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12 Congruent Triangles
12 Congruent Triangles

5 Trigonometric Functions H
5 Trigonometric Functions H

File - IGCSE/O
File - IGCSE/O

PowerPoint 簡報 - Browser Express
PowerPoint 簡報 - Browser Express

Greenwich Public Schools Mathematics Curriculum Objectives
Greenwich Public Schools Mathematics Curriculum Objectives

Assignments Quadrilaterals
Assignments Quadrilaterals

Geometry
Geometry

Chapter 4
Chapter 4

No Slide Title
No Slide Title

Trigonometry
Trigonometry

... good understanding and familiarity with them is essential for an engineer. The trouble with maths is that a lot of the important results depend on other important results which I can’t write about yet, because I haven’t yet talked about calculus or complex numbers. So – this is just a short introduc ...
Honors Geometry Problem book 2013
Honors Geometry Problem book 2013

Testing for Congruent Triangles Examples
Testing for Congruent Triangles Examples

... Testing for Congruent Triangles Examples 1. Why is congruency important? In 1913, Henry Ford began producing automobiles using an assembly line. When products are mass-produced, each piece must be interchangeable, so they must have the same size and shape. Each piece is an exact copy of the others, ...
to view a detailed breakdown. Year 9 Higher
to view a detailed breakdown. Year 9 Higher

Congruence Of Triangles
Congruence Of Triangles

Isosceles Triangle Theorem states that if two sides of t
Isosceles Triangle Theorem states that if two sides of t

TEKS Content Topics
TEKS Content Topics

math_i_triangle_congruence
math_i_triangle_congruence

JMAP REGENTS BY DATE
JMAP REGENTS BY DATE

Reference
Reference

File
File

Determine whether each pair of triangles is congruent by
Determine whether each pair of triangles is congruent by

Congruent Triangles
Congruent Triangles

1. PETS Out of a survey of 1000 households, 460 had at least one
1. PETS Out of a survey of 1000 households, 460 had at least one

Geometry
Geometry

geometrych5
geometrych5

< 1 ... 3 4 5 6 7 8 9 10 11 ... 552 >

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.
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