Johann Bernoulli
Born: 27 July 1667 in Basel, Switzerland
Died: 1 Jan 1748 in Basel, Switzerland
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Johann Bernoulli studied reflection and refraction of light, orthogonal trajectories of families of curves, quadrature of areas by series and the brachystochrone.
Johann Bernoulli was the brother of Jacob Bernoulli and the father of Daniel Bernoulli, Nicolaus Bernoulli, and Johann(II) Bernoulli. He was meant to take charge of his families trading interests which he avoided by studying medicine. His elder brother tutored him in mathematics and Johann began to study Leibniz's papers.
He was appointed to a chair in Groningen, the Netherlands, in 1695 and after Jacob Bernoulli's death in 1705 he succeeded to his brother's chair in Basel.
He remained in Basel for the rest of his life.
His lectures were published by de l'Hôpital and became the first calculus textbook. Among the topics he studied : reflection and refraction of light, orthogonal trajectories of families of curves, quadrature of areas by series and the brachystochrone (curve of quickest descent of a weighted particle moving between two points in a gravitational field). The methods used in the calculus of variations show that the minimising curve is a cycloid.
He also studied the tautochrone (the curve on which a weighted particle will always arrive at a fixed point in the same time independent of its initial position). This was used in clock construction.
Johann Bernoulli examined the problem of a particle moving under the influence of gravity with a drag proportional to the nth power of the velocity. He changed the equations of motion by substituting, for time, the angle of inclination of the tangent to the trajectory as the independent variable. The Bernoulli solution, obtained in 1719, was widely employed to compute trajectories during the 19th century. Even today it continues to have some application for the motion of projectiles fired at low velocities.
References elsewhere in this archive:
Show me the Bernoulli family tree
Johann Bernoulli worked on complex trigonometric functions of a Complex variable
Tell we about Johann Bernoulli's contibution to the development of Calculus
Among the curves studied by Johann Bernoulli were the Astroid, the Catenary, the Cycloid, the Epicycloid, the Hypocycloid, the Equiangular spiral, the Hyperbolic spiral, the Kappa curve and the Tractrix
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