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Area of a triangle (related to the two of its altitudes)

Altitude of a triangle is a straight line through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). The area of ... more

Gamma distribution Mean (With a shape parameter α and a rate parameter β )

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The parameterization with α ... more

Diatomic ideal gas heat capacity at constant volume

Heat capacity or thermal capacity is a physical quantity equal to the ratio of the heat that is added to (or removed from) an object to the resulting ... more

Semi-Major Axis - Ellipse

In geometry, the major axis of an ellipse is the longest diameter: a line (line segment) that runs through the center and both foci, with ends at the ... more

Product of the diagonals in a convex quadrilateral(Bretschneider's formula for diagonals)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. In any convex quadrilateral ABCD, the ... 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

Relation between the inradius and exradii of an equilateral triangle

an equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also equiangular; ... more

Law of sines ( related to the sides of the triangle)

Law of sines is an equation relating the lengths of the sides of any shaped triangle to the sines of its angles. The law of sines can be used to compute ... more

Pell's equation

Pell’s equation is a Diophantine equation (a polynomial equation in two or more unknowns ).
In Cartesian coordinates, the equation has the form ... more

Fracture of ductile materials (Dissipated energy)

In ductile materials, a plastic zone develops at the tip of the crack. The plastic loading and unloading cycle near the crack tip leads to the dissipation ... more

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