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hypotrochoid

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hypotrochoid
hypotrochoid Geom. (h(a)ɪpəʊˈtrəʊkɔɪd, h(a)ɪˈpɒtrəʊkɔɪd) [f. hypo- 2 + trochoid.] The curve described by a point rigidly connected with the centre of a circle which rolls on the inside of another circle.1843 Penny Cycl. XXV. 282/1 A class [of curves] called..hypotrochoids, of which one particular ca... Oxford English Dictionary
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Hypotrochoid
In geometry, a hypotrochoid is a roulette traced by a point attached to a circle of radius rolling around the inside of a fixed circle of radius , where The classic Spirograph toy traces out hypotrochoid and epitrochoid curves. wikipedia.org
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hypocycloid
hypocycloid Geom. (hɪpəʊ-, haɪpəʊˈsaɪklɔɪd) [f. hypo- 2 + cycloid. Cf. F. hypocycloïde.] A curve traced by a point in the circumference of a circle which rolls round the interior circumference of another circle (cf. epicycloid).1843 [see hypotrochoid]. 1854 Moseley Astron. lxi. (ed. 4) 183 This curv... Oxford English Dictionary
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Hypocycloid
The area enclosed by a hypocycloid is given by: The arc length of a hypocycloid is given by: Examples The hypocycloid is a special kind of hypotrochoid See also Roulette (curve) Special cases: Tusi couple, Astroid, Deltoid List of periodic functions Cyclogon Epicycloid Hypotrochoid Epitrochoid wikipedia.org
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calculate the period of an hypotrochoid I'm curious how to find out the period of an hypotrochoid. x = (a-b) * cos(t) + h * cos( ((a-b)/b) * t ) y = (a-b) * sin(t) - h * sin( ((a-b)/b) * t ) I...
The period of $\cos t$ and $\sin t$ is $2\pi$. For any positive constant $k$, the period of $\cos kt$ and $\sin kt$ is $2\pi/k$. (Because $\cos (k(t+p)) = \cos (kt +kp)$ so $kp$ has to be the period $2\pi$ of $\cos t$.) So, now each of the two coordinates is a sum of a function with period $2\pi$ an...
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This Week At Bungie - 03/23/2023 | Bungie.net
Mar 23, 2023Known Issues List / Help Forums / Bungie Help Twitter. KNOWN ISSUES . While we continue investigating various known issues, here is a list of the latest issues that were reported to us in our #Help forum: The Dimensional Hypotrochoid Grenade Launcher can have a range Masterwork. Non-Lightfall quests show up under the Lightfall quest category.
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Epitrochoid
The classic Spirograph toy traces out epitrochoid and hypotrochoid curves. See also Cycloid Cyclogon Epicycloid Hypocycloid Hypotrochoid Spirograph List of periodic functions Rosetta (orbit) Apsidal precession References wikipedia.org
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Come up with a solution to the following problem: You are given a hypotrochoid with parameters a, b, h and need to find the equation for the curve.
The equation for the hypotrochoid can be found by using the parametric equations, x = a(cos(t) + h cos((a/b)t)) and y = a(sin(t) - h sin((a/b)t)).
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Trochoid
The number of cusps given above also hold true for any epitrochoid and hypotrochoid, with "cusps" replaced by either "radial maxima" or "radial minima" See also Aristotle's wheel paradox Brachistochrone Cyclogon Cycloid Epitrochoid Hypotrochoid List of periodic functions Roulette (curve) Spirograph wikipedia.org
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trochoid
trochoid, n. and a. (ˈtrɒkɔɪd, ˈtrəʊkɔɪd) [ad. Gr. τροχοειδής round like a wheel, f. τροχός wheel + εἶδος form: see -oid; cf. F. trochoïde (1658 in Hatz.-Darm.).] A. n. 1. Geom. A curve traced by a point on or connected with a rolling circle; orig. = cycloid 1: now usually restricted to the curtate ... Oxford English Dictionary
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Centered trochoid
The term encompasses both epitrochoid and hypotrochoid. The center of this curve is defined to be the center of the fixed circle. (Spanish) Flash Animation of Epitrochoid Flash Animation of Hypotrochoid Epitrochoid at Mathworld Hypotrochoid at Mathworld Visual Dictionary of wikipedia.org
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Cycloid
Hypotrochoid: generalization of a hypocycloid where the generating point may not be on the edge of the rolling circle. The classic Spirograph toy traces out hypotrochoid and epitrochoid curves. wikipedia.org
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عجلي تحتي
عندما R = 2r نحصل على قطع ناقص انظر أيضًا عجلي فوقي عجلي دويري دويري تحتي دويري فوقي المراجع وصلات خارجية Flash Animation of Hypocycloid Hypotrochoid wikipedia.org
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Equation of a star About three years back I read an article in wikipedia about equation(it was more like how to draw a curve that remembled a star) of a star. Though I dont remember vividly in that article there was a...
You seem to refer to a hypotrochoid, the thing one can draw with a Spirograph toy. It can be drawn with sine and cosine, see the Wikipedia article.
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摆线
更进一步，如果我们让圆也沿着一个圆滚动而不是直线的话，我们会得到外摆线（epicycloid，沿着圆的外部运动，定点在圆的边缘），内摆线（hypocycloid，沿着圆内部滚动，定点在圆的边缘）以及外旋轮线（epitrochoid）和内旋轮线（hypotrochoid，定点可以在圆内的任一点包括边界。 wikipedia.org
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