Origami robert lang pdf

This work was composed during a trip to Kenya, then fine-tuned and folded after my return to Alamo. Crease patterns CPs provide a one-step connection from the unfolded square to the folded form, compressing hundreds of creases, and sometimes hours of folding, into a single diagram! A CP can sometimes be more illuminating than a detailed folding sequence, conveying not just "how to fold," but also how the figure was originally designed.

Mathematical and geometric CPs usually show all the creases, but representational origami rarely shows every crease in the finished form, as it would make the crease pattern impossibly busy. Instead, the crease pattern gives the creases needed to fold the "base," that is, a geometric shape that has the right number and arrangements of flaps.

It is still left up to the folder to add thinning and shaping folds. Office of Government Relations. Mathematics Calendar. One uncut square of St. One uncut square, 15", , a composition in the series of origami fish. One uncut square of kozo paper with lnclusions, 8", composed , folded One uncut square of Korean hanji, 8", composed , folded One uncut square of Origamido paper, 3", composed and folded One uncut square of paper, 4", composed and folded One uncut triskadecagon of Mexican yucca paper, 8", composed and folded One uncut rectangle of Thai unryu paper, 8", composed and folded One uncut dollar, 2", composed and folded Lang Skip to main content Due to a planned power outage, our services will be reduced today June 15 starting at am PDT until the work is complete.

Featuring all 29 pieces from the album Lang Lang Piano Book, this is a collection of the most significant pieces from Lang Lang's personal. It encompasses a range of resources printed books and digital products - for pianists of all levels, from beginners to advanced players, through which Lang Lang shares his passion for the piano.

Featuring all 29 pieces from the album Lang Lang Piano Book, this is a collection of the most significant pieces from Lang Lang's personal musical journey. This is a book for all pianists to treasure and revisit again and again. In many ways, art and science work together to unveil what already exists. Since Lang was a teenager, he has worked to bridge the gap between these two seemingly unrelated fields.

Introduced to origami in elementary school by a teacher who exhausted other methods of keeping him engaged in class, Lang established a lifelong partnership with paper — a relationship that kept his head afloat even in tough situations. By following instructions from origami books, he created life with paper. With one continuous movement, his hands give exact directions to the sheet that obediently stays in place: lining up the edges, creasing it, flipping it over, smoothing the borders, and repeating.

When asked about how he started the process of designing something completely new, he said that it varied. Then I work on how the different parts will be laid out on the paper, i.

With that overall notion in mind, then I start working on the specific plan, which is usually a combination of designing making drawings and folding to test out elements of the design.

Often, those designs start from a desire to explore geometric or mathematical principles of folding, so I am looking for expressions of those principles that also create something beautiful.

He would create new designs, record them, and then throw them away. Lang made the connection between math and origami quite early on in his design career.

And if I could identify what those laws were explicitly, then I could use mathematical tools to make the things I really wanted to make. Alongside his studies at Stanford, Lang started planning for his first book, The Complete Book of Origami , which was published in After Stanford, he returned to Caltech for a doctorate in applied physics and, after graduation, moved to Germany with his wife, Diane Davis.

Here he spent three months designing one of his most famous works — a life-size paper cuckoo clock featuring a deer head with antlers , a bird perched on an extended platform, a face with hour and minute hands, pinecone-shaped weights, and a pendulum. In , he quit his day job to focus completely on the completion of his book, Origami Design Secrets: Mathematical Methods for an Ancient Art , which was published in In an attempt to demonstrate how anyone can make origami, he explained the four basic laws that one can employ to translate a vision onto paper.

You can color any crease pattern with just two colors without ever having the same color meeting. The directions of the folds at any vertex — the number of mountain folds, the number of valley folds — always differ by two.

If you look at the angles around the fold, you find that if you number the angles in a circle, all the even-numbered lines add up to a straight line, and all the odd-numbered angles add up to a straight line.

Lang then diagramed how to plan out the shapes of a desired subject using his original design of a stag beetle. I abstract it.