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  2. Involute - Wikipedia

    en.wikipedia.org/wiki/Involute

    In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve. [1] The evolute of an involute is the original curve.

  3. Involute gear - Wikipedia

    en.wikipedia.org/wiki/Involute_gear

    The involute gear profile, sometimes credited to Leonhard Euler, [1] was a fundamental advance in machine design, since unlike with other gear systems, the tooth profile of an involute gear depends only on the number of teeth on the gear, pressure angle, and pitch. That is, a gear's profile does not depend on the gear it mates with.

  4. Involution (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Involution_(mathematics)

    Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...

  5. Evolute - Wikipedia

    en.wikipedia.org/wiki/Evolute

    If = (), [,] is the parametric representation of a regular curve in the plane with its curvature nowhere 0 and () its curvature radius and () the unit normal pointing to the curvature center, then = + () describes the evolute of the given curve.

  6. Radius of curvature - Wikipedia

    en.wikipedia.org/wiki/Radius_of_curvature

    Let γ be as above, and fix t.We want to find the radius ρ of a parametrized circle which matches γ in its zeroth, first, and second derivatives at t.Clearly the radius will not depend on the position γ(t), only on the velocity γ′(t) and acceleration γ″(t).

  7. Envelope (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Envelope_(mathematics)

    The envelope E 1 is the limit of intersections of nearby curves C t.; The envelope E 2 is a curve tangent to all of the C t.; The envelope E 3 is the boundary of the region filled by the curves C t.

  8. Detroit Lions Take Away Season Tickets from Fan Who Got into ...

    www.aol.com/lifestyle/detroit-lions-away-season...

    The Detroit Lions have taken away a fan's season tickets after he was involved in a verbal altercation with Green Bay Packers coach Matt LaFleur.

  9. Epicycloid - Wikipedia

    en.wikipedia.org/wiki/Epicycloid

    The red curve is an epicycloid traced as the small circle (radius r = 1) rolls around the outside of the large circle (radius R = 3).. In geometry, an epicycloid (also called hypercycloid) [1] is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle.