Crown moulding (interchangeably spelled Crown molding in American English) is a form of cornice created out of decorative moulding installed atop an interior wall. It is also used atop doors, windows, pilasters and cabinets.
Historically made of plaster or wood, modern crown moulding installation may be of a single element, or a build-up of multiple components into a more elaborate whole.
Crown moulding is typically installed at the intersection of walls and ceiling, but may also be used above doors, windows, or cabinets. Crown treatments made out of wood may be a single piece of trim, or a build-up of multiple components to create a more elaborate look. The main element, or the only in a plain installation, is a piece of trim that is sculpted on one side and flat on the other, with standard angles forming 90-degrees milled on both its top and bottom edges. When placed against a wall and ceiling a triangular void is created behind it. Cutting inside and outside corners requires complex cuts at standard angles, typically done with powered compound miter saws that feature detents at these angles to aid the user.
An alternative method, coping, is a two step process that begins with cutting a simple miter on both mating trim ends, then uses a coping saw to back-cut at least one of the miters along its profiled edge to provide relief during installation.
Simplified crown installation is possible when using manufactured corner blocks, requiring only simple butt cuts on each end of lengths of trim. Plastic and foam versions of crown are now available, typically with corner blocks, for easy installation by DIY home improvement enthusiasts.
Fitting crown moulding requires a cut at the correct combination of miter angle and bevel angle. The calculation of these angles is affected by two variables: (1) the spring angle (or crown angle, typically sold in 45° and 38° formats), and (2) the wall angle.
Pre-calculated crown moulding tables or software can be used to facilitate the determination of the correct angles. Given the spring angle and the wall angle, the formulas used to calculate the miter angle and the bevel angle are:
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three real numbers: the radial distancer along the radial line connecting the point to the fixed point of origin; the polar angleθ between the radial line and a polar axis; and the azimuthal angleφ as the angle of rotation of the radial line around the polar axis. (See graphic re the "physics convention".) Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates.
In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
In astronomy, coordinate systems are used for specifying positions of celestial objects relative to a given reference frame, based on physical reference points available to a situated observer. Coordinate systems in astronomy can specify an object's relative position in three-dimensional space or plot merely by its direction on a celestial sphere, if the object's distance is unknown or trivial.
In mathematics, the inverse trigonometric functions are the inverse functions of the trigonometric functions, under suitably restricted domains. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.
In mathematics, a trigonometric substitution replaces a trigonometric function for another expression. In calculus, trigonometric substitutions are a technique for evaluating integrals. In this case, an expression involving a radical function is replaced with a trigonometric one. Trigonometric identities may help simplify the answer. Like other methods of integration by substitution, when evaluating a definite integral, it may be simpler to completely deduce the antiderivative before applying the boundaries of integration.
The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path between the two points on the surface of the sphere.
Projectile motion is a form of motion experienced by an object or particle that is projected in a gravitational field, such as from Earth's surface, and moves along a curved path under the action of gravity only. In the particular case of projectile motion on Earth, most calculations assume the effects of air resistance are passive and negligible.
Moulding, or molding, also coving, is a strip of material with various profiles used to cover transitions between surfaces or for decoration. It is traditionally made from solid milled wood or plaster, but may be of plastic or reformed wood. In classical architecture and sculpture, the moulding is often carved in marble or other stones. In historic architecture, and some expensive modern buildings, it may be formed in place with plaster.
A miter saw or mitre saw is a saw used to make accurate crosscuts and miters in a workpiece by positioning a mounted blade onto a board. A miter saw in its earliest form was composed of a back saw in a miter box, but in modern implementation consists of a powered circular saw that can be positioned at a variety of angles and lowered onto a board positioned against a backstop called the fence.
In computing and mathematics, the function atan2 is the 2-argument arctangent. By definition, is the angle measure between the positive -axis and the ray from the origin to the point in the Cartesian plane. Equivalently, is the argument of the complex number
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle, and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle , the sine and cosine functions are denoted as and .
A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, a two-dimensional simple wave, is a centered expansion process that occurs when a supersonic flow turns around a convex corner. The fan consists of an infinite number of Mach waves, diverging from a sharp corner. When a flow turns around a smooth and circular corner, these waves can be extended backwards to meet at a point.
There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides. The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles, see Trigonometric functions.
The Cassini projection is a map projection first described in an approximate form by César-François Cassini de Thury in 1745. Its precise formulas were found through later analysis by Johann Georg von Soldner around 1810. It is the transverse aspect of the equirectangular projection, in that the globe is first rotated so the central meridian becomes the "equator", and then the normal equirectangular projection is applied. Considering the earth as a sphere, the projection is composed of the operations:
The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect to a variable. For example, the derivative of the sine function is written sin′(a) = cos(a), meaning that the rate of change of sin(x) at a particular angle x = a is given by the cosine of that angle.
In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in Figure 1. By convention the positive real axis is drawn pointing rightward, the positive imaginary axis is drawn pointing upward, and complex numbers with positive real part are considered to have an anticlockwise argument with positive sign.
Solution of triangles is the main trigonometric problem of finding the characteristics of a triangle, when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.
The position of the Sun in the sky is a function of both the time and the geographic location of observation on Earth's surface. As Earth orbits the Sun over the course of a year, the Sun appears to move with respect to the fixed stars on the celestial sphere, along a circular path called the ecliptic.
