Euclid
... 5. G is either a new prime or one of the original set, {P1,P2,P3,...Pk} 6. If G is one of the original set, it is divisible into P1P2P3...Pk If so, G is also divisible into 1, (since G is divisible into Q) 7. This is an absurdity. ...
... 5. G is either a new prime or one of the original set, {P1,P2,P3,...Pk} 6. If G is one of the original set, it is divisible into P1P2P3...Pk If so, G is also divisible into 1, (since G is divisible into Q) 7. This is an absurdity. ...
Day 6 -Triangle_Congruence
... Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 5 ...
... Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 5 ...
c - WordPress.com
... Problem Solving as Homework: You should approach each problem as an exploration. You are not expected to come to class every day with every problem completely solved. Your presentations in class are expected to be unfinished solutions. Useful strategies to keep in mind are: o create an easier prob ...
... Problem Solving as Homework: You should approach each problem as an exploration. You are not expected to come to class every day with every problem completely solved. Your presentations in class are expected to be unfinished solutions. Useful strategies to keep in mind are: o create an easier prob ...
Congruent Figures
... You can use properties, postulates, and previously proven theorems as reasons / statements in a proof. 3. Multiple Choice What is a postulate? a convincing argument using deductive reasoning a conjecture or statement that you can prove true a statement accepted as true without being proven true a co ...
... You can use properties, postulates, and previously proven theorems as reasons / statements in a proof. 3. Multiple Choice What is a postulate? a convincing argument using deductive reasoning a conjecture or statement that you can prove true a statement accepted as true without being proven true a co ...
3. TRIGONOMETRIC FUNCTIONS
... We have discussed trigonometry at two levels so far. The first involves angles in triangles and the second involved rotations. But now we leave any geometrical interpretation behind and consider sin x etc as functions of a real number x. One reason for doing this is that the majority of uses of the ...
... We have discussed trigonometry at two levels so far. The first involves angles in triangles and the second involved rotations. But now we leave any geometrical interpretation behind and consider sin x etc as functions of a real number x. One reason for doing this is that the majority of uses of the ...
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.