isosceles triangles
... In geometry, the centroid, geometric center, or barycenter of a plane figure is the intersection of all straight lines that divide the figure into two parts of equal moment about the line. ...
... In geometry, the centroid, geometric center, or barycenter of a plane figure is the intersection of all straight lines that divide the figure into two parts of equal moment about the line. ...
Lesson 9 Redone CC
... Sherlock Holmes: Master of Deduction! Could you follow Sherlock Holmes’s reasoning as he described his thought process? ...
... Sherlock Holmes: Master of Deduction! Could you follow Sherlock Holmes’s reasoning as he described his thought process? ...
Math Notes-chap 1
... Slope indicates both how ____________ a line is and its direction. If a slope is _____________, the line goes up from left to right, and if a slope is negative, the line goes________. A horizontal line has ___________slope, and the slope of a vertical line is ______________. Parallel Lines: ...
... Slope indicates both how ____________ a line is and its direction. If a slope is _____________, the line goes up from left to right, and if a slope is negative, the line goes________. A horizontal line has ___________slope, and the slope of a vertical line is ______________. Parallel Lines: ...
Chapter 3.angles
... 1. The point that the two rays intersect is called the ________________________. 2. The two rays are called the ______________ of the angle. 3. When naming angles, it is typical to use one or three letters. Sometimes one cannot use one letter. When using three letters, the _________________ must be ...
... 1. The point that the two rays intersect is called the ________________________. 2. The two rays are called the ______________ of the angle. 3. When naming angles, it is typical to use one or three letters. Sometimes one cannot use one letter. When using three letters, the _________________ must be ...
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.