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Triangles' trigonometric condition (related to the tangents of the half-angles)

Three positive angles “A”, “B”, and “C”, each of them less than 180°, are the angles of a triangle if and only if ... more

Turbine specific speed

The specific speed value (radian/second) for a turbine is the speed of a geometrically similar turbine which would produce one unit of the specific speed ... more

Horizontal curve - Sight obstraction distance (S>L)

Horizontal Curves are one of the two important transition elements in geometric design for highways (along with Vertical Curves). A horizontal curve ... more

Gaussian beam ( radius of curvature )

In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are well ... more

Solid angle (in spherical coordinates)

In geometry, a solid angle is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the ... more

Critical Speed of a Rotating Shaft - Dunkerley's method

In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating ... more

Mechanical Advantage - Differential Pulley

Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves ... more

Hyperbolic law of cosines - 2nd law

In hyperbolic geometry, the law of cosines is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar ... more

Length of an arc of a circle (central angle in radians)

Circular arc is a segment of a circle, or of its circumference (boundary) if the circle is considered to be a disc. Central angle is an angle whose apex ... more

Angle of elevation (for object following a ballistic trajectory)

A trajectory or flight path is the path that a moving object follows through space as a function of time. A trajectory can be described mathematically ... more

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