# Involution

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## involution

[‚in·və′lü·shən]
(biology)
A turning or rolling in.
(embryology)
Gastrulation by ingrowth of blastomeres around the dorsal lip.
(mathematics)
Any transformation that is its own inverse.
In particular, a correspondence between the points on a line that is its own inverse, given algebraically by x ′ = (ax + b)/(cx-a), where a 2+ bc ≠ 0.
A correspondence between the lines passing through a given point on a plane such that corresponding lines pass through corresponding points of an involution of points on a line.
(medicine)
The retrogressive change to their normal condition that organs undergo after fulfilling their functional purposes, as the uterus after pregnancy.
The period of regression or the processes of decline or decay which occur in the human constitution after middle life.

## Involution

(raising to a power), an algebraic operation consisting in repeating a quantity a n number of times:

The number a is the base of the power, n is the exponent, and an is the power. For example, 3x3x3x3 = 34 = 81. The second power of a number is called its square and the third power, its cube.

## Involution

(regression), in biology, a reduction or loss, in the process of evolution, of certain organs, and a simplification of their organization and functions (for example, various degrees of intestinal reduction in certain parasitic worms and arthropods). Degenerative changes in protozoans and bacteria caused by unfavorable conditions in the habitat are also called involutional. In medicine, the term sometimes refers to atrophy of organs and tissues, such as in aging.

References in periodicals archive ?
4 Binary words invariant under two involutory antimorphisms
The alphabet [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] allows many finite groups generated by involutory antimorphisms.
2b+1,4]) is an infinite word over the binary alphabet {1, 3} and it is H-rich (here H stands for the group generated by the both involutory antimorphisms over the binary alphabet {1, 3}).

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