involute$554040$ - ορισμός. Τι είναι το involute$554040$
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Τι (ποιος) είναι involute$554040$ - ορισμός

MATHEMATICAL CURVE CONSTRUCTED FROM ANOTHER CURVE
Evolvent; Involute of a circle; Involute of a Circle
  • Involutes of a circle
  • Involutes of a semicubic parabola (blue). Only the red curve is a parabola. Notice how the involutes and tangents make up an orthogonal coordinate system. This is a general fact.
  • Two involutes (red) of a parabola
  • Involutes of a cycloid (blue): Only the red curve is another cycloid
  • Involute: properties. The angles depicted are 90 degrees.
  • The red involute of a catenary (blue) is a tractrix.

involute         
['?nv?l(j)u:t]
¦ adjective
1. formal complicated.
2. technical curled spirally.
Zoology (of a shell) having the whorls wound closely round the axis.
Botany rolled inwards at the edges.
¦ noun Geometry the locus of a point considered as the end of a taut string being unwound from a given curve in the plane of that curve. Compare with evolute.
Origin
C17: from L. involutus, past participle of involvere (see involve).
Involute         
In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve.
Evolvent         
·noun The involute of a curve. ·see Involute, and Evolute.

Βικιπαίδεια

Involute

In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve.

The evolute of an involute is the original curve.

It is generalized by the roulette family of curves. That is, the involutes of a curve are the roulettes of the curve generated by a straight line.

The notions of the involute and evolute of a curve were introduced by Christiaan Huygens in his work titled Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae (1673), where he showed that the involute of a cycloid is still a cycloid, thus providing a method for constructing the cycloidal pendulum, which has the useful property that its period is independent of the amplitude of oscillation.