Plane Curves

<p>3D space</p> Signup and view all the answers

<p>No</p> Signup and view all the answers

<p>Plane curves can be described using algebraic equations or in terms of a parameter (parametric).</p> Signup and view all the answers

<p>Explicit analytical curves can be described by equations of the form $y = f(x)$, where for every $x$ there is one value of $y$. Implicit analytical curves can be described by equations of the form $f(x, y) = 0$, which can be multi-valued or represent closed curves.</p> Signup and view all the answers

<p>Curves are important in engineering because many objects in the real world are not just polyhedral, but also have curved shapes. Describing these curved objects and their boundaries requires different types of curves.</p> Signup and view all the answers

<p>No, a circle (or any closed curve) cannot be represented by an explicit equation of the form $y = f(x)$, as this type of representation only allows for one value of $y$ for every $x$.</p> Signup and view all the answers

<p>To describe curved objects and their boundaries, we can use algebraic equations of the form $f(x, y) = 0$ for plane curves, or equations like $g(x, y, z) = 0$ for curves in 3D space.</p> Signup and view all the answers