1829 in science
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- Peter Gustav Lejeune Dirichlet publishes a memoir giving the Dirichlet conditions, showing for which functions the convergence of the Fourier series holds; introducing Dirichlet's test for the convergence of series; the Dirichlet function as an example that not any function is integrable; and, in the proof of the theorem for the Fourier series, the Dirichlet kernel and Dirichlet integral. He also introduces a general modern concept for a function.
- Nikolai Ivanovich Lobachevsky publishes his work on hyperbolic non-Euclidean geometry.
- S. D. Poisson publishes Sur l'attraction des sphéroides.
- Jules Desnoyers names the Quaternary period.
- Philippe-Charles Schmerling discovers a Neandertal fossil, the partial cranium of a small child.
- May – Cyrill Demian patents a version of the accordion in Vienna.
- June 30 – Henry Robinson Palmer files a British patent application for corrugated iron for use in buildings.
- July 23 – In the United States, William Burt obtains the first patent for a form of typewriter, the typographer.
- October 6–14 – The Rainhill Trials, a steam locomotive competition, are run in England and won by Stephenson's Rocket.
- December 19 – Charles Wheatstone patents the concertina in Britain.
- Louis Braille publishes the first description of his method of embossed printing that allows the visually impaired to read.
- Chalmers University of Technology founded in Gothenburg, Sweden.
- Technical University of Denmark (originally named 'College of Advanced Technology') founded in Copenhagen, Denmark.
- University of Stuttgart founded in Stuttgart, Germany.
- Ecole Centrale Paris (originally named 'École Centrale des Arts et Manufactures') founded in Paris, France.
- Copley Medal: not awarded
- February 2
- March 23 – N. R. Pogson (died 1891 in science), astronomer.
- April 28 – Charles Bourseul (died 1912), telegraph engineer.
- April 30 – Ferdinand von Hochstetter (died 1884), geologist.
- August 13 (O.S. August 1) – Ivan Sechenov (died 1905), "the father of Russian physiology".
- August 23 – Moritz Cantor (died 1920), historian of mathematics.
- September 7 – Friedrich August Kekulé von Stradonitz (died 1896), chemist.
- September 30
- March 1 – Thomas Earnshaw (born 1749), watchmaker.
- April 6 – Niels Henrik Abel (born 1802), mathematician.
- May 10 – Thomas Young (born 1773), physicist.
- May 29 – Humphry Davy (born 1778), chemist.
- June 29 – James Smithson (born 1764), mineralogist, chemist and benefactor.
- November 14 – Louis Nicolas Vauquelin (born 1763), chemist.
- October 10 – Maria Elizabetha Jacson (born 1755), botanist.
- December 28 – Jean-Baptiste Lamarck (born 1744), naturalist.
- Bressoud, David M. (2007). A radical approach to real analysis (2nd ed.). [Washington, D.C.]: Mathematical Association of America. pp. 218–227. ISBN 978-0-88385-747-2.
- Elstrodt, Jürgen (2007). "The Life and Work of Gustav Lejeune Dirichlet (1805–1859)" (PDF). Clay Mathematics Proceedings 7. Retrieved 2011-10-20.
- Crilly, Tony (2007). 50 Mathematical Ideas you really need to know. London: Quercus. pp. 108–111. ISBN 978-1-84724-008-8.
- Radomski, Teresa (2005). "Manuel García (1805–1906): a bicentenary reflection" (PDF). Australian Voice 11: 25–41. Retrieved 2012-02-07.
- Thomson, Nick (2011). Corrugated Iron Buildings. Oxford: Shire Publications. pp. 7–8. ISBN 978-0-7478-0783-4.
- U.S. Patent 5581X.
- Procédé pour écrire les Paroles, la Musique et le Plain-chant au moyen de points, à l'usage des Aveugles et disposés pour eux. Paris.