.. _CarlGauss:

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.. This file is part of the OpenDSA eTextbook project. See
.. http://algoviz.org/OpenDSA for more details.
.. Copyright (c) 2015-2016 by Dave Parillo`
.. This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

.. avmetadata::
   :author: Dave Parillo
   :topic: Biography

Spotlight: Carl Friedrich Gauss
===============================

Spotlight: Carl Friedrich Gauss
-------------------------------

.. index:: Gauss, Carl Friedrich Gauss

.. index:: least squares regression

.. epigraph::

   He lives everywhere in mathematics.

   -- E.T. Bell, *Men of Mathematics*


.. sidebar:: Portrait of Carl Gauss [#]_

   .. odsafig:: Images/Carl_Friedrich_Gauss.jpg
      
      Oil painting of mathematician and philosopher Carl Friedrich Gauss by G. Biermann (1824-1908)


Carl Friedrich Gauss is considered by many the greatest mathematician who ever lived.
He was born in Brunswick, Germany on April 30, 1777.
Gauss was a child prodigy, who was reported as able to perform long computations in
his head. At age 10 he studied algebra and analysis. 
He made his first fundamental discoveries while still a teenager.
Among these was the `least squares <http://en.wikipedia.org/wiki/Least_squares>`_ 
method for handling statistical data and a proof
that a regular 17-sided polygon can be constructed with only a straightedge and a compass.
This was the first result of its kind since discoveries by the Greeks 2,000 years earlier.

He completed his monumental book on number theory, *Disquisitiones Arithmeticae* 
in 1798 at the age of 21 [Gauss65]_.
It summarized previous work in a systematic way and introducing many fundamental ideas of his own.

In 1801, the same year *Disquisitiones Arithmeticae* was published, the asteroid Ceres was observed by
astronomers.  Unfortunately, they could only make observations across 3 degrees of the sky
before it was obscured by the sun.
Several months later, when Ceres should have reappeared, Piazzi could not locate it: 
the mathematical tools of the time were not able to extrapolate a position from such a scant 
amount of data |---| three degrees represent less than 1% of the total orbit.
In what seemed a superhuman feat at the time, Gauss used the available data to calculate
the orbit of Ceres.
As part of his work, he showed that experimental data varies within a bell-shaped curve,
now called the `Gaussian distribution <http://en.wikipedia.org/wiki/Normal_distribution>`_.
This achievement established his reputation as a genius before the age of 25.

.. index:: logarithm

Gauss also developed tables of logarithms now known as 
`Gaussian logarithms <http://en.wikipedia.org/wiki/Logarithmic_number_system>`_.

Gaussian logarithms are designed to facilitate finding the common logarithm of a 
sum or difference of two numbers whose common logarithms are known. 
The object of a table of Gaussian logarithms, sometimes known as Addition and Subtraction Logarithms, 
is to give :math:`\log (a \pm b)` by single entry when :math:`\log a` and :math:`\log b` are known.

When Gauss died, many unpublished notes and manuscripts were found in his desk.
When his complete *Collected Works* were finally published later,
it had taken a group of scientists nearly seventy years to review and edit his writings.

Today Gauss's name occurs in many places in mathematics and science:

- The normal probability distribution as also called the Gaussian curve or distribution
- Gauss's Laws for 
  `Gravity <http://en.wikipedia.org/wiki/Gauss's_law_for_gravity>`_
  and 
  `Electrostatics <http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html>`_
- The hypergeometric series, a.k.a the Gaussian series
- Gaussian equations in spherical trigonometry
- Gaussian curvature in differential geometry
- Gaussian optics and Gaussian beams describing electromagnetic radiation

Gauss died in Göttingen, at the age of 78 on February 23, 1855.
In Brunswick, there is a statue of him.
Its base is, appropriately, a 17 pointed star.

.. [#] Gottlieb Biermann, *Portrait of Carl Friedrich Gauss*
   By Gottlieb Biermann A. Wittmann (photo) [Public domain], via Wikimedia Commons