Gerolamo Cardano in the context of "Binomial coefficients"

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⭐ Core Definition: Gerolamo Cardano

Gerolamo Cardano (Italian: [dʒeˈrɔːlamo karˈdaːno]; also Girolamo or Geronimo; French: Jérôme Cardan; Latin: Hieronymus Cardanus; 24 September 1501– 21 September 1576) was an Italian polymath whose interests and proficiencies ranged through those of mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, music theorist, writer, and gambler. He became one of the most influential mathematicians of the Renaissance and one of the key figures in the foundation of probability; he introduced the binomial coefficients and the binomial theorem in the Western world. He wrote more than 200 works on science.

Cardano partially invented and described several mechanical devices including the combination lock, the gimbal consisting of three concentric rings allowing a supported compass or gyroscope to rotate freely, and the Cardan shaft with universal joints, which allows the transmission of rotary motion at various angles and is used in vehicles to this day. He made significant contributions to hypocycloids - published in De proportionibus, in 1570. The generating circles of these hypocycloids, later named "Cardano circles" or "cardanic circles", were used for the construction of the first high-speed printing presses.

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Gerolamo Cardano in the context of Federico Commandino

Federico Commandino (1509 – 5 September 1575) was an Italian humanist and mathematician.

Born in Urbino, he studied at Padua and then at Ferrara, where he received his doctorate in medicine under Antonio Musa Brassavola. He had numerous patrons throughout his life. Initially, aided by Grassi, the bishop of Viterbo, he then came under the patronage of Pope Clement VIII. In Urbino, he was sponsored by Guidobaldo II della Rovere, but then came to Rome with cardinal Ranuccio Farnese. In Rome, he was patronized by Cardinal Cervini, who served briefly as Pope. Lured back to Urbino by Francesco Maria II della Rovere. In Urbino, he putatively met John Dee, and corresponded with the scholars Conrad Dasypodius (il Dasipodio), Gerolamo Cardano, Francesco Maurolico, and Christopher Clavius.

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Gerolamo Cardano in the context of Gimbal

A gimbal is a pivoted support that permits rotation of an object about an axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of the rotation of its support (e.g. vertical in the first animation). For example, on a ship, the gyroscopes, shipboard compasses, stoves, and even drink holders typically use gimbals to keep them upright with respect to the horizon despite the ship's pitching and rolling.

The gimbal suspension used for mounting compasses and the like is sometimes called a Cardan suspension after Italian mathematician and physicist Gerolamo Cardano (1501–1576) who described it in detail. However, Cardano did not invent the gimbal, nor did he claim to. The device has been known since antiquity, first described in the 3rd c. BC by Philo of Byzantium, although some modern authors support the view that it may not have a single identifiable inventor.

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