Search results
Results from the WOW.Com Content Network
In the United States, Canada, and Mexico, ring sizes are specified using a numerical scale with 1 ⁄ 4 steps, where whole sizes differ by 0.032 inches (0.81 mm) of internal diameter, equivalent to 0.1005 inches (2.55 mm) of internal circumference.
Animation of a cut napkin ring with constant height In geometry , the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere , i.e. the part that remains after a hole in the shape of a circular cylinder is drilled through the center of the sphere.
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.
The first four partial sums of 1 + 2 + 4 + 8 + ⋯. 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.
where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]
Today, a more standard phrasing of Archimedes' proposition is that the partial sums of the series 1 + 1 / 4 + 1 / 16 + ⋯ are: + + + + = +. This form can be proved by multiplying both sides by 1 − 1 / 4 and observing that all but the first and the last of the terms on the left-hand side of the equation cancel in pairs.
For premium support please call: 800-290-4726 more ways to reach us
1. An upper bound is a disc of diameter equal to the length of the worm. 2. By symmetry, half the disc is sufficient. 3. The cover must support a width at least the worm's length divided by π: 4. A solution by John E. Wetzel. [1]