ExamReviewSheet.Dec2016INK
... What are the loci of points that are equidistant from two points, A and B and also equidistant from two parallel planes? The loci is the intersection of a plane which is equidistant from A and B and the perpendicular bisector of AB , and a plane which is between the parallel planes. This intersectio ...
... What are the loci of points that are equidistant from two points, A and B and also equidistant from two parallel planes? The loci is the intersection of a plane which is equidistant from A and B and the perpendicular bisector of AB , and a plane which is between the parallel planes. This intersectio ...
sat math review
... An integer can be divided into a limited set of factors; there are an infinite number of multiples that can be divided by a specific integer. An integer with only 2 factors (itself and 1) is a prime number. 1 is not a prime number, but 2 is. The least common multiple of two integers is the smallest ...
... An integer can be divided into a limited set of factors; there are an infinite number of multiples that can be divided by a specific integer. An integer with only 2 factors (itself and 1) is a prime number. 1 is not a prime number, but 2 is. The least common multiple of two integers is the smallest ...
Common Core Curriculum Map 2012
... variable on both sides. Review of midpoint and distance formulas along with Pythagorean theorem. They will also review finding the area and perimeter of triangles, rectangles, and squares. Students need to know the geometric vocabulary and the appropriate symbol :point, line, plane, segment, ray, ve ...
... variable on both sides. Review of midpoint and distance formulas along with Pythagorean theorem. They will also review finding the area and perimeter of triangles, rectangles, and squares. Students need to know the geometric vocabulary and the appropriate symbol :point, line, plane, segment, ray, ve ...
Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required. They can be given in several ways, Euler angles being one of them; see charts on SO(3) for others. Euler angles are also used to describe the orientation of a frame of reference (typically, a coordinate system or basis) relative to another. They are typically denoted as α, β, γ, or φ, θ, ψ.Euler angles represent a sequence of three elemental rotations, i.e. rotations about the axes of a coordinate system. For instance, a first rotation about z by an angle α, a second rotation about x by an angle β, and a last rotation again about z, by an angle γ. These rotations start from a known standard orientation. In physics, this standard initial orientation is typically represented by a motionless (fixed, global, or world) coordinate system; in linear algebra, by a standard basis.Any orientation can be achieved by composing three elemental rotations. The elemental rotations can either occur about the axes of the fixed coordinate system (extrinsic rotations) or about the axes of a rotating coordinate system, which is initially aligned with the fixed one, and modifies its orientation after each elemental rotation (intrinsic rotations). The rotating coordinate system may be imagined to be rigidly attached to a rigid body. In this case, it is sometimes called a local coordinate system. Without considering the possibility of using two different conventions for the definition of the rotation axes (intrinsic or extrinsic), there exist twelve possible sequences of rotation axes, divided in two groups: Proper Euler angles (z-x-z, x-y-x, y-z-y, z-y-z, x-z-x, y-x-y) Tait–Bryan angles (x-y-z, y-z-x, z-x-y, x-z-y, z-y-x, y-x-z). Tait–Bryan angles are also called Cardan angles; nautical angles; heading, elevation, and bank; or yaw, pitch, and roll. Sometimes, both kinds of sequences are called ""Euler angles"". In that case, the sequences of the first group are called proper or classic Euler angles.