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24 relations: Arc length, Boundary (topology), Convex combination, Convex position, Convex set, Curvature, Curve, Four-vertex theorem, Geometry, Half-space (geometry), Heinz Hopf, Length, Line segment, List of convexity topics, Oval, Oval (projective plane), Projective geometry, Rotational symmetry, Smoothness, Supporting line, Tangent, Two-dimensional space, Vertex (curve), Without loss of generality.
Arc length
Determining the length of an irregular arc segment is also called rectification of a curve.
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Boundary (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.
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Convex combination
In convex geometry, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1.
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Convex position
In discrete and computational geometry, a set of points in the Euclidean plane is said to be in convex position or convex independent if none of the points can be represented as a convex combination of the others.
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Convex set
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
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Curvature
In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.
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Curve
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.
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Four-vertex theorem
The classical four-vertex theorem states that the curvature function of a simple, closed, smooth plane curve has at least four local extrema (specifically, at least two local maxima and at least two local minima).
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Half-space (geometry)
In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space.
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Heinz Hopf
Heinz Hopf (19 November 1894 – 3 June 1971) was a German mathematician who worked on the fields of topology and geometry.
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Length
In geometric measurements, length is the most extended dimension of an object.
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Line segment
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
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List of convexity topics
This is a list of convexity topics, by Wikipedia page.
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Oval
An oval (from Latin ovum, "egg") is a closed curve in a plane which "loosely" resembles the outline of an egg.
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Oval (projective plane)
In projective geometry an oval is a circle-like pointset (curve) in a plane that is defined by incidence properties.
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Projective geometry
Projective geometry is a topic in mathematics.
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Rotational symmetry
Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Supporting line
In geometry, a supporting line L of a curve C in the plane is a line that contains a point of C, but does not separate any two points of C."The geometry of geodesics", Herbert Busemann, In other words, C lies completely in one of the two closed half-planes defined by L and has at least one point on L.
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Tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.
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Two-dimensional space
Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).
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Vertex (curve)
In the geometry of planar curves, a vertex is a point of where the first derivative of curvature is zero.
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Without loss of generality
Without loss of generality (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics.
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References
[1] https://en.wikipedia.org/wiki/Convex_curve
