For a time didn't update this series because at the invitation of the proceedings where open column "whom painting", and they hope that my new starting in the column.This is the reason for the delay, I am here to enjoy this series of bloggers to modest.Today the main part of the post has been published in science, so according to the promise, I can continue this series.Unlike column limited word count and the number of figure, I can speak freely here.
Front bloggers have pointed out that in the comments said painting is most closely relationship with mathematics escher.Indeed, talk about painting on the maths escher is unthinkable.But precisely because this kind of close relationship just let I hesitated.Of course it is difficult to imagine is to face.Escher's thesis episode is hard to say, then I try to talk about the next few episode escher, wrong place, please.
The ritz, nai, Escher, (Maurits Cornelis Escher, 1898-1972), the Dutch graphic artists.With his derived from mathematical inspiration is famous for its wood, prints and other works.His works implied intriguing mathematical ideas and philosophical thinking but not attributable to any one genre.He created the style of a little state of epic proportions, not only unprecedented, as if also can't see followers, but by many scientists.The spirit of his art shows the mathematics, the beauty of philosophy.He will mathematical symmetry, precise, rules, step by step, fantasy and other abstract characteristics with incredible performance in magic work, and the dimension of seemingly contradictory state with unspeakable mix to the plane in the form of canvas.For example, it is up to the second floor stair somehow has returned to the first floor, the bird in the constantly changing don't know when suddenly turned into a fish.The magic of his art is full of difficult to resist, to conquer the people's hearts.Although for a long time his art was fine arts as a heresy, but the scientists around the world in the extensive and profound appreciation has established unshakable position.
Tian and Wang Bei ever translation Bruno. Ernst, a book "the magic mirror - escher impossible world".The author of the book through and escher exchanges and close observation, trying to interpret escher people through the brush to render impossible in the world., however, the author's escher seems to be no different and ordinary people, and even popular love mathematicians of his mathematical training is very limited, he said: "I never pass my math. Funny is that I don't seem to know what happened to understand mathematics theory. Indeed, I am in school math is very poor. But now, boy -- mathematician in with my print book illustrations for them. Can't imagine, I unexpectedly with these guys learned pool, as if I was their long-lost brother. I guess they know nothing about my ignorance in mathematics must."This information is released, escher without too much math training, and the traditional math grades are not good.But he is in a form of "intuition" to understand a lot of people feel more esoteric math, and you can use his brush with the unknown excitation real mathematicians communication.Such a phenomenon, in addition to the "genius", don't release it.
Escher oil painting from the view of mathematics, can be roughly divided into the limit, the mutual coupling and transformation, Yi Wei, empty, etc.Later we appreciate respectively.In this episode we appreciate his limit diagram.
Two pictures below, on the left side of the call Circle Limit III (Limit Circle. 1959), the right is Smaller and Smaller
(smaller and smaller. 1956).Painting problem, point out the limit.
Limit of budding have long, chuang tzu in ancient China, recorded in the "zhuangzi. The article" the "take its half a foot of civic, day, Jesus Christ."Reflects the simple limit thought.Accurate portrayal of the concept of limit in mathematics is in the 18th century, with the improvement of the mathematics calculus discipline by Cauchy (AugustinLouis Cauchy, 1789-1857) and Wei Ersi terra si (Karl Theodor Wilhelm Weierstra decide, 1815-1897) and others strict and complete.It refers to the variables in the process of certain changes, from the trend could not be accused of scattered or gradually stable change process, the former is called the divergence becomes infinite, which is known as the convergence to the limit.In the modern mathematical analysis, almost all the basic concepts, such as continuous and differential, integral is based on the concept of limit, that is the limit is the soul of the calculus.And the "bad at math" escher is adept to the limit of the abstract concept vividly expressed in the concrete of the canvas, with limited challenge, using static depict variation.
Chuang tzu is in one dimensional space in interpretation of civic limit of infinitesimal calculus, and escher, is described in the two-dimensional canvas limit.He painted many limit diagram, the figure is a typical two above.Respectively through a circle and a square, with the image of the animal (escher favorite painting of animals, fish and lizards) growing and the smaller the convergence to the edge and center respectively.Because in the two-dimensional space, the limit is generally a one-dimensional curve in the two-dimensional space, also may degenerate into a point.Limit in the left is the week of the round edge, on the right limit is in the center.
In spite of the computer today, it is easy to through the program to draw similar graphics.But consider in an era of escher, this process is the "foreseen to realize" escher genius.
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