inertia of a body about any given axis is the moment of inertia about a parallel axis through the center of mass, plus the moment of inertia that the body would have about the given axis if all the mass of the body were located at the center of mass. Also known as Steiner's theorem...
2. Let α be the set of all lines in the surface of a cylinder parallel to the axis of revolution. Let β be the set of all circles formed as plane sections by planes cutting through the cylinder perpendicular to the axis of revolution. See Fig. 6. Then the two families of lines co...
A Real Proof of the Principal Axis TheoremA Real Proof of the Principal Axis TheoremMathematics InstructionCollege MathematicsValidityMathematical LogicNumbersTeaching MethodsIn this capsule we give an elementary proof of the principal axis theorem within therealfield, i.e., without using complex numbers...
b], and differentiable over the open interval (a, b), then there exists at least one point c in the interval (a, b) such that f '(c) is theaverage rate of changeof the function over [a, b] and it is parallel to the secant line over [a, b]. ...
entire functions of exponential typeapproximation on subsets of the real axisIn this study, we consider an approximation of entire functions of Hlder classes on a countable union of segments by entire functions of exponential type. It is essential that the approximation rate in the neighborhood of...
The action is stationary on the particle path, so the square squiggle which translates over, goes up parallel, and comes back has the same action as the original path. The original path, however, has the same action as just the squiggle part of the other path, therefore the two horizontal...
A Carnot engine is a theoretical engine that operates on the Carnot cycle. Carnot engine estimates the maximum possible efficiency that a heat engine during the conversion process of heat into work and, conversely, working between two reservoirs can poss
We can interpret this quantity geometrically as the volume of an -dimensional parallelopiped whose generating vectors are independent real gaussian vectors in (i.e. their coefficients are iid with law ). Using the classical base-times-height formula, we thus have where is the -dimensional ...
Find the equation of the line passing through (-3,4) and parallel to the x-axis. What is the result when you fold or draw the perpendicular bisectors of the three sides of a triangle? In an oblique pyramid, are any triangle faces congruent? Can a scalene triangle be a right ang...
Its vertical axis must go from 00 to 11 because it represents probabilities. The left plot is meant to be read sideways: it is the PDF of the Beta(n/2+1,n/2+1)(n/2+1,n/2+1) distribution. It shows how the median in the box will vary, when the median is measured in terms ...