Plainfield Public Schools Mathematics Unit Planning Organizer
... paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the defin ...
... paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the defin ...
HW3 Solutions - Stony Brook Mathematics
... Exercise 86. Can an exterior angle of an isosceles triangle be smaller than the supplementary interior angle? Consider the cases (a) where the angle is at the base, and (b) where the angle is at the vertex. In the case (a), the answer is no. For, let a and b be the base angles of an isosceles triang ...
... Exercise 86. Can an exterior angle of an isosceles triangle be smaller than the supplementary interior angle? Consider the cases (a) where the angle is at the base, and (b) where the angle is at the vertex. In the case (a), the answer is no. For, let a and b be the base angles of an isosceles triang ...
Applying Angle Theorems - the Mathematics Assessment Project
... assessment lesson, allow them to return to their usual seats. Experience has shown that this produces more profitable discussions. Assessing students’ responses Collect students’ responses to the task and read through their papers. Make some notes on what their work reveals about their current level ...
... assessment lesson, allow them to return to their usual seats. Experience has shown that this produces more profitable discussions. Assessing students’ responses Collect students’ responses to the task and read through their papers. Make some notes on what their work reveals about their current level ...
Angles and Parallel Lines
... CLASSIFYING ANGLES An angle is formed when two rays meet at a point called a vertex. For the purposes of this course, angles will always be measured in degrees, and can be measured with a protractor. There are 3600 in a circle, and the angle measure you will be dealing with range from 00 to 3600. O ...
... CLASSIFYING ANGLES An angle is formed when two rays meet at a point called a vertex. For the purposes of this course, angles will always be measured in degrees, and can be measured with a protractor. There are 3600 in a circle, and the angle measure you will be dealing with range from 00 to 3600. O ...
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.