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2. Cross section (geometry) - Wikipedia

   en.wikipedia.org/wiki/Cross_section_(geometry)

   In analogy with the cross-section of a solid, the cross-section of an n-dimensional body in an n-dimensional space is the non-empty intersection of the body with a hyperplane (an (n − 1)-dimensional subspace). This concept has sometimes been used to help visualize aspects of higher dimensional spaces. [7]

3. Saint-Venant's theorem - Wikipedia

   en.wikipedia.org/wiki/Saint-Venant's_theorem

   In solid mechanics, it is common to analyze the properties of beams with constant cross section. Saint-Venant's theorem states that the simply connected cross section with maximal torsional rigidity is a circle. [1] It is named after the French mathematician Adhémar Jean Claude Barré de Saint-Venant.

4. Shell integration - Wikipedia

   en.wikipedia.org/wiki/Shell_integration

   The shell method goes as follows: Consider a volume in three dimensions obtained by rotating a cross-section in the xy-plane around the y-axis. Suppose the cross-section is defined by the graph of the positive function f(x) on the interval [a, b]. Then the formula for the volume will be: ()

5. List of second moments of area - Wikipedia

   en.wikipedia.org/wiki/List_of_second_moments_of_area

   The parallel axis theorem can be used to determine the second moment of area of a rigid body about any axis, given the body's second moment of area about a parallel axis through the body's centroid, the area of the cross section, and the perpendicular distance (d) between the axes. ′ = +

6. Section (fiber bundle) - Wikipedia

   en.wikipedia.org/wiki/Section_(fiber_bundle)

   A section of a tangent vector bundle is a vector field. A vector bundle over a base with section . In the mathematical field of topology, a section (or cross section) [1] of a fiber bundle is a continuous right inverse of the projection function.

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8. Chain rule - Wikipedia

   en.wikipedia.org/wiki/Chain_rule

   In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g.More precisely, if = is the function such that () = (()) for every x, then the chain rule is, in Lagrange's notation, ′ = ′ (()) ′ (). or, equivalently, ′ = ′ = (′) ′.

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