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  • 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
    • ***
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.
    • ***
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.
    • ***
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
    • ***


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


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
This may be caused by an involution of one part of the intestine within another.
"Domestic Animals" by Richard L. Allen
And if I was able to make a dim guess or two at these involutions, what of this woman to whom it was not guessing, but open knowledge?
"The Tower of Oblivion" by Oliver Onions
The first curve is called the involute of the second.
"The New Gresham Encyclopedia" by Various
Old age represents the period of retrogression, of involution, and hence readily transmits the mark of degeneracy.
"Degeneracy" by Eugene S. Talbot
The plot, without involution, progresses through the acts.
"Amenities of Literature" by Isaac Disraeli
Merely to admit the need for all this involution of ambiguity and double-dealing grievously affronted self-esteem.
"Linda Lee, Incorporated" by Louis Joseph Vance
For the cause of this quarrel is no dim, half-avoidable involution of mean interests and errors, as some would have us believe.
"Modern Painters Vol. III." by John Ruskin
This is the process of the involution of life in matter, the descending arc.
"Evolution of Life and Form" by Annie Wood Besant
But the involute edges of the pileus are bearded with close hairs.
"Mushroom Culture" by W. Robinson
The Wolffian duct arises by a series of such involutions, all of which are behind (nearer the tail) the involution to form the Oviduct.
"The Works of Francis Maitland Balfour, Volume 1" by Francis Maitland Balfour

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.

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
Since (S, (ξ, η, φ, g )) is Sasakian then its bundle C ⊗ ξ ⊕ N is involutive.
Locally Sasakian Manifolds
The dual conditions to conditions (4)-(5) imply that N is involutive and that [ξ, Γ(N )] ⊂ Γ(N ).
Locally Sasakian Manifolds
II) (Global version) Every almost contact metric structure which satisfies condition (6) of Definition 1 is Sasakian if and only if its canonical decomposition TCS = C ⊗ ξ ⊕ N ⊕ ¯N, consists of involutive C ⊗ ξ ⊕ N part.
Locally Sasakian Manifolds
The purpose of this section is to show that these three examples appear very naturally as tangent spaces to symmetric spaces. A symmetric space G/K is given by a semi-simple Lie group G and a Lie group involution σ : G → G such that K = {x ∈ G, σ(x) = x}.
Integrable Lattices: Random Matrices and Random Permutations
In the last equality, we have used property (1.4.11): an involution has no fixed points iff all columns of P have even length.
Integrable Lattices: Random Matrices and Random Permutations
In section 1, we discussed random matrix problems over different finite and infinite matrix ensembles, generating functions for the statistics of the length of longest increasing sequences in random permutations and involutions.
Integrable Lattices: Random Matrices and Random Permutations
Notice that the reflection σ about the equator of this sphere is an orientationreversing involution, σ2 = id.
Conformal field theory, boundary conditions and applications to string theory
If σ is an orientation reversing homeomorphism of ˆΣ, it induces by the same procedure an antiholomorphic involution σ∗ on the Teichm¨uller space.
Conformal field theory, boundary conditions and applications to string theory
One can show that for ˆΣ of genus ˆg, there are [ 3ˆg+4 ] inequivalent involutions.
Conformal field theory, boundary conditions and applications to string theory
It can be verified that ∗ is an involutive anti-automorphism of Ψ.
Nongraded Infinite-Dimensional Simple Lie Algebras