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In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle ), so that the height of the cap is equal to the radius of the sphere, the spherical ...
The first geodesic dome was designed after World War I by Walther Bauersfeld, [1] chief engineer of Carl Zeiss Jena, an optical company, for a planetarium to house his planetarium projector. An initial, small dome was patented and constructed by the firm of Dykerhoff and Wydmann on the roof of the Carl Zeiss Werke in Jena, Germany. A larger ...
A hemispherical head ("hemi-head") gives an efficient combustion chamber with minimal heat loss to the head, and allows for two large valves.However, a hemi-head usually allows no more than two valves per cylinder due to the difficulty in arranging the valve gear for four valves at diverging angles, and these large valves are necessarily heavier than those in a multi-valve engine of similar ...
The solid angle of a sphere measured from any point in its interior is 4 π sr. The solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2 π /3 sr. The solid angle subtended at the corner of a cube (an octant) or spanned by a spherical octant is π /2 sr, one-eight of the solid angle of a sphere. [1]
The user may choose to replace the inclination angle by its complement, the elevation angle (or altitude angle), measured upward between the reference plane and the radial line—i.e., from the reference plane upward (towards to the positive z-axis) to the radial line. The depression angle is the negative of the elevation angle.
In Magnus Wenninger's Spherical models, polyhedra are given geodesic notation in the form {3,q+} b,c, where {3,q} is the Schläfli symbol for the regular polyhedron with triangular faces, and q-valence vertices.
The projection onto the hemisphere, giving the solid angle subtended by A j, takes care of the factors cos(θ 2) and 1/r 2; the projection onto the circle and the division by its area then takes care of the local factor cos(θ 1) and the normalisation by π.
Hemispherical photograph used to study microclimate of winter roosting habitat at the Monarch Butterfly Biosphere Reserve, Mexico.. Hemispherical photography, also known as canopy photography, is a technique to estimate solar radiation and characterize plant canopy geometry using photographs taken looking upward through an extreme wide-angle lens or a fisheye lens (Rich 1990).