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  2. Rotation formalisms in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_formalisms_in...

    This is Rodrigues' formula for the axis of a composite rotation defined in terms of the axes of the two component rotations. He derived this formula in 1840 (see page 408). [3] The three rotation axes A, B, and C form a spherical triangle and the dihedral angles between the planes formed by the sides of this triangle are defined by the rotation ...

  3. Exterior algebra - Wikipedia

    en.wikipedia.org/wiki/Exterior_algebra

    The exterior algebra is named after Hermann Grassmann, [3] and the names of the product come from the "wedge" symbol and the fact that the product of two elements of is "outside" . The wedge product of k {\displaystyle k} vectors v 1 ∧ v 2 ∧ ⋯ ∧ v k {\displaystyle v_{1}\wedge v_{2}\wedge \dots \wedge v_{k}} is called a blade of degree k ...

  4. Trigonometry of a tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Trigonometry_of_a_tetrahedron

    Consider the projective (spherical) triangle at the point ; the vertices of this projective triangle are the three lines that join with the other three vertices of the tetrahedron. The edges will have spherical lengths α i , j , α i , k , α i , l {\displaystyle \alpha _{i,j},\alpha _{i,k},\alpha _{i,l}} and the respective opposite spherical ...

  5. Wedge (geometry) - Wikipedia

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

    A wedge is a polyhedron of a rectangular base, with the faces are two isosceles triangles and two trapezoids that meet at the top of an edge. [1]. A prismatoid is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces are triangles, trapezoids, and parallelograms; [2] the wedge is an example of prismatoid because of its top edge is parallel to the ...

  6. Spherical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Spherical_coordinate_system

    The elevation is the signed angle from the x-y reference plane to the radial line segment OP, where positive angles are designated as upward, towards the zenith reference. Elevation is 90 degrees (= ⁠ π / 2 ⁠ radians) minus inclination. Thus, if the inclination is 60 degrees (= ⁠ π / 3 ⁠ radians), then the elevation is 30 degrees ...

  7. Wedge - Wikipedia

    en.wikipedia.org/wiki/Wedge

    The mechanical advantage or MA of a wedge can be calculated by dividing the height of the wedge by the wedge's width: [1] M A = L e n g t h W i d t h {\displaystyle {\rm {MA={Length \over Width}}}} The more acute , or narrow, the angle of a wedge, the greater the ratio of the length of its slope to its width, and thus the more mechanical ...

  8. List of second moments of area - Wikipedia

    en.wikipedia.org/wiki/List_of_second_moments_of_area

    Regular polygons; Description Figure Second moment of area Comment A filled regular (equiliteral) triangle with a side length of a = = [6] The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through the origin.

  9. Surface triangulation - Wikipedia

    en.wikipedia.org/wiki/Surface_triangulation

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