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2. Differential geometry of surfaces - Wikipedia

   en.wikipedia.org/wiki/Differential_geometry_of...

   A ruled surface is one which can be generated by the motion of a straight line in E 3. [46] Choosing a directrix on the surface, i.e. a smooth unit speed curve c(t) orthogonal to the straight lines, and then choosing u(t) to be unit vectors along the curve in the direction of the lines, the velocity vector v = c t and u satisfy

3. Developable surface - Wikipedia

   en.wikipedia.org/wiki/Developable_surface

   The cylinder is an example of a developable surface. In mathematics, a developable surface (or torse: archaic) is a smooth surface with zero Gaussian curvature. That is, it is a surface that can be flattened onto a plane without distortion (i.e. it can be bent without stretching or compression).

4. Smooth structure - Wikipedia

   en.wikipedia.org/wiki/Smooth_structure

   This atlas contains every chart that is compatible with the smooth structure. There is a natural one-to-one correspondence between smooth structures and maximal smooth atlases. Thus, we may regard a smooth structure as a maximal smooth atlas and vice versa. In general, computations with the maximal atlas of a manifold are rather unwieldy.

5. Surface (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Surface_(mathematics)

   A sphere is the surface of a solid ball, here having radius r. In mathematics, a surface is a mathematical model of the common concept of a surface.It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line.

6. Roku Sets Streaming Deal With X Games for Aspen Return ... - AOL

   www.aol.com/roku-sets-streaming-deal-x-130000610...

   Roku has struck a deal with the X Games for its Roku Channel to become the U.S. streaming home of both the upcoming Winter 2025 competition in Aspen as well as an event set for next summer. The X ...

7. Lode coordinates - Wikipedia

   en.wikipedia.org/wiki/Lode_Coordinates

   The upper portion of the plot depicts yield surface behavior in triaxial extension and the lower portion depicts yield surface behavior in triaxial compression. The meridional profile is a 2D plot of ( z , r ) {\displaystyle (z,r)} holding θ {\displaystyle \theta } constant and is sometimes plotted using scalar multiples of ( z , r ...