involute

Definitions

  • WordNet 3.6
    • adj involute (of some shells) closely coiled so that the axis is obscured
    • adj involute especially of petals or leaves in bud; having margins rolled inward
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Webster's Revised Unabridged Dictionary
    • n Involute (Geom) A curve traced by the end of a string wound upon another curve, or unwound from it; -- called also evolvent. See Evolute.
    • Involute (Bot) Rolled inward from the edges; -- said of leaves in vernation, or of the petals of flowers in æstivation.
    • Involute (Zoöl) Rolled inward spirally.
    • Involute (Zoöl) Turned inward at the margin, as the exterior lip of the Cyprea.
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Century Dictionary and Cyclopedia
    • involute Rolled up; wrapped up. Specifically— In botany, rolled inward from the edge or edges: said of leaves in vernation, of the petals of flowers in estivation, and of the margin of the cup in the Discomycetes, etc. Also involutive.
    • involute Involved; confusedly mingled.
    • n involute That which is involved.
    • n involute In geometry, the curve traced by any point of a flexible and inextensible string when the latter is unwrapped, under tension, from a given curve; or, in other words, the locus of a point in a right line which rolls, without sliding, over a given curve. The curve by unwrapping which a series of involutes is obtained is said to be their common evolute, and auy two involutes of a curve constitute a pair of parallel curves, their corresponding tangents being parallel, and their corresponding points, situated on the same normal, being at a constant distance from one another.
    • involute Noting a form of tooth-profile, used in gearing, traced by a point at the end of a tangent as it is unwrapped from a base-circle. The base-circle is the circle at the root of the teeth. All involute teeth of the same circular pitch will work together. They are much used in cases where the distance between the centers of the two shafts has to be slightly variable.
    • involute To return to a normal condition.
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Chambers's Twentieth Century Dictionary
    • n Involute in′vo-lūt that which is involved or rolled inward: a curve traced by the end of a string unwinding itself from another curve
    • adjs Involute (bot.) rolled spirally inward: turned inward, of shells
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Etymology

Webster's Revised Unabridged Dictionary
L. involutus, p. p. of involvere,. See Involve
Chambers's Twentieth Century Dictionary
See Involve.

Usage

In literature:

The margin is sometimes free and involute.
"Studies of American Fungi. Mushrooms, Edible, Poisonous, etc." by George Francis Atkinson
The involutions, the suggestiveness so attractive to adult ears, he cannot hear.
"Here and Now Story Book" by Lucy Sprague Mitchell
They were not perfect plants but I judged them to be T. acerbum from their taste and involute margin.
"The Mushroom, Edible and Otherwise" by M. E. Hard
Involution, delightfulness of, in ornament, ii.
"The Stones of Venice, Volume III (of 3)" by John Ruskin
The ethmoturbinal bones of the nasal chamber are involuted.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 2" by Various
C. Below is the true branching, above, the distorted involution form.
"The Bacillus of Long Life" by Loudon Douglas
It is possible to make toothed wheels that drive with perfect uniformity by using for the curve of the teeth involutes of circles.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 5" by Various
The cap is fleshy, and the margin at first involute.
"Student's Hand-book of Mushrooms of America, Edible and Poisonous" by Thomas Taylor
In the opinion of the world involution is depth.
"A Yankee from the West" by Opie Read
Involution is a direct process, consisting of successive multiplications; the other two are inverse processes.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5" by Various
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In news:

The lab also calibrates reference involute, lead and pitch masters that are used worldwide to calibrate and verify gear inspection instruments.
Advent Tool & Manufacturing Debuts New Involute Spline Milling Solution.
After an incisional biopsy, marsupialization of the lesion promoted its involution and stimulated osteogenesis.
Advent Tool & Manufacturing released its indexable form milling platform for involute splines , spur gears.
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In science:

So, the equation GA,2 = 0, subject to condition of Proposition 6.1 de fines an algebraic variety Mr of stationary points of all Hamiltonians in involution with respect to Poisson bracket (6.2).
Solutions to WDVV from generalized Drinfeld-Sokolov hierarchies
To describe his result, an involution on polynomials with non-zero constant term is needed.
Random matrix theory over finite fields: a survey
We say that a vector subbundle Z of TCS is involutive if and only if [Γ(Z ), Γ(Z )] ⊂ Γ(Z ), where Γ(Z ) denotes the set of all sections of Z .
Locally Sasakian Manifolds
For an almost contact structure the condition Nφ + dη ⊗ ξ = 0 is satisfied if and only if the bundle N is involutive, [Γ(N ), Γ(N )] ⊂ Γ(N ), and [ξ , Γ(N )] ⊂ Γ(N ).
Locally Sasakian Manifolds
For an almost contact structure satisfying Nφ + dη ⊗ ξ = 0 (in particular for a Sasaki structure) the bundle C ⊗ ξ ⊕ N is involutive.
Locally Sasakian Manifolds
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