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For 36” posts or 42" posts, 4 feet of spacing (center to center) is recommended to minimize deflection between the cables when pushing a 4" ball in between two cables. To accommodate such standards, railing projects may incorporate 3 ½" or less of spacing between cables taking into account the cable deflection caused by the posts spacing.
Building codes also require that no opening in a guard be of a size such that a 4-inch (10 cm) sphere may pass. There are three exceptions according to the 2003 International Building Code Section 1012.3 which allow openings to not exceed 8 or 21 inches (20 or 53 cm) depending on occupancy groups or special areas.
The minimum width of the handrail above the recess shall be 1 + 1 ⁄ 4 inches (32 mm) to a maximum of 2 + 3 ⁄ 4 inches (70 mm). Edges shall have a minimum radius of 0.01 inches (0.25 mm). Handrails are located at a height between 34 and 38 inches (864 and 965 mm).
In even dimensions it is known that the smooth Poincaré conjecture is true in dimensions 2, 6, 12 and 56. This results from the construction of the exotic spheres, manifolds that are homeomorphic, but not diffeomorphic, to the standard sphere, which can be interpreted as non-standard smooth structures on the standard (topological) sphere.
The width of the slide rule is quoted in terms of the nominal width of the scales. Scales on the most common "10-inch" models are actually 25 cm, as they were made to metric standards, though some rules offer slightly extended scales to simplify manipulation when a result overflows. Pocket rules are typically 5 inches (12 cm).
The minimum height of the handrail for landings may be different and is typically 36 inches (914 mm). Handrail diameter. The size has to be comfortable for grasping and is typically between 1.25 and 2.675 inches (31.8 and 67.9 mm). Maximum space between the balusters of the handrail. This is typically 4 inches (102 mm).
Bonnesen and Fenchel [4] conjectured that Meissner tetrahedra are the minimum-volume three-dimensional shapes of constant width, a conjecture which is still open. [5] In 2011 Anciaux and Guilfoyle [6] proved that the minimizer must consist of pieces of spheres and tubes over curves, which, being true for the Meissner tetrahedra, supports the conjecture.
Given a unit sphere, a "spherical triangle" on the surface of the sphere is defined by the great circles connecting three points u, v, and w on the sphere (shown at right). If the lengths of these three sides are a (from u to v ), b (from u to w ), and c (from v to w ), and the angle of the corner opposite c is C , then the (first) spherical ...