Search results
Results from the WOW.Com Content Network
is the number of collisions made (in ideal conditions, perfectly elastic with no friction) by an object of mass m initially at rest between a fixed wall and another object of mass b 2N m, when struck by the other object. [1] (This gives the digits of π in base b up to N digits past the radix point.)
((x),(y) = {239, 13 2} is a solution to the Pell equation x 2 − 2 y 2 = −1.) Formulae of this kind are known as Machin-like formulae . Machin's particular formula was used well into the computer era for calculating record numbers of digits of π , [ 39 ] but more recently other similar formulae have been used as well.
The total curvature of a closed curve is always an integer multiple of 2 π, where N is called the index of the curve or turning number – it is the winding number of the unit tangent vector about the origin, or equivalently the degree of the map to the unit circle assigning to each point of the curve, the unit velocity vector at that point.
[2] The accuracy of Milü to the true value of π can be explained using the continued fraction expansion of π , the first few terms of which are [3; 7, 15, 1, 292, 1, 1, ...] . A property of continued fractions is that truncating the expansion of a given number at any point will give the " best rational approximation " to the number.
In mathematics, the values of the trigonometric functions can be expressed approximately, as in (/), or exactly, as in (/) = /.While trigonometric tables contain many approximate values, the exact values for certain angles can be expressed by a combination of arithmetic operations and square roots.
The average rate for shorter 15-year terms is 6.11% for purchase and 6.13% for refinance, down 3 basis points from 6.14% for purchase and 2 basis points from 6.15% for refinance this time last week.
Mortgage rates rose for a fifth straight week as pre-election volatility continued to rock the bond market. The average 30-year fixed-rate mortgage was 6.72% in the week through Wednesday ...
For the above isosceles triangle with unit sides and angle , the area 1 / 2 × base × height is calculated in two orientations. When upright, the area is sin θ cos θ {\displaystyle \sin \theta \cos \theta } .