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For example, the allowed values of the sum of diagonal entries for a matrix in SU(3), are precisely the points in the complex plane lying inside a hypocycloid of three cusps (a deltoid). Likewise, summing the diagonal entries of SU(4) matrices gives points inside an astroid, and so on.
The cycloid, epicycloids, and hypocycloids have the property that each is similar to its evolute. If q is the product of that curvature with the circle's radius, signed positive for epi- and negative for hypo-, then the similitude ratio of curve to evolute is 1 + 2q. The classic Spirograph toy traces out hypotrochoid and epitrochoid curves.
Abbrev. [1]Meaning [1] Latin (or Neo-Latin) origin [1]; a.c. before meals: a.d., ad, AD right ear auris dextra a.m., am, AM morning: ante meridiem: nocte every night ...
In the original 1960 announcement of the program, the three hypocycloids were said to represent "the modernity, lightness and stylishness" of consumer products made of American steel. [2] Later interpretations were that the Steelmark highlighted the attributes of steel, with yellow representing "lightens your work", the orange denoting ...
In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes. On a basic level, it is the path traced by a curve while rolling on another curve without slipping.
The red curve is a hypotrochoid drawn as the smaller black circle rolls around inside the larger blue circle (parameters are R = 5, r = 3, d = 5).. In geometry, a hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle.
The disturbing images from the Marcy infirmary have yanked back the curtain on a prison culture advocates and attorneys say is fueled by racism, cover-ups and an us-against-them approach that ...
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.