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vertices    
vertex的复数形

vertex的复数形

vertices
顶点

Vertex \Ver"tex\, n.; pl. E. {Vertexes}, L. {Vertices}. [L.
vertex, -icis, a whirl, top of the head, top, summit, from
vertere to turn. See {Verse}, and cf. {Vortex}.]
A turning point; the principal or highest point; top; summit;
crown; apex. Specifically:
[1913 Webster]
(a) (Anat.) The top, or crown, of the head.
[1913 Webster]
(b) (Astron.) The zenith, or the point of the heavens
directly overhead.
[1913 Webster]
(c) (Math.) The point in any figure opposite to, and farthest
from, the base; the terminating point of some particular
line or lines in a figure or a curve; the top, or the
point opposite the base.
[1913 Webster]

Note: The principal vertex of a conic section is, in the
parabola, the vertex of the axis of the curve: in the
ellipse, either extremity of either axis, but usually
the left-hand vertex of the transverse axis; in the
hyperbola, either vertex, but usually the right-hand
vertex of the transverse axis.
[1913 Webster]

{Vertex of a curve} (Math.), the point in which the axis of
the curve intersects it.

{Vertex of an angle} (Math.), the point in which the sides of
the angle meet.

{Vertex of a solid}, or {Vertex of a surface of revolution}
(Math.), the point in which the axis pierces the surface.
[1913 Webster]


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  • geometry - Orientation of a triangles vertices in 3D space: Clockwise . . .
    I would approach the issue from a completely different direction Consider a triangle in 3D with vertices at $\vec {v}_0$, $\vec {v}_1$, and $\vec {v}_2$ It has a directed normal $\vec {n}$, $$\vec {n} = \left (\vec {v}_1 - \vec {v}_0\right)\times\left (\vec {v}_2 - \vec {v}_0\right) \tag {1}\label {1}$$ If we look along $\vec {n}$ in one direction, the vertices are clockwise; in the opposite
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    Think about the vertices of the polygon as potential candidates for vertices of the triangle Using that, you get (n choose 3) as the number of possible triangles that can be formed by the vertices of a regular polygon of n sides
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    A cube has vertices and edges, and these form the vertex set and edge set of a graph At page 55 Remark 1 4 8 of the Second Edition: We often use the same names for corresponding concepts in the graph and digraph models Many authors replace "vertex" and "edge" with "node" and "arc" to discuss digraphs, but this obscures the analogies
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    1 Can we find a $“special”$ point inside a $\triangle {ABC}$ such that sum of squares of distances from any two vertices is equal to the square of the distance from third vertex? I know a variety (?) of this problem which asks us to minimize the sum of distances or distances squared from three vertices of a triangle
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    1 I was reading about the moment of inertia of a triangular plate and stumbled upon some properties which directly imply the fact that the sum of squares of distances from the vertices of an equilateral triangle to a line is dependent only on the distance of the line from its centroid
  • Minimum distance from the vertices of a quadrilateral
    This is not an answer, but a visual comment The sum of the distances to the four points as a graph: This is somewhat reminiscent of 3D metaballs, an approach in computer graphics to produce organic-looking isosurfaces Compare to the graph describing the minimum distance to any of the four points: Both graphs are clipped to within the quadrilateral for simplicity





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