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1/2 + 1/4 + 1/8 + 1/16 + ⋯. First six summands drawn as portions of a square. The geometric series on the real line. In mathematics, the infinite series 1 2 + 1 4 + 1 8 + 1 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation ...
In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser 's circle problem, has a solution by an inductive method. The greatest possible number of regions, rG = , giving the sequence 1, 2, 4 ...
In 1961, at a meeting in Scottsdale, Arizona, the Committee on Grade Simplification and Standardization agreed to what is now the current U.S. standard: in part, the dressed size of a 1-inch (nominal) board was fixed at 3 ⁄ 4 inch; while the dressed size of 2 inch (nominal) lumber was reduced from 1 + 5 ⁄ 8 inch to the current 1 + 1 ⁄ 2 inch.
In mathematics, 1 + 2 + 4 + 8 + ⋯ is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2. As a series of real numbers it diverges to infinity, so the sum of this series is infinity. However, it can be manipulated to yield a number of ...
These factorizations work not only over the complex numbers, but also over any field, where either –1, 2 or –2 is a square. In a finite field , the product of two non-squares is a square; this implies that the polynomial x 4 + 1 , {\displaystyle x^{4}+1,} which is irreducible over the integers, is reducible modulo every prime number .
The beams are continuously formed, so the length of the beam is limited only to the maximum length that can be handled and transported. Typical widths are 3 + 1 ⁄ 2, 5 + 1 ⁄ 4 or 7 inches (89, 133 or 178 mm); typical depths are 9 + 1 ⁄ 2, 11 + 7 ⁄ 8, 14, 16 and 18 inches (240, 300, 360, 410 and 460 mm). Typically the beams are made to a ...
A method for logs over 19 in (48 cm) Quarter sawing or quartersawing is a woodworking process that produces quarter-sawn or quarter-cut boards in the rip cutting of logs into lumber. The resulting lumber can also be called radially-sawn or simply quartered. There is widespread confusion between the terms rift sawn and quarter sawn with the ...
US Customary. 1⁄12 ft 3. The board foot or board-foot is a unit of measurement for the volume of lumber in the United States and Canada. It equals the volume of a board that is one-foot (305 mm) in length, one-foot (305 mm) in width, and one-inch (25.4 mm) in thickness. Board foot can be abbreviated as FBM (for "foot, board measure"), BDFT ...