.. _sphx_glr_api_gallery_geometry_surfaces:

Surfaces
--------

Gaussian and mean curvature of parametric surfaces.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Computes the Gaussian curvature K of a sphere, a cylinder, and a torus. The cylinder bends in space but has K = 0, because it can be unrolled flat without stretching, while no piece of a sphere can. Integrating K over the whole surface gives 4 pi for the sphere and 0 for the torus, as the Gauss-Bonnet theorem predicts.">

.. only:: html

  .. image:: /api/gallery/geometry/surfaces/images/thumb/sphx_glr_plot_01_theorema_egregium_thumb.png
    :alt:

  :doc:`/api/gallery/geometry/surfaces/plot_01_theorema_egregium`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gauss's Theorema Egregium: curvature you can measure from inside</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/geometry/surfaces/plot_01_theorema_egregium