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Johann Jakob Balmer (Lausen, 1 May 1825 - Basel, 12 March 1898) was a Swiss mathematician, teacher and lecturer.
He studied mathematics and architecture in Karlsruhe and Berlin, earning a doctorate in Basel in 1849 with a thesis on cycloids. From 1850 he was a mathematics teacher at the Basel secondary school for women and from 1865 to 1890 a professor of geometry at the University of Basel. He also taught courses on the ancient temples of Jerusalem, in particular on the numerical interpretation of architectural symmetries. In 1865 his first child was born, Wilhelm, who became a painter. In 1868 he married Christine Pauline Rinck. The couple had six children in all. In 1885 he derived, based on experimental spectroscopic data provided by the Swedish physicist Anders Jonas Ångström, the empirical formula that describes the spectral series that bears his name.
The Swiss scientist told friends and colleagues that, by giving him a series of numbers, he could find a mathematical formula that would relate them. A colleague challenged him to do so with the recent hydrogen spectrum measurements and Balmer succeeded.
An integer number n is associated with each spectral line, the wavelengths are proportional to the quotient n ^ 2 / (n ^ 2-2 ^ 2) where n takes the values 3,4, etc. The constant of proportionality is 364.56 nm.
As suggested by Balmer himself, they could be extended to other spectral lines by replacing 2 ^ 2 by the squares of successive integers.

Description

*Google Translate Warning*

Johann Jakob Balmer (Lausen, 1 May 1825 - Basel, 12 March 1898) was a Swiss mathematician, teacher and lecturer.
He studied mathematics and architecture in Karlsruhe and Berlin, earning a doctorate in Basel in 1849 with a thesis on cycloids. From 1850 he was a mathematics teacher at the Basel secondary school for women and from 1865 to 1890 a professor of geometry at the University of Basel. He also taught courses on the ancient temples of Jerusalem, in particular on the numerical interpretation of architectural symmetries. In 1865 his first child was born, Wilhelm, who became a painter. In 1868 he married Christine Pauline Rinck. The couple had six children in all. In 1885 he derived, based on experimental spectroscopic data provided by the Swedish physicist Anders Jonas Ångström, the empirical formula that describes the spectral series that bears his name.
The Swiss scientist told friends and colleagues that, by giving him a series of numbers, he could find a mathematical formula that would relate them. A colleague challenged him to do so with the recent hydrogen spectrum measurements and Balmer succeeded.
An integer number n is associated with each spectral line, the wavelengths are proportional to the quotient n ^ 2 / (n ^ 2-2 ^ 2) where n takes the values 3,4, etc. The constant of proportionality is 364.56 nm.
As suggested by Balmer himself, they could be extended to other spectral lines by replacing 2 ^ 2 by the squares of successive integers.