Math 100
... An angle consists of two rays, R1 and R2, with a common vertex. Often we think of an angle as being a rotation of R1 onto R2. R1 is called the initial side and R2 is called the terminal side. When the rotation is counterclockwise, the angle is said to be positive, and when the rotation is clockwise, ...
... An angle consists of two rays, R1 and R2, with a common vertex. Often we think of an angle as being a rotation of R1 onto R2. R1 is called the initial side and R2 is called the terminal side. When the rotation is counterclockwise, the angle is said to be positive, and when the rotation is clockwise, ...
Introduction to Hyperbolic Geometry - Conference
... the words „point‟ and „line‟. To help visualize objects within the geometry, and to make calculations more convenient we use a model. We define points and lines as certain „idealized‟ physical objects that are consistent with the axioms. This system of lines and points is the model of the geometry. ...
... the words „point‟ and „line‟. To help visualize objects within the geometry, and to make calculations more convenient we use a model. We define points and lines as certain „idealized‟ physical objects that are consistent with the axioms. This system of lines and points is the model of the geometry. ...
The Effect of Dynamic Geometry Software_Redacted A+ 81
... basic numeracy, it is most obvious in the presentation of geometry. This is because, one of the strangest contradictions of the presentation of geometry is that we use concrete signifiers to represent abstract mathematical objects that can never have a physical realisation, for example that of a tab ...
... basic numeracy, it is most obvious in the presentation of geometry. This is because, one of the strangest contradictions of the presentation of geometry is that we use concrete signifiers to represent abstract mathematical objects that can never have a physical realisation, for example that of a tab ...
Geometry - Singapore American School
... Verify experimentally the properties of dilations given by a center and a scale factor. HSG.SRT.1a A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves ...
... Verify experimentally the properties of dilations given by a center and a scale factor. HSG.SRT.1a A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves ...
Learning Activities - 4B 2014 Term 2 Program
... What is a shape? A polygon (Greek term meaning many angles) is a closed shape with three or more angles and sides. The angles are the focus for the general naming system used for shapes. What is a regular shape? Shapes which have equal angles and sides of equal length. This means that a rectangle is ...
... What is a shape? A polygon (Greek term meaning many angles) is a closed shape with three or more angles and sides. The angles are the focus for the general naming system used for shapes. What is a regular shape? Shapes which have equal angles and sides of equal length. This means that a rectangle is ...
The Measure of Angles and their Related Arcs Hour
... Double click on the table. Drag point ‘A’ to a new location and double click on the table. Drag point ‘C’ to a new location and double click on the table. Finally, drag vertex ‘B’ to a new location and double click on the table. From your observations in the table write a mathematical formula for th ...
... Double click on the table. Drag point ‘A’ to a new location and double click on the table. Drag point ‘C’ to a new location and double click on the table. Finally, drag vertex ‘B’ to a new location and double click on the table. From your observations in the table write a mathematical formula for th ...
Unit 2.2
... Each statement is true. a) Write the converse of the statement and decide whether the converse is true or false. b) If the converse is true, conbine it with the original statement to form a true biconditional statement. c) If the converse is false, state a counterexample. Writing a Biconditional Sta ...
... Each statement is true. a) Write the converse of the statement and decide whether the converse is true or false. b) If the converse is true, conbine it with the original statement to form a true biconditional statement. c) If the converse is false, state a counterexample. Writing a Biconditional Sta ...
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.