Many GA-style guitars also have a convex back panel to increase the volume of space in the soundbox without making the soundbox deeper at the edges, which would affect comfort and playability.

In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.

* Convex cone, a subset C of a vector space V is a convex cone if αx + βy belongs to C, for any positive scalars α, β, and any x, y in C

In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object.

is in C. In other words, every point on the line segment connecting x and y is in C. This implies that a convex set in a real or complex topological vector space is path-connected, thus connected.

Some examples of convex subsets of a Euclidean 3-dimensional space are the Archimedean solids and the Platonic solids.

The collection of convex subsets of a vector space has the following properties:

Every subset A of the vector space is contained within a smallest convex set ( called the convex hull of A ), namely the intersection of all convex sets containing A.

Instead, with the topology of compact convergence, C ( a, b ) can be given the structure of a Fréchet space: a locally convex topological vector space whose topology can be induced by a complete translation-invariant metric.

The problem of finding the Delaunay triangulation of a set of points in d-dimensional Euclidean space can be converted to the problem of finding the convex hull of a set of points in ( d + 1 )- dimensional space, by giving each point p an extra coordinate equal to | p |< sup > 2 </ sup >, taking the bottom side of the convex hull, and mapping back to d-dimensional space by deleting the last coordinate.

In Euclidean space R < sup > n </ sup >, or any convex subset of R < sup > n </ sup >, there is only one homotopy class of loops, and the fundamental group is therefore the trivial group with one element.

In fact, it is a locally convex topological vector space, with the seminorms being the suprema on compact subsets.

Radon measures have an alternative definition in terms of linear functionals on the locally convex space of continuous functions with compact support.

Another convex polyhedron is formed by the small central space common to all members of the compound.

Whitehead did not define the topology of his actual entities in modern terms, but it seems that he envisaged them as convex compact or ' oval ' sets in Minkowski space.

If X is equipped with the weak topology, then addition and scalar multiplication remain continuous operations, and X is a locally convex topological vector space.

In the third book, Dürer gives principles by which the proportions of the figures can be modified, including the mathematical simulation of convex and concave mirrors ; here Dürer also deals with human physiognomy.

It has been called the Archimedean honeycombs by analogy with the convex uniform ( non-regular ) polyhedra, commonly called Archimedean solids.

The Ionic base has two convex moldings called tori which are separated by a scotia.

At rough vacuum, this asymmetric heating effect generates a net gas movement across each vane, from the concave side to the convex side, as shown by the researchers ' Direct Simulation Monte Carlo ( DSMC ) modeling.

Paradoxically, it is possible to reduce the divergence of a laser beam by first expanding it with one convex lens, and then collimating it with a second convex lens whose focal point is coincident with that of the first lens.

It is worth noting that the vertices and edges of a convex polyhedron can be projected to form a graph ( sometimes called a Schlegel diagram ) on the sphere or on a flat plane, and the corresponding graph formed by the dual of this polyhedron is its dual graph.

Euler's formula relating the number of edges, vertices, and faces of a convex polyhedron was studied and generalized by Cauchy and L ' Huillier, and is at the origin of topology.

They may be obtained by stellating the regular convex dodecahedron and icosahedron, and differ from these in having regular pentagrammic faces or vertex figures.

A properly constructed machete will have a convex or flat primary bevel from the spine to the edge, which is formed by a secondary bevel.

Parabolic mirrors were also described by the physicist Ibn Sahl in the 10th century, and Ibn al-Haytham discussed concave and convex mirrors in both cylindrical and spherical geometries, carried out a number of experiments with mirrors, and solved the problem of finding the point on a convex mirror at which a ray coming from one point is reflected to another point.

They are distinguished by a hypothesized convex bend with a discontinuity at the bend –" kink ".

Incoming parallel rays are focused by a convex lens into an inverted real image one focal length from the lens, on the far side of the lens.

In fact, a bounded linear functional on C < sub > c </ sub >( X ) need not remain so if the locally convex topology on C < sub > c </ sub >( X ) is replaced by the supremum norm, the norm of C < sub > 0 </ sub >( X ).

* Church of San Francesco all ' Immacolata, with a convex façade intermingled by columns and pilaster strips.

For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape formed by a rubber band stretched around X.

Each convex set containing X must ( by the assumption that it is convex ) contain all convex combinations of points in X, so the set of all convex combinations is contained in the intersection of all convex sets containing X. Conversely, the set of all convex combinations is itself a convex set containing X, so it also contains the intersection of all convex sets containing X, and therefore the sets given by these two definitions must be equal.

In the 1950s and 1960s in Canada, John Carver Meadows Frost at Avro Canada started experimenting with the Coandă effect and noticed that he could produce a ring of airflow by blowing the air down over a convex surface.

: The triple object-glass, consisting of a combination of two convex lenses of crown glass with a concave flint lens between them, was introduced in 1765 by Peter, son of, John Dollond, and many excellent telescopes of this kind were made by him.

In 2009, researchers at the University of Texas, Austin created a monocolored light mill which has four curved vanes ; each vane forms a convex and a concave surface.

* In the plane ( d = 2 ), if there are b vertices on the convex hull, then any triangulation of the points has at most 2n − 2 − b triangles, plus one exterior face ( see Euler characteristic ).

As in any strictly convex solid, at least three faces meet at every vertex, and the total of their angles is less than 360 degrees.

* Exterior angle – Tracing around a convex n-gon, the angle " turned " at a corner is the exterior or external angle.

It is a thin, curved device, with the sensors on the convex side, that covers the eyes and attaches at small input jacks implanted in the temples.

The constrictor and double constrictor are both extremely secure when tied tightly around convex objects with cord scaled for the task at hand.

In fact, according to Carathéodory's theorem, if X is a subset of an N-dimensional vector space, convex combinations of at most N + 1 points are sufficient in the definition above.

Therefore, the convex hull of a set X of three or more points in the plane is the union of all the triangles determined by triples of points from X, and more generally in N-dimensional space the convex hull is the union of the simplices determined by at most N + 1 vertices from X.

In telecommunications and radar, a Cassegrain antenna is a parabolic antenna in which the feed radiator is mounted at or behind the surface of the concave main parabolic reflector dish and is aimed at a smaller convex secondary reflector suspended in front of the primary reflector.

File: NAMA Mycènes bouclier 1. jpg | Wall painting depicting a Mycenaean Greek " figure eight " shield with a suspension strap at the middle, 15th century BC, National Archaeological Museum, Athens-The faces of figure eight shields were quite convex.

The anterior arch forms about one-fifth of the ring: its anterior surface is convex, and presents at its center the anterior tubercle for the attachment of the Longus colli muscles and the anterior longitudinal ligament ; posteriorly it is concave, and marked by a smooth, oval or circular facet ( fovea dentis ), for articulation with the odontoid process ( dens ) of the axis.

For n = 2 the theorem claims that a convex figure in the plane symmetric about the origin and with area greater than 4 encloses at least one lattice point in addition to the origin.

As in fuzzy numbers, the membership function must be convex, normalized, at least segmentally continuous.

Other noteworthy unknots are those that consist of rigid line segments connected by universal joints at their endpoints ( linkages ), that yet cannot be reconfigured into a convex polygon, thus acquiring the name stuck unknots.

Note the fact that the set of points mapped into any hyperplane can be quite convoluted as a result, allowing much more complex discrimination between sets which are not convex at all in the original space.

They usually have the form of a cylinder of gold ( although some of the crowns at the Church of Our Lady Mary of Zion in Axum have the form of a gold cube ) with a convex dome on the top with usually some form of cross on a pedestal.

For a converging lens ( for example a convex lens ), the focal length is positive, and is the distance at which a beam of collimated light will be focused to a single spot.