What is envelope of family of curves?

What is envelope of family of curves?

envelope, in mathematics, a curve that is tangential to each one of a family of curves in a plane or, in three dimensions, a surface that is tangent to each one of a family of surfaces. For example, two parallel lines are the envelope of the family of circles of the same radius having centres on a straight line.

Who discovered curves?

Many textbooks refer to it as the Gaussian Curve, reflecting the fact that the brilliant 19th-Century German mathematician Karl Friedrich Gauss deduced the shape of the curve while studying how data are affected by random errors.

What is Equation family?

A family of functions is a set of functions whose equations have a similar form. The “parent” of the family is the equation in the family with the simplest form. For example, y = x2 is a parent to other functions, such as y = 2×2 – 5x + 3.

What is the relation between Evolutes and envelopes?

What is the relation between evolutes and envelopes? Explanation: Evolute is the locus of the all the centres of curvature of the curve whereas envelope is the curve which touches all the members of the family of the curve i.e Envelope is tangent to all the curves in a family of curves.

What is straight line family?

A family of intersecting straight lines, is the set of infinite straight lines that pass through a point P(p1,p2): Example: y – 3 = m (x – 2), m Є R, is the family of lines that pass through the point (2,3).

What is relation between Evolutes and envelopes?

What is Jordan arc?

A Jordan arc in the plane is the image of an injective continuous map of a closed and bounded interval [a, b] into the plane. It is a plane curve that is not necessarily smooth nor algebraic.

What are the names of curves?

Rational curves

  • Circle. Unit circle.
  • Ellipse.
  • Parabola.
  • Hyperbola. Unit hyperbola.

What kind of function is Y X?

linear functions
All linear functions have a straight line as a graph. The parent function of linear functions is y = x, and it passes through the origin. The domain and range of all linear functions are all real numbers. These functions represent relationships between two objects that are linearly proportional to each other.

What are family functions?

The basic functions of the family are to: (1) regulate sexual access and activity; (2) provide an orderly context for procreation; (3) nurture and socialize children; (4) ensure economic stability; and (5) ascribe social status. …