By von Neumann J.

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But the first ordered patterns, and the first representation of figures and animals in mosaic, appeared around the late fifth and early fourth centuries BC in cities of the Ancient Greek world. 6 The mosaics were probably made by African artists in the early fourth century CE. The North African provinces were at the economic and artistic forefront in the fourth century, and polychrome mosaics were one of the specialties of the North African artists. Very similar mosaics have been found in Carthage and other places in North Africa.

You can mark these lines by weaving yarn of a different color on your model, as was done in these pictures. Draw two parallel lines on a piece of paper: how many common perpendiculars can you construct for these two lines? If you do it in different places, then, of course, you can draw as many as you want. What is common to these perpendiculars? If you measure them between the two parallel lines, then all of them are the same length. This property is sometimes used in practice to construct straight lines on fields.

2500 BC (British Museum). Buliding/Structures Strand 49 All Gizah Pyramids (photo by Ricardo Liberato). Ancient building in Uxmal, Mexico (photo by Pedro Sánchez). The Parthenon, Athens. 50 Chapter 3. Four Strands in the History of Geometry The construction of such structures requires very good knowledge of angles and proportions. Some of these proportions also had religious significance. One of the most popular proportions used in ancient architecture was the so-called golden ratio. There is much literature13 available about the golden ratio in architecture, nature, art, and other connections.

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Collected works. Vol.4 Continuous geometry and other topics by von Neumann J.

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Download e-book for kindle: Collected works. Vol.4 Continuous geometry and other topics by von Neumann J.
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