evolute

[ ev-uh-lootor, especially British, ee-vuh- ]

Phonetic (Standard)IPA

noun

, Geometry.

the locus of the centers of curvature of, or the envelope of the normals to, another curve. Compare involute ( def 5 ).

evolute

/ ˈɛvəˌluːt /

a geometric curve that describes the locus of the centres of curvature of another curve (the involute ). The tangents to the evolute are at right angles to the involute

Origin of evolute¹

1720–30; < Latin ēvolūtus (past participle of ēvolvere to roll out, unfold, evolve )

Origin of evolute¹

C19: from Latin ēvolūtus unrolled, from ēvolvere to roll out, evolve

The adjective translated evolute (udanh) is of frequent occurrence in the formulas, but has no exact equivalent in English.

The evolute of a curve is the curve which is the envelope of all its normals or the locus of all its centres of curvature.

These names are given to the curves because the end of a stretched thread unwound from the evolute will describe the involute.

The locus of the centres of curvature, or envelope of the normals, of a curve is called the “evolute.”

The involutes are “orthogonal trajectories” of the tangents to the common evolute.

April 25, 2024firkin

[fur-kin ]

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