogs, butterflies, and flowers. In Europe, origami was introduced by travelers and traders who brought paper from Asia. Origami was also influenced by other paper arts such as kirigami (cutting paper), quilling (rolling paper), and papier-mâché (molding paper).


Origami has evolved over time as new techniques, styles, and materials were developed. Some of the most influential origami masters include Akira Yoshizawa, who pioneered the use of wet-folding and created thousands of realistic origami models; Robert J. Lang, who applied computer algorithms and engineering principles to design complex and realistic origami models; and Toshikazu Kawasaki, who discovered the mathematical formulas and methods for folding regular polygons from paper.


The benefits and challenges of origami




Origami has many benefits for people of all ages and backgrounds. Origami can improve one's cognitive skills, such as spatial reasoning, logic, problem-solving, memory, and concentration. Origami can also enhance one's artistic skills, such as creativity, imagination, color sense, and aesthetics. Origami can also foster one's emotional skills, such as patience, perseverance, confidence, and satisfaction. Origami can also promote one's social skills, such as communication, cooperation, and friendship.


Origami also has some challenges that require one's attention and effort. Origami can be frustrating and difficult at times, especially when the paper is too thick or too thin, when the folds are not precise or symmetrical, when the model is too complex or too simple, or when the instructions are not clear or complete. Origami can also be expensive and wasteful at times, especially when the paper is rare or imported, when the model is large or intricate, or when the paper is damaged or discarded.


Who is Toshikazu Kawasaki and what is his dream?




Toshikazu Kawasaki is a Japanese mathematician and origamist who was born in 1955 in Sapporo, Hokkaido. He graduated from Hokkaido University with a degree in mathematics in 1979. He then worked as a high school teacher for 10 years before becoming a lecturer at Sasebo College of Technology in 1989. He is currently a professor at Kawasaki University of Medical Welfare in Kurashiki.


Toshikazu Kawasaki is best known for his contributions to the field of origami mathematics and geometry. He has published several books and papers on origami theory and practice, such as "The Science of Origami", "Origami for the Connoisseur", "Origami Dream World", and "The Greatest Dream Origami". He has also created hundreds of original origami models that are admired for their elegance, beauty, and simplicity.


Toshikazu Kawasaki has a dream of creating a perfect origami model that can be folded from any shape of paper, with any number of sides, without any cuts or glue. He calls this model the "universal molecule". He believes that this model would be the ultimate expression of origami as an art and a science. He has been working on this dream for over 30 years, and he has not given up yet.


The biography and achievements of Toshikazu Kawasaki




Toshikazu Kawasaki was fascinated by origami since he was a child. He learned how to fold origami from his mother and his grandmother, who taught him traditional Japanese origami models such as cranes, boats, boxes, and flowers. He also learned how to fold origami from books and magazines that he borrowed from libraries and bookstores. He started to create his own origami models when he was in elementary school.


Toshikazu Kawasaki became interested in mathematics when he was in high school. He enjoyed studying geometry, algebra, calculus, and trigonometry. He also liked to solve puzzles and problems that involved numbers, shapes, patterns, and logic. He decided to pursue mathematics as his major in college.


Toshikazu Kawasaki combined his passion for origami and mathematics when he was in college. He began to explore the mathematical principles and formulas that govern the folding of paper into various shapes and forms. He also began to experiment with different types of paper and folding techniques to create new and original origami models.


Toshikazu Kawasaki made several breakthroughs in origami mathematics and geometry that earned him recognition and respect from the origami community. Some of his most notable achievements include:


  • Discovering the Kawasaki theorem in 1989, which states that the sum of the odd angles around a vertex on a flat-folded crease pattern is equal to 180 degrees.



  • Discovering the Kawasaki-Justin theorem in 1997, which states that a flat-foldable crease pattern with only one vertex must have an even number of creases.



  • Discovering the Kawasaki formula in 2003, which gives the exact angle for folding any regular polygon from a square paper.



  • Discovering the Kawasaki method in 2005, which gives a general procedure for folding any regular polygon from any shape of paper.



  • Twist the center of the star with your fingers or a tool to create a spiral. Twist it firmly and tightly, making sure it stays in place.



  • Fold and tuck some edges and corners of the paper to create details such as thorns, leaves, stems, or buds. You can use scissors to cut some parts of the paper if you want.



  • Your Kawasaki rose is complete! You can use it as a decoration, a gift, or a part of a larger origami structure.



How to make a Kawasaki snowflake




The Kawasaki snowflake is another famous origami model by Toshikazu Kawasaki. It was invented by Toshikazu Kawasaki in 2005, and it is based on his mathematical method for folding any regular polygon from any shape of paper. The Kawasaki snowflake has a symmetrical appearance with six arms and six pockets. It is also modular, meaning that it can be combined with other snowflakes or other origami models to create complex structures.


Step 1: Fold a hexagon from a square paper




The first step to make a Kawasaki snowflake is to fold a hexagon from a square paper. This is based on the Kawasaki method, which gives a general procedure for folding any regular polygon from any shape of paper. The method involves finding the center of the paper, dividing the paper into equal parts, and folding along bisectors of angles. Here are the instructions:


  • If you are working with colored paper, start with the color you want the finished snowflake to be facing up. (if you are working with printer paper, you may have a diagonal crease as a result of creating a perfect square, this is fine) Fold the paper in half from the edge, then turn the paper 90 degrees and repeat.



  • Unfold the paper and mark the center point of the paper by pinching it lightly with your fingers.



  • Fold one corner of the paper to the center point. Do this on all four corners.



  • Unfold the paper and mark the midpoint of each edge by pinching it lightly with your fingers.



  • Fold one edge of the paper to the midpoint of the opposite edge. Do this on all four edges.



  • Unfold the paper and mark the intersection point of each pair of creases by pinching it lightly with your fingers.



  • Fold one corner of the paper to the intersection point that is closest to it. Do this on all four corners.