a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going...

crescent shape, is not convex. The boundary of a convex set in the plane is always a convex curve. The intersection of all the convex sets that contain a...

triangle is strictly convex. Convex curve – Type of plane curve Concave polygon – Simple polygon which is not convex Convex polytope – Convex hull of a finite...

or by intersecting circles centered on a partial curve. Every body of constant width is a convex set, its boundary crossed at most twice by any line...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

nonnegative matrix is a convex function of its diagonal elements. Concave function Convex analysis Convex conjugate Convex curve Convex optimization Geodesic...

continuous curve evolution. If the curve is non-convex, its total absolute curvature decreases monotonically, until it becomes convex. Once convex, the isoperimetric...

mathematics, an orientation of a curve is the choice of one of the two possible directions for travelling on the curve. For example, for Cartesian coordinates...

smooth or convex curve such as a circle or triangle, but it remains unsolved whether a square can be inscribed in every simple closed curve. Several problems...

A curved mirror is a mirror with a curved reflecting surface. The surface may be either convex (bulging outward) or concave (recessed inward). Most curved...

plane): Algebraic geometry Convex curve Differential geometry Osgood curve Plane curve fitting Projective varieties Skew curve Coolidge, J. L. (April 28...

while for others it is false. If "oval" means merely a continuous closed convex curve, then there are counterexamples, such as triangles or one of the lobes...

but 1/2. Since a convex curve intersects almost every line either twice or not at all, the unoriented Crofton formula for convex curves can be stated without...

In architecture, entasis is the application of a convex curve to a surface for aesthetic purposes, or increasing strength. Its best-known use is in certain...

ellipse. Both are algebraic curves of degree 2. For any number n of foci, the n-ellipse is a closed, convex curve.: (p. 90)  The curve is smooth unless it goes...

Demand curve are, however, considered to be generally convex in accordance with diminishing marginal utility. Theoretically, the Demand curve is equivalent...

indifference curve, that is the magnitude of the slope is decreasing or becoming less steep, then the preference is convex. The theory of indifference curves was...

Since they lie on a parabola, which is a convex curve, it is easy to see that the vertices of the convex hull, when traversed along the boundary, produce...

It is a form of back for an automobile body consisting of a single convex curve from the top to the rear bumper. This automotive design element "relates...

scimitar (/ˈsɪmɪtər/ or /ˈsɪmɪtɑːr/) is a single-edged sword with a convex curved blade of about 75 to 90 cm (30 to 36 inches) associated with Middle...

combinations with positive coefficients. It follows that convex cones are convex sets. The definition of a convex cone makes sense in a vector space over any ordered...

and solved. A generalized solution for any smooth convex curve like an ellipse, and even unclosed curves, has been formulated. The question about the grazable...

semicircular curves or arcs that, as a result of a point of inflection from concave to convex or vice versa,: 218  have ends of the overall curve that point...

figure with three vertices connected by curves that are concave to the exterior, making the interior points a non-convex set. A hypocycloid can be represented...

well-behaved) forms a curve with one tangent line in each direction, regardless of orientation. Every closed strictly convex curve is the envelope of its...

smooth, convex curve the angle of the tangent line changes monotonically, and the resulting dual curve is also smooth and convex. Further, both curves above...

of each of its supporting lines. The interior of a closed convex curve is a convex set. Convex function - a function in which the line segment between any...

a shape is. The curve-shortening flow decreases the isoperimetric ratio of any smooth convex curve so that, in the limit as the curve shrinks to a point...

restrictions convex sets in topological vector spaces convex sets in 2 dimensions (including convex curves) convex sets in 3 dimensions (including convex surfaces)...

the curve, and can be computed as the total curvature divided by 2π. In polygons, the turning number is referred to as the polygon density. For convex polygons...