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In mathematics, the Regiomontanus's angle maximization problem, is a famous optimization problem [1] posed by the 15th-century German mathematician Johannes Müller [2] (also known as Regiomontanus). The problem is as follows: The two dots at eye level are possible locations of the viewer's eye. A painting hangs from a wall.
Gimbal lock can occur in gimbal systems with two degrees of freedom such as a theodolite with rotations about an azimuth (horizontal angle) and elevation (vertical angle). These two-dimensional systems can gimbal lock at zenith and nadir , because at those points azimuth is not well-defined, and rotation in the azimuth direction does not change ...
Clock angle problems relate two different measurements: angles and time. The angle is typically measured in degrees from the mark of number 12 clockwise. The time is usually based on a 12-hour clock. A method to solve such problems is to consider the rate of change of the angle in degrees per minute.
It is tempting to attempt to solve the inscribed square problem by proving that a special class of well-behaved curves always contains an inscribed square, and then to approximate an arbitrary curve by a sequence of well-behaved curves and infer that there still exists an inscribed square as a limit of squares inscribed in the curves of the sequence.
The tangent half-angle substitution parametrizes the unit circle centered at (0, 0). Instead of +∞ and −∞, we have only one ∞, at both ends of the real line. That is often appropriate when dealing with rational functions and with trigonometric functions. (This is the one-point compactification of the line.)
Because the "sweep" of the area under the involute is bounded by a tangent line (see diagram and derivation below) which is not the boundary (¯) between overlapping areas, the decomposition of the problem results in four computable areas: a half circle whose radius is the tether length (A 1); the area "swept" by the tether over an angle of 2 ...
Trio the Buffalos won Season 12 of "The Masker Singer" marking the first win from a group in the show's nearly six year run.
This problem per se is quite clumsy to solve in closed form. However, by employing a very simple conformal mapping, the inconvenient angle is mapped to one of precisely radians, meaning that the corner of two planes is transformed to a straight line. In this new domain, the problem (that of calculating the electric field impressed by a point ...