Car Friedrich Gauss was an intellectual colossus, whose work informed or revolutionized broad and seemingly unrelated swathes of science and math. In computational science, his name is attached to numerous methods for solving equations, integrating functions, and describing probabilities.
Interestingly, perhaps two of his most enduring contributions - Gaussian elimination to solve systems of linear equations, and normal or Gaussian distribution are linked through the fascinating story of how Gauss determined the orbit of Ceres (great read!).
While there is plenty of geometry involved, this example illustrates how multiple observations of the asteroid by astronomers, lead to an over-determined system of equations. Assuming that these measurements were tainted by normal or Gaussian error, Gauss built the resulting "normal equations" and solved for the orbit.
When Ceres was lost to the glare of the sun, he was able to use these calculations to direct astronomers to the part of the sky where they should point their telescopes.
Interestingly, perhaps two of his most enduring contributions - Gaussian elimination to solve systems of linear equations, and normal or Gaussian distribution are linked through the fascinating story of how Gauss determined the orbit of Ceres (great read!).
While there is plenty of geometry involved, this example illustrates how multiple observations of the asteroid by astronomers, lead to an over-determined system of equations. Assuming that these measurements were tainted by normal or Gaussian error, Gauss built the resulting "normal equations" and solved for the orbit.
When Ceres was lost to the glare of the sun, he was able to use these calculations to direct astronomers to the part of the sky where they should point their telescopes.
No comments:
Post a Comment