Diagonal in the context of Endpoint (geometry)

In geometry, a hypotenuse is the side of a right triangle opposite to the right angle. It is the longest side of any such triangle; the two other shorter sides of such a triangle are called catheti or legs. Every rectangle can be divided into a pair of right triangles by cutting it along either diagonal; the diagonals are the hypotenuses of these triangles.

The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two legs. As an algebraic formula, this can be written as ${\displaystyle a^{2}+b^{2}=c^{2}}$, where ⁠${\displaystyle a}$⁠ is the length of one leg, ⁠${\displaystyle b}$⁠ is the length of the other leg, and ⁠${\displaystyle c}$⁠ is the length of the hypotenuse. For example, if the two legs of a right triangle have lengths 3 and 4, respectively, then the hypotenuse has length ⁠${\displaystyle 5}$⁠, because ⁠${\displaystyle \textstyle 3^{2}+4^{2}=25=5^{2}}$⁠.

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary, and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides) meet. A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.

An edge may also be an infinite line separating two half-planes.The sides of a plane angle are semi-infinite half-lines (or rays).

In geometry, a line segment is a part of a straight line that is bounded by two distinct endpoints (its extreme points), and contains every point on the line that is between its endpoints. It is a special case of an arc, with zero curvature. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry, a line segment is often denoted using an overline (vinculum) above the symbols for the two endpoints, such as in AB.

Examples of line segments include the sides of a triangle or square. More generally, when both of the segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (of that polygon or polyhedron) if they are adjacent vertices, or a diagonal. When the end points both lie on a curve (such as a circle), a line segment is called a chord (of that curve).

On 2D displays, such as computer monitors and TVs, display size or viewable image size (VIS) refers to the physical size of the area where pictures and videos are displayed. The size of a screen is usually described by the length of its diagonal, which is the distance between opposite corners, typically measured in inches. It is also sometimes called the physical image size to distinguish it from the "logical image size," which describes a screen's display resolution and is measured in pixels.

In typography and handwriting, a descender is the portion of a grapheme that extends below the baseline of a font.

For example, in the letter y, the descender is the "tail", or that portion of the diagonal line which lies below the v created by the two lines converging. In the letter p, it is the stem reaching down past the ɒ.

In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals. A kite may also be called a dart, particularly if it is not convex.

Every kite is an orthodiagonal quadrilateral (its diagonals are at right angles) and, when convex, a tangential quadrilateral (its sides are tangent to an inscribed circle). The convex kites are exactly the quadrilaterals that are both orthodiagonal and tangential. They include as special cases the right kites, with two opposite right angles; the rhombi, with two diagonal axes of symmetry; and the squares, which are also special cases of both right kites and rhombi.

In geometry, a face diagonal of a polyhedron is a diagonal on one of the faces, in contrast to a space diagonal passing through the interior of the polyhedron.

A cuboid has twelve face diagonals (two on each of the six faces), and it has four space diagonals. The cuboid's face diagonals can have up to three different lengths, since the faces come in congruent pairs and the two diagonals on any face are equal. The cuboid's space diagonals all have the same length. If the edge lengths of a cuboid are a, b, and c, then the distinct rectangular faces have edges (a, b), (a, c), and (b, c); so the respective face diagonals have lengths ${\displaystyle {\sqrt {a^{2}+b^{2}}},}$ ${\displaystyle {\sqrt {a^{2}+c^{2}}},}$ and ${\displaystyle {\sqrt {b^{2}+c^{2}}}.}$

Rigatoni (/rɪɡəˈtoʊni/, Italian: [riɡaˈtoːni]) is a type of pasta. They are larger than penne and ziti, and sometimes slightly curved, but not as curved as elbow macaroni. Rigatoni are characterized by ridges along their length, sometimes spiraling around the tube; unlike penne, the ends of rigatoni are cut perpendicular to the tube walls instead of diagonally.

The word rigatoni comes from the Italian word rigato (that stands for 'lined', 'striped', 'ruled', rigatone being the augmentative, and rigatoni the plural form), which means 'ridged' or 'lined', and is associated with the cuisine of southern and central Italy. Rigatoncini are a smaller version, close to the size of penne. Their name takes on the diminutive suffix -ino (pluralized -ini), denoting their relative size.

In geometry, a Schönhardt polyhedron is a polyhedron with the same combinatorial structure as a regular octahedron, but with dihedral angles that are non-convex along three disjoint edges. Because it has no interior diagonals, it cannot be triangulated into tetrahedra without adding new vertices. It has the fewest vertices of any polyhedron that cannot be triangulated. It is named after the German mathematician Erich Schönhardt, who described it in 1928, although the artist Karlis Johansons had exhibited a related structure in 1921.

One construction for the Schönhardt polyhedron starts with a triangular prism and twists the two equilateral triangle faces of the prism relative to each other, breaking each square face into two triangles separated by a non-convex edge. Some twist angles produce a jumping polyhedron whose two solid forms share the same face shapes. A 30° twist instead produces a shaky polyhedron, rigid but not infinitesimally rigid, whose edges form a tensegrity prism.