Block G: Geometry – properties of shapes, position and direction
... identify and describe the properties of 2-D shapes, including the number of sides, corners and line symmetry in a vertical line identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces compare and sort common 2-D and 3-D shapes and everyday objects; ...
... identify and describe the properties of 2-D shapes, including the number of sides, corners and line symmetry in a vertical line identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces compare and sort common 2-D and 3-D shapes and everyday objects; ...
Geometry Module 2, Topic C, Lesson 15: Teacher
... We know that for two triangles, when two pairs of corresponding angles are equal and the included corresponding sides are equal in length, the triangles are congruent. By the triangle sum theorem, we can actually state that all three pairs of corresponding angles of the triangles are equal. Since a ...
... We know that for two triangles, when two pairs of corresponding angles are equal and the included corresponding sides are equal in length, the triangles are congruent. By the triangle sum theorem, we can actually state that all three pairs of corresponding angles of the triangles are equal. Since a ...
Source-receiver offset ranges for P-SV seismic data
... In the design of converted-wave (P-SV) reflection seismic surveys, it has generally been accepted that longer source-receiver offsets are required than those used for conventional (P-P) reflection surveys (Garotta, 1987). This is due to the fact that no converted waves are recorded at zero-offset (n ...
... In the design of converted-wave (P-SV) reflection seismic surveys, it has generally been accepted that longer source-receiver offsets are required than those used for conventional (P-P) reflection surveys (Garotta, 1987). This is due to the fact that no converted waves are recorded at zero-offset (n ...
Park Forest Math Team 2015-16
... By completing around O to 360 degrees we get ∠BOA=46 degrees. Complete triangle ACO to 180 to get ∠OAC=54 degrees. Finally Z supplements it, so is 126 degrees. ...
... By completing around O to 360 degrees we get ∠BOA=46 degrees. Complete triangle ACO to 180 to get ∠OAC=54 degrees. Finally Z supplements it, so is 126 degrees. ...
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.