Oval(redirected from ovals)
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a closed convex plane curve. A convex curve is a curve that has no more than two real points in common with any line. The ellipse and the circle are examples of ovals. If an oval has a tangent at every point, then to any direction in the plane there correspond just two tangents parallel to that direction.
Many theorems deal with properties of ovals. We mention two such theorems. (1) On every oval there are at least four points at which the curvature reaches a maximum or minimum. This is the so-called four-vertex theorem. The ellipse has precisely four such points—the ends of the major and minor axes. (2) If we have an oval of constant width, that is, if the distance d between any two parallel tangents to the oval is the same for all directions, then the length of the oval is equal to π d. The circle is the simplest oval of constant width. Another example is the figure obtained (Figure 1) by drawing six arcs of circles with centers at the vertices of an equilateral triangle with side a, where three of the circles have radii c, c arbitrary, and three have radii a + c.
In algebraic geometry the term “oval” is also applied to closed connected components of plane algebraic curves. There, however, the component is not necessarily convex.