involution

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. The act of involving.
2. n. The state of being involved.
3. n. Intricacy; complexity.
4. n. Something, such as a long grammatical construction, that is intricate or complex.
5. n. Mathematics An operation, such as negation, which, when applied to itself, returns the original number.
6. n. Embryology The ingrowth and curling inward of a group of cells, as in the formation of a gastrula from a blastula.
7. n. Medicine A decrease in size of an organ, as of the uterus following childbirth.
8. n. Medicine A progressive decline or degeneration of normal physiological functioning occurring as a result of the aging process.

Century Dictionary and Cyclopedia

1. n. The act of involving, infolding, or inwrapping; a rolling or folding in or round.
2. n. The state of being entangled or involved; complication.
3. n. Something involved or entangled; a complication.
4. n. A membranous covering or envelop; an involucre.
5. n. In grammar, complicated construction; the lengthening out of a sentence by the insertion of member within member; the separation of the subject from its predicate by the interjection of matter that should follow the verb or be placed in another sentence.
6. n. In mathematics: The multiplication of a quantity into itself any number of times, so as to produce a positive integral power of that quantity. Thus, the operation by which the third power of 5 is found, namely, the multiplication of 5 by itself, making 25, and of the product by 5 again, making 125, is involution. In this sense involution is opposed to evolution, 3 .
7. n. The raising of a quantity to any power, positive, negative, fractional, or imaginary. In this sense involution includes evolution as a particular case.
8. n. A unidimensional continuous series of elements (such as the points of a line), considered as having a definite one-to-one correspondence with themselves, such that infinitely neighboring elements correspond to infinitely neighboring elements, and such that if A corresponds to B, then B corresponds to A: in other words, the elements are associated in conjugate pairs, so that any pair of conjugate elements may by a continuous motion come into coincidence with any other without ceasing, at any stage of the motion, to be conjugate. This is the usual meaning of involution in geometry; it dates from Desargues (1639). There are either two real sibi-conjugate or self-corresponding elements in an involution, when it is called a hyperbolic involution; or there are none, when it is called an elliptic involution. If U = 0, V = 0, W = 0 are three quadratic equations determining three pairs of points in an involution, then these three equations are in a syzygy λU + μ V + ν W = 0; or if the three equations are ax + bxy + cy = 0, a′ x + b′ xy + c′ y = 0, a″x + b″xy + c″y = 0, then the syzygy may be thus written: The six elements are said to be an involution of six, or, if one or two of them are sibi-conjugate, an involution of five or of four elements. If the points of a line in a plane are in involution, let any conic (or degenerate conic) be drawn through any pair of conjugate points, and another conic through any other pair; then any conic through the four intersections of these conics will cut the line in a pair of conjugate points. That point of an involution which cor. responds to the point at infinity is termed the center of the involution.
9. n. Any series of pairs of loci represented by an equation λU + µ V = 0, where λ and µ are numerical constants for each locus, and U = 0 and V = 0 are equations to two loci of the same order.
10. n. Any unidimensional continuum of elements associated in sets of any constant number by a continuous law. According as there are two, three, four, etc., in each set, the involution is said to be quadratic, cubic, quartic (or biquadratic), etc.
11. n. The implication of a relation in a system of other relations.
12. n. In physiology, the resorption which organs undergo after enlargement or distention: as, the involution of the uterus, which is thus restored to its normal size after pregnancy.
13. n. The atrophic or regressive changes occurring in old age.
14. n. In biology, the possession by an organism which is adapted to conditions that are simpler than those under which its allies live, of an organization that is simpler than that of its allies, considered as evidence of inverse or retrograde evolution.

Wiktionary

1. n. entanglement; a spiralling inwards; intricacy
2. n. mathematics An endofunction whose square is equal to the identity function; a function equal to its inverse.
3. n. physiology The regressive changes in the body occurring with old age.
4. n. mathematics, obsolete A power: the result of raising one number to the power of another.

GNU Webster's 1913

1. n. The act of involving or infolding.
2. n. The state of being entangled or involved; complication; entanglement.
3. n. That in which anything is involved, folded, or wrapped; envelope.
4. n. (Gram.) The insertion of one or more clauses between the subject and the verb, in a way that involves or complicates the construction.
5. n. (Math.) The act or process of raising a quantity to any power assigned; the multiplication of a quantity into itself a given number of times; -- the reverse of evolution.
6. n. (Geom.) The relation which exists between three or more sets of points, a.a', b.b', c.c', so related to a point O on the line, that the product Oa.Oa' = Ob.Ob' = Oc.Oc' is constant. Sets of lines or surfaces possessing corresponding properties may be in involution.
7. n. (Med.) The return of an enlarged part or organ to its normal size, as of the uterus after pregnancy.

WordNet 3.0

1. n. marked by elaborately complex detail
2. n. a long and intricate and complicated grammatical construction
3. n. the act of sharing in the activities of a group
4. n. the action of enfolding something
5. n. reduction in size of an organ or part (as in the return of the uterus to normal size after childbirth)
6. n. the process of raising a quantity to some assigned power