Unit 1 – Transformations Terms and Definitions
... If a and b are both positive, for the general coordinate rule (x, y) → (x + a, y + b), each point moves a units to the right and b units up. If a and b are negative, then points move a units to the left and b units down. b The slope of the translation vector is . a Participants should discuss any ...
... If a and b are both positive, for the general coordinate rule (x, y) → (x + a, y + b), each point moves a units to the right and b units up. If a and b are negative, then points move a units to the left and b units down. b The slope of the translation vector is . a Participants should discuss any ...
Geometry B - Arkansas Department of Education
... The distance around a polygon Perpendicular bisector The perpendicular bisector of a segment is a line, segment or ray that is perpendicular to the segment at its midpoint. ...
... The distance around a polygon Perpendicular bisector The perpendicular bisector of a segment is a line, segment or ray that is perpendicular to the segment at its midpoint. ...
Triangle formulae
... the original, but larger or smaller. All will have the same angles but the sizes of the triangles will be different. We cannot define a unique triangle when we know just the three angles. This behaviour is illustrated in Figure 2 where the corresponding angles in the two triangles are the same, but ...
... the original, but larger or smaller. All will have the same angles but the sizes of the triangles will be different. We cannot define a unique triangle when we know just the three angles. This behaviour is illustrated in Figure 2 where the corresponding angles in the two triangles are the same, but ...
Angles and Polygons
... What shape is made by all possible angles formed by the two rays? _______________________ Draw this shape onto the picture you made above. IMP Activity: How Does That Spaghetti Intersect? ...
... What shape is made by all possible angles formed by the two rays? _______________________ Draw this shape onto the picture you made above. IMP Activity: How Does That Spaghetti Intersect? ...
Lesson 1: Construct an Equilateral Triangle
... for the most efficient use of material. Although there are many types of geometry, school mathematics is devoted primarily to plane Euclidean geometry, studied both synthetically (without coordinates) and analytically (with coordinates). Euclidean geometry is characterized most importantly by the Pa ...
... for the most efficient use of material. Although there are many types of geometry, school mathematics is devoted primarily to plane Euclidean geometry, studied both synthetically (without coordinates) and analytically (with coordinates). Euclidean geometry is characterized most importantly by the Pa ...
G.2 - DPS ARE
... We wish to show that line AM is the perpendicular bisector of BC. It passes through the midpoint of BC so it is sufficient to show that line AM is perpendicular to BC. We will accomplish this by showing that triangles AMB and AMC are congruent. Since angles AMB and AMC make a line and are congruent, ...
... We wish to show that line AM is the perpendicular bisector of BC. It passes through the midpoint of BC so it is sufficient to show that line AM is perpendicular to BC. We will accomplish this by showing that triangles AMB and AMC are congruent. Since angles AMB and AMC make a line and are congruent, ...
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.