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In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum.It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus.
Their product was used on large housing projects in the northeast and was purportedly the siding of choice for a 1947 Pennsylvania development, the first subdivision to solely use aluminium siding. Products such as 4,-6,-8-and-10-inch (100, 150, 200 and 250 mm) by 12-foot (3.7 m) unpainted aluminium panels, starter strips, corner pieces and ...
Thermal insulation – CLT panels provide air tightness and great thermal insulation to buildings as the thermal conductivity (U) of a panel is approximately 0.3458 W/m 2 K. [18] Other common building materials can have U values ranging from 0.4 to 2.5 W/m 2 K. [19] The various layers of wood also serve as a thermal mass, which can help reduce ...
In integral calculus, Euler's formula for complex numbers may be used to evaluate integrals involving trigonometric functions. Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely e i x {\displaystyle e^{ix}} and e − i x {\displaystyle e^{-ix}} and then integrated.
In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
Minkowski sums act linearly on the perimeter of two-dimensional convex bodies: the perimeter of the sum equals the sum of perimeters. Additionally, if K {\textstyle K} is (the interior of) a curve of constant width , then the Minkowski sum of K {\textstyle K} and of its 180° rotation is a disk.
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Since every integer is congruent to its own cube modulo 6, it follows that every integer is the sum of five cubes of integers. In 1966, V. A. Demjanenko [ de ] proved that any integer that is congruent neither to 4 nor to −4 modulo 9 is the sum of four cubes of integers.