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  2. Turn (angle) - Wikipedia

    en.wikipedia.org/wiki/Turn_(angle)

    An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian. A full circle corresponds to a full turn, or approximately 6.28 radians, which is expressed here using the Greek letter tau (τ). Some special angles in radians, stated in terms of 𝜏. A comparison of angles expressed in degrees and radians.

  3. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    The radian is determined by the circumference of a circle that is equal in length to the radius of the circle (n = 2 π = 6.283...). It is the angle subtended by an arc of a circle that has the same length as the circle's radius. The symbol for radian is rad. One turn is 2 π radians, and one radian is ⁠ 180° / π ⁠, or

  4. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    A convenient choice is the Frobenius norm, ‖ Q − M ‖ F, squared, which is the sum of the squares of the element differences. Writing this in terms of the trace, Tr, our goal is, Find Q minimizing Tr( (Q − M) T (Q − M) ), subject to Q T Q = I. Though written in matrix terms, the objective function is just a quadratic polynomial. We can ...

  5. Angular displacement - Wikipedia

    en.wikipedia.org/wiki/Angular_displacement

    Figure 1: Euler's rotation theorem. A great circle transforms to another great circle under rotations, leaving always a diameter of the sphere in its original position. Figure 2: A rotation represented by an Euler axis and angle. In three dimensions, angular displacement is an entity with a direction and a magnitude.

  6. Spherical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Spherical_coordinate_system

    The sign of the azimuth is determined by designating the rotation that is the positive sense of turning about the zenith. This choice is arbitrary, and is part of the coordinate system definition. (If the inclination is either zero or 180 degrees (= π radians), the azimuth is arbitrary. If the radius is zero, both azimuth and inclination are ...

  7. Clock angle problem - Wikipedia

    en.wikipedia.org/wiki/Clock_angle_problem

    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. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute.

  8. AOL Mail

    mail.aol.com

    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  9. Quaternions and spatial rotation - Wikipedia

    en.wikipedia.org/wiki/Quaternions_and_spatial...

    The identity rotation is a point, and a small angle of rotation about some axis can be represented as a point on a sphere with a small radius. As the angle of rotation grows, the sphere grows, until the angle of rotation reaches 180 degrees, at which point the sphere begins to shrink, becoming a point as the angle approaches 360 degrees (or ...