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Roof pitch is the steepness of a roof expressed as a ratio of inch(es) rise per horizontal foot (or their metric equivalent), or as the angle in degrees its surface deviates from the horizontal. A flat roof has a pitch of zero in either instance; all other roofs are pitched .
(This is the angle α opposite the "rise" side of a triangle with a right angle between vertical rise and horizontal run.) as a percentage, the formula for which is which is equivalent to the tangent of the angle of inclination times 100. In Europe and the U.S. percentage "grade" is the most commonly used figure for describing slopes.
Satari: A Swedish variant on the monitor roof; a double hip roof with a short vertical wall usually with small windows, popular from the 17th century on formal buildings. [citation needed] (Säteritak in Swedish.) Mansard (French roof): A roof with the pitch divided into a shallow slope above a steeper slope. The steep slope may be curved.
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]
Picture Name Schläfli symbol Vertex/Face configuration exact dihedral angle (radians) dihedral angle – exact in bold, else approximate (degrees) Platonic solids (regular convex)
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