STEM Problems with Mathcad and Python by unknow

Author:unknow
Language: eng
Format: epub
Publisher: CRC Press LLC
Published: 2022-09-02T00:00:00+00:00

Jupyter Notebook symmetric_curves. ipynb provides galleries of curves generated for different . So, Figure 7.26 shows one of the gallery pages for i.e. the minimum symmetry. In the gallery, there are five curves, numbered 11–13, 16, 17, which do not have the symmetry elements we have considered. Rotation by 360o, which corresponds to 1, we do not consider for an element of symmetry.

FIGURE 7.26 Page for curve gallery for . As you increase m, the number of symmetry elements increases, and the complexity of the curves increases. Figure 7.27 shows one of the pages of the curve gallery for . Some of the curves have a very whimsical shape, for example, 43–45, 55–58. As a rule, this is due to the fact that one of the elements of the tuple is negative.

FIGURE 7.27 Page for curve gallery for. Figure 7.28 shows curves for . On it, the curves, although they have a large number of symmetry elements, are overloaded with details, which interferes with their perception.

FIGURE 7.28 Page for curve gallery for . Most of the generated curves can be broken down into classes, for example, Figure 7.29 shows curves belonging to the “gears” class.

FIGURE 7.29 «Gears». Another class is “sockets” (Figure 7.30).

FIGURE 7.30 «Rosettes». In the following Figure 7.31, you can observe the evolution of “rosettes”. “Stars” are similar to “rosettes”, moreover, “rosettes” can turn into “stars”.

FIGURE 7.31 Stars with number of peaks from four to nine. Next, we embark on a rather slippery slope, attributing to “magic” a few curves that are distinguished by their unusual behavior. In Figure 7.32 there are four such curves corresponding to m = . The most attractive are the curves obtained for . When m enlarged, the magic curves turn into hybrids of “stars” and “gears”.

FIGURE 7.32 “Magic” curves. The left curve in Figure 7.33 corresponds to , and the right curve corresponds to

FIGURE 7.33 Hybrids of “stars” and “gears”. We have to see what happens to the curves when the tuple changes and the tuple is fixed, for example: . Figure 7.34 shows how the “magic” curves change when the elements of the tuple change.

FIGURE 7.34 The influence of the tuple a on the shape of the “magic” curves. It would seem that increasing the lengths of the tuple coefficients should generate more attractive curves, but this is not the case. Figure 7.35 shows the first page for and .

FIGURE 7.35 Curve gallery page for and . Note also that as the lengths of the tuples increase, the number of curves generated increases rapidly, for example, if the length of the tuple is five and , the number of generated curves is 5,040, and at length 7, the number of drawings increases to 151,200. Therefore, it is recommended to generate not all, but only selected pages of pattern galleries.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.