Concepts 10
... Hypotenuse-‐Leg Theorem (HL) If the _______________________________ of one right triangle is congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent. ...
... Hypotenuse-‐Leg Theorem (HL) If the _______________________________ of one right triangle is congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent. ...
file
... Then α + β < γ + δ if and only if the lines L and M meet on the right side of the transversal N. Definition 1.11. Two distinct lines are said to be parallel if they never intersect. Theorem 1.12. Given a line L and a point P not on L, there exists a unique line parallel to L through P . As part of t ...
... Then α + β < γ + δ if and only if the lines L and M meet on the right side of the transversal N. Definition 1.11. Two distinct lines are said to be parallel if they never intersect. Theorem 1.12. Given a line L and a point P not on L, there exists a unique line parallel to L through P . As part of t ...
Test #1 Review
... Questions on the test will be of various types: Short answer or fill-in-the-blank, State certain definitions, theorems, postulates. Compute various numbers, figures, correspondences, and equations using the concepts we have studied (e.g., congruence of triangles, and the Poincare Half-plane model o ...
... Questions on the test will be of various types: Short answer or fill-in-the-blank, State certain definitions, theorems, postulates. Compute various numbers, figures, correspondences, and equations using the concepts we have studied (e.g., congruence of triangles, and the Poincare Half-plane model o ...
THEOREMS & POSTULATES
... If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. P ...
... If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. P ...
Planetary motion, the hydrogen atom, and superintegrablity
... the planets without knowing Newton’s equations or calculus. ...
... the planets without knowing Newton’s equations or calculus. ...
Proportions: A ratio is the quotient of two
... Two triangles are said to be similar to each other if they have the same shape (not necessarily the same size). If two triangles are similar, then all three of their angles are congruent to each other, and their corresponding sides are in proportion. This means that the ratio of their corresponding ...
... Two triangles are said to be similar to each other if they have the same shape (not necessarily the same size). If two triangles are similar, then all three of their angles are congruent to each other, and their corresponding sides are in proportion. This means that the ratio of their corresponding ...
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.