* 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 ).

* June 24 – British Airways Flight 9 suffers a temporary 4-engine flameout and damage to the exterior of the plane, after flying through the otherwise undetected ash plume from Indonesia's Mount Galunggung.

The Jordan curve theorem states that such curves divide the plane into an " interior " and an " exterior ".

Also like the cross product, the exterior product is anticommutative, meaning that for all vectors u and v. One way to visualize a bivector is as a family of parallelograms all lying in the same plane, having the same area, and with the same orientation of their boundaries — a choice of clockwise or counterclockwise.

The Jordan curve theorem asserts that every Jordan curve divides the plane into an " interior " region bounded by the curve and an " exterior " region containing all of the nearby and far away exterior points, so that any continuous path connecting a point of one region to a point of the other intersects with that loop somewhere.

The lobby is a double height space on the ground floor, articulated by large sheets of plate glass held back from the exterior column line, providing for an overhang around the perimeter of the building, behind which the travertine-clad elevator cores are the only elements to touch the ground plane.

Its structure consists of a large steel roof deck supported by eight exterior columns, creating an effect of a shelter with a single floating plane.

In the plane, angles about a point add up to 360 °, while interior angles in a triangle add up to 180 ° ( equivalently, exterior angles add up to 360 °).

Controlled water penetration is defined as water that penetrates beyond the inner most vertical plane of the test specimen, but has a designed means of drainage back to the exterior.

In 1987, collector Frederick Weisman had Ruscha paint the exterior of his private plane, a Lockheed JetStar.

But in working with general relativity, it turns out to be very useful to admit solutions which are not everywhere smooth ; examples include many solutions created by matching a perfect fluid interior solution to a vacuum exterior solution, and impulsive plane waves.

Most exterior scenes of the plane involve a model with one tenth of the aircraft's actual size, with the images being subsequently enhanced through computer-generated imagery.

Martha takes Wasserstein, Raggy Ann, Rexall ’ s encased brain, and Rexall ’ s wife and escapes the bombing in a plane, with the still-functioning Surgeon General clinging to the plane ’ s exterior.

Above that height, the buildings are required to set back behind a theoretical inclined plane, called sky exposure plane, which cannot be penetrated by the building's exterior wall.

Naming the central ray passing through the entrance pupil the axis of the pencil or principal ray, it can be said: the rays of the pencil intersect, not in one point, but in two focal lines, which can be assumed to be at right angles to the principal ray ; of these, one lies in the plane containing the principal ray and the axis of the system, i. e. in the first principal section or meridional section, and the other at right angles to it, i. e. in the second principal section or sagittal section.

Hilbert first enumerates the undefined concepts: point, line, plane, lying on ( a relation between points and planes ), betweenness, congruence of pairs of points, and congruence of angles.

Many results about plane figures are proved, e. g., If a triangle has two equal angles, then the sides subtended by the angles are equal.

# If two straight lines in a plane are crossed by another straight line ( called the transversal ), and the interior angles between the two lines and the transversal lying on one side of the transversal add up to less than two right angles, then on that side of the transversal, the two lines extended will intersect ( also called the parallel postulate ).

All minerals which are not part of the cubic system are double refracting, where ordinary light passing through them is broken up into two plane polarized rays that travel at different velocities and refracted at different angles.

The fluid enters along the axial plane, is accelerated by the impeller and exits at right angles to the shaft ( radially ).

It is an angular velocity about a line that makes an angle with the permanent rotation axis, and this angle lies in a plane at right angles to the plane of the couple producing the torque.

The strike is the line of intersection between the planar feature and a horizontal plane, taken according to the right hand convention, and the dip is the magnitude of the inclination, below horizontal, at right angles to strike.

When the system is used for physical three-space, it is customary to use positive sign for azimuth angles that are measured in the counter-clockwise sense from the reference direction on the reference plane, as seen from the zenith side of the plane.

Because the Earth's axis is tilted relative to its orbital plane, sunlight is incident at different angles at different times of the year.

Because the Earth's axis is tilted relative to its orbital plane, sunlight is incident at different angles at different times of the year.

However, in plane mapping there are two other angles to consider: the hyperbolic angle and the slope, which is the analogue of angle for dual numbers.

* Another more typical example in physics and engineering is the measure of plane angles.

Mutual inclination of two orbits may be calculated from their inclinations to another plane using cosine rule for angles.

The difference is that as a model of elliptic geometry a metric is introduced permitting the measurement of lengths and angles, while as a model of the projective plane there is no such metric.

However, when Cassini made targeted observations of the putative ring plane from several angles, no evidence of ring material was found, suggesting that another explanation for the earlier observations is needed.

In geometry, two lines or planes ( or a line and a plane ) are considered perpendicular ( or orthogonal ) to each other if they form congruent adjacent angles ( a T-shape ).

In 2-dimension plane, right angles can be formed by two intersected lines which the product of their slopes equals to − 1.

Angle excess, also known as spherical excess is the amount by which the sum of the angles of a polygon on a sphere exceeds the sum of the angles of a polygon with the same number of sides in a plane.

Some examples of convex subsets of the Euclidean plane are solid regular polygons, solid triangles, and intersections of solid triangles.

* Miller indices in parentheses such as ( 100 ) denote a plane of the crystal structure, and regular repetitions of that plane with a particular spacing.

Coxeter inspired Escher's interest in hyperbolic tessellations, which are regular tilings of the hyperbolic plane.

Overall, his early love of Roman and Italian landscapes and of nature led to his interest in the concept of regular division of a plane, which he applied in over 150 colored works.

In Metamorphosis I, he transformed convex polygons into regular patterns in a plane to form a human motif.

This effect symbolizes his change of interest from landscape and nature to regular division of a plane.

One type of solution represents an electron moving indefinitely through the crystal as a plane wave ; the particular solutions for a periodic regular crystal lattice are called Bloch functions.

Moiré patterns are often an undesired artifact of images produced by various digital imaging and computer graphics techniques, for example when scanning a halftone picture or ray tracing a checkered plane ( the latter being a special case of aliasing, due to undersampling a fine regular pattern ).

Stevin was the first to show how to model regular and semiregular polyhedra by delineating their frames in a plane.

The regular services could be done with a round trip time of nine to ten days, including overnighting in Cairo, Karachi and Bangkok, and with technical revision of the plane in Hong Kong.

This formula shows that on the complex plane the nth roots of unity are at the vertices of a regular n-sided polygon inscribed in the unit circle, with one vertex at 1.

In 1975 Aeroflot started regular service on the Tu-144 — the first supersonic passenger plane.

There are no squares as such in the hyperbolic plane, although there are regular quadrilaterals, meaning quadrilaterals with all sides congruent and all angles congruent ( but these angles are strictly smaller than right angles ).

There exist, in the hyperbolic plane, ( countably ) infinitely many pairs of constructible circles and constructible regular quadrilaterals of equal area.

All of Saturn's regular moons except Iapetus orbit very nearly in the plane of Saturn's equator.

Examples of infinite Coxeter groups include the triangle groups corresponding to regular tessellations of the Euclidean plane and the hyperbolic plane, and the Weyl groups of infinite-dimensional Kac – Moody algebras.

In 1618 Johannes Kepler made one of the first documented studies of tessellations when he wrote about regular and semiregular tessellation, which are coverings of a plane with regular polygons.

; Thue's theorem: The regular hexagonal packing is the densest sphere packing in the plane.

; The hexagonal honeycomb conjecture: The most efficient partition of the plane into equal areas is the regular hexagonal tiling.

For points in the plane or on an algebraic curve, the notion of general position is made algebraically precise by the notion of a regular divisor, and is measured by the vanishing of the higher sheaf cohomology groups of the associated line bundle ( formally, invertible sheaf ).

A regular 3D mesh object, such as a cube or a plane, can be used as an emitter.