.. _sphx_glr_api_gallery_calculus_exhaustion:

Method of exhaustion
--------------------

Archimedes' polygon bounds on pi, the oldest convergent approximation
scheme.


.. 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="Doubles the sides of inscribed and circumscribed regular polygons from 6 to 96, reproducing Archimedes&#x27; bounds 3 10/71 &lt; pi &lt; 3 1/7, and shows that the gap shrinks by a factor of four with each doubling.">

.. only:: html

  .. image:: /api/gallery/calculus/exhaustion/images/thumb/sphx_glr_plot_01_archimedes_pi_thumb.png
    :alt:

  :doc:`/api/gallery/calculus/exhaustion/plot_01_archimedes_pi`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Archimedes' method of exhaustion: squeezing pi</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/calculus/exhaustion/plot_01_archimedes_pi