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Spirograph is a geometric drawing device that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. The well-known toy version was developed by British engineer Denys Fisher and first sold in 1965.
For <, spiral-ring pattern; =, regular spiral; >, loose spiral. R is the distance of spiral starting point (0, R) to the center. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by ( − θ {\displaystyle -\theta } ) for plotting.
Special cases are right triangles (p q 2). Uniform solutions are constructed by a single generator point with 7 positions within the fundamental triangle, the 3 corners, along the 3 edges, and the triangle interior. All vertices exist at the generator, or a reflected copy of it. Edges exist between a generator point and its image across a mirror.
The pattern used in this instance is called a spirograph in mathematics, that is, a hypotrochoid generated by a fixed point on a circle rolling inside a fixed circle. It has parametric equations. These patterns bear a strong resemblance to the designs produced on the Spirograph, a children's toy.
The vertex figure can be discovered by considering the Wythoff symbol: p|q r - 2p edges, alternating q-gons and r-gons. Vertex figure (q.r) p. p|q 2 - p edges, q-gons (here r=2 so the r-gons are degenerate lines).
As a young man in 1827 he had developed a so-called "Speiragraph", an early prototype for the spirograph. He evidently continued on with experiments and inventions, and on 27 February 1860 received British patent no. 537 for 28 monocular and stereoscopic variations of cylindrical stroboscopic devices (see zoetrope ). [ 7 ]
A rosette or cam-like pattern mounted on the spindle is controlled by moving against a cam follower(s) while the lathe spindle rotates. Rose engine work can make flower patterns, as well as convoluted, symmetrical, multi-lobed geometric patterns. The patterns it produces are similar to that of a Spirograph, in metal. No other ornamental lathe ...
The snub square tiling, made of two squares and three equilateral triangles around each vertex, has a bilaterally symmetric Cairo tiling as its dual tiling. [13] The Cairo tiling can be formed from the snub square tiling by placing a vertex of the Cairo tiling at the center of each square or triangle of the snub square tiling, and connecting ...