Teaching Geometry in Grade 8 and High School
... The first is to caution against the premature use of computer software for learning about basic rigid motions. While computer software will eventually be employed for the purpose of geometric explorations, it is strongly recommended, on the basis of professional judgment and available experience, t ...
... The first is to caution against the premature use of computer software for learning about basic rigid motions. While computer software will eventually be employed for the purpose of geometric explorations, it is strongly recommended, on the basis of professional judgment and available experience, t ...
Module 5 Lesson 1: Investigating Angles of Triangles Characteristics
... Let’s focus now on two types of triangles in particular – the isosceles triangle and the equilateral triangle. The definition of an isosceles triangle is one that has at least two congruent sides. These congruent sides are called legs and the remaining side is called the base. The angle formed by th ...
... Let’s focus now on two types of triangles in particular – the isosceles triangle and the equilateral triangle. The definition of an isosceles triangle is one that has at least two congruent sides. These congruent sides are called legs and the remaining side is called the base. The angle formed by th ...
Interacting Fock spaces: central limit theorems and quantum
... ii) we are able to construct the approximating sequence of random variables. The main technical tool used to reach such a theorem is given by a special class of interacting Fock spaces (IFS), namely the 1-mode type Free interacting Fock spaces. More precisely, after introducing a new basic operator ...
... ii) we are able to construct the approximating sequence of random variables. The main technical tool used to reach such a theorem is given by a special class of interacting Fock spaces (IFS), namely the 1-mode type Free interacting Fock spaces. More precisely, after introducing a new basic operator ...
Noether's theorem
Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalization of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g. systems with a Rayleigh dissipation function). In particular, dissipative systems with continuous symmetries need not have a corresponding conservation law.