# alternating

Pronunciation: US say "AWL-ter-nayt-ing" /ˈɔl.tɚ.neɪt.ɪŋ/; UK say "OL-tuh-nayt-ing" /ˈɒl.tə(ɹ)ˌneɪt.ɪŋ/

## Verb

1. Present participle and gerund of alternate. — present participle and gerund of alternate
   - Simple: Present participle and gerund of alternate. Use it after "is" or "are", or to name the action itself.
   - _Bands of heavy rain were alternating with brief spells of sunshine all afternoon._
   - _The farmer has been alternating corn and soybeans in that field for years._

## Adjective

2. Happening or acting by turns, or changing repeatedly from one state to another and back.
   - Simple: Taking turns, or switching back and forth again and again.
   - _The hallway floor is laid in alternating black and white tiles._
   - _The infection brought alternating bouts of fever and chills._
3. Of a mathematical series, having terms whose signs switch between positive and negative from one term to the next.
   - Simple: Describes a long sum of numbers whose signs keep switching between plus and minus.
   - _The series 1 − 1/2 + 1/3 − 1/4 + … is alternating, and it converges even though its terms made positive would not._
   - _She applied the alternating series test to show that the sum settles on a limit._
4. Of a multilinear map whose arguments all lie in the same space, taking the value zero whenever any two adjacent arguments are equal.
   - Simple: Describes a math rule with several inputs of one kind that gives zero when two inputs next to each other match.
   - _The cross product is alternating: the cross product of any vector with itself is zero._
   - _Every alternating bilinear form is also skew-symmetric._
5. Of a knot, having a flat diagram in which the crossings switch between over and under, one after another, as you follow the strand.
   - Simple: Describes a knot that can be drawn flat so the string goes over, then under, at each crossing in turn.
   - _The trefoil is an alternating knot: trace its strand and you pass over, under, over, under._
   - _Every knot with seven or fewer crossings is alternating, but some eight-crossing knots are not._

Source: DictionaryAI, https://dictionaryai.com/define/alternating (written from Wiktionary data, CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/).