The development of the first mathematical system of perspective (apex)
The development of the first mathematical system of perspective (apex)
The goal of art was to spread a religious message, not to create mathematically correct canvases ----- There are many kinds of perspective, and the medieval artists used several of them. This question, however, is almost certainly about linear perspective. The stock answer is that medieval artists were interested in spiritual things rather than highly accurate renderings of appearances, so they forgot the perspective that had once been used in ancient times. If you want to pass the test or provide the expected answer on homework, that is the answer to use. If you want to understand the issue, you must know there is much more to it. I don't like the stock answer because it is so simple that it conveys more misunderstanding than truth. The claim that linear perspective was developed during ancient times is really true only to an extent. Some ancient artists seem to have understood the fact that more distant things looked smaller than things that were closer. But they did not investigate the issue fully enough to systematize it and produce the mathematical constructions necessary for thorough understanding. They did not do this because they could not; the mathematics needed for the job had not been developed. The whole question of linear perspective was one of a simple technique that could be used, to make distant things look smaller, one trick in a tool box of tricks. Medieval artists were, in fact, more interested in spiritual stories than somewhat accurate rendering, and so they did let that old trick fall into disuse. There are other kinds of perspective in addition to linear. One is a system of that makes the most important thing in the picture biggest; in a picture of Jesus surrounded by his disciples, Jesus would be the biggest figure. Another is the reverse perspective used by medieval artists, which makes things bigger if they are farther away; the purpose of this is hard to understand, and it may have had no purpose other than being in fashion. Medieval artists used both of these, and there are other types of perspective as well. Some medieval artists did use linear perspective. Linear perspective, with its mathematical approach to accurate rendering, was developed during the Middle Ages. It was used by Giotto di Bondone in about the year 1300. We do not know what he based his work on, but the underlying mathematical principles were established by Arab writers of the 11th century, and their works had been translated by the time of Giotto. The mathematical basis of linear perspective was carefully investigated by artists of the Late Middle Ages and the Renaissance. It was probably believed at the time that linear perspective was in some sense absolutely accurate, based on the mathematics involved. This idea was certainly reinforced when Photography appeared, and any disbeliever could compare a careful perspective drawing with the product of the camera. They used to say, "Cameras don't lie." There were people who pointed out that the direction lines appeared slightly curved in the real world, but this was attributed to visual distortion produced by the eye, because photographs produced the same results as linear perspective, so it had to be the eye that was wrong. Unfortunately, cameras do lie, causing distortions, and since the distortions of the camera happen to be the same as those produced by the linear perspective developed in the Late Middle Ages, they made those distortions seem somehow correct, in some absolute sense. Linear perspective had to be revisited and improved when computers appeared and pictures had to be redrawn in real time by software as a view changed. It became understood that the projection lines of linear perspective, straight lines going to vanishing points, needed to be represented in new ways. In fact, they had to be treated as small parts of big sine waves. So computers use a different mathematics for perspective, and we have new understanding of the subject. Interestingly, the computer based perspective was not the first change in the subject in the 20th century. Cubist artists had introduced a new sort. They investigated a type of perspective in which the artist could decide what part of an object should be viewed from what angle, and even at different points in time. They regarded the purpose of perspective as related to a story, rather than accurate rendering, just as some medieval artists had. The point that I am making is that medieval artists did use perspective. They used several kinds of perspective. Some of them developed and used the linear perspective used by Renaissance artists. And new kinds of perspective continue to be introduced. Perspective is just a matter of your point of view.
there is difficulty in the mathematical opperations there is no zero
The Maya developed a mathematical system based on the number 20 and they were the first people to use zero. By using their math system, the Maya made great advances in astronomy. The Maya also produced a very accurate calendar system.
Brunelleschi: Linear perspective.
Aerial perspective.
Ancient Greeks
ancient Greeks
The development of the first mathematical system of perspective (apex)
The first mathematical system of painting perspective
Ancient Greeks
Linear perspective is a mathematical system for projecting the three-dimensional world onto a two-dimensional surface, such as paper or canvas
The development of the first mathematical system of perspective (apex)
They developed the first mathematical system of painting perspective
The development of the first mathematical system of perspective
The development of the first mathematical system of perspective (apex)