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Jean-Dominique Cassini

Giovanni Domenico Cassini, known in France as Jean-Dominique Cassini and called Cassini I (1625–1712), was an astronomer of Italian origin, founder of the Cassini family and first director of the Paris Observatory. Born in Perinaldo, in the County of Nice, then under Italian rule, he studied in Genoa before becoming professor of astronomy at the University of Bologna, where he taught Ptolemaic cosmology, in accordance with the official doctrine of the Church, despite the advances of Copernicus, Galileo and Kepler. His reputation as an observer led the pope to entrust him with missions before Louis XIV and his minister Colbert called him to France to help build and run the Paris Observatory. Naturalized as a French citizen in 1673, he became a member of the Académie des sciences and settled permanently in Paris, where he directed the Observatory until the end of his life. His observational work was considerable: he discovered Jupiter's Great Red Spot in 1665, determined the rotation periods of Jupiter, Mars and Venus, discovered four satellites of Saturn—Iapetus in 1671, Rhea in 1672, Tethys and Dione in 1684—and identified the Cassini Division in Saturn's rings in 1675. In 1672, he made the first accurate measurement of the Earth–Sun distance, and in 1683, he determined the Sun's parallax. Around 1690, he was the first to observe differential rotation in Jupiter's atmosphere. He took part in measuring the Observatory's meridian and contributed to determining the variation of gravity with latitude during observations conducted in Cayenne. Furthermore, he maintained that the Sun describes an oval with the Earth as one of its foci, a geometric curve that has remained associated with his name as the Cassini oval. From 1668 to 1693, he published the Éphémérides des satellites de Jupiter, produced a detailed map of the lunar surface and wrote numerous papers. Having become blind in 1710, he died on 17 September 1712 at the age of 87. The asteroid (24101) Cassini and the Cassini-Huygens space probe were named in his honour.

Jacques Cassini

Jacques Cassini (1677–1756), known as Cassini II, was a French astronomer and the son of Giovanni Domenico Cassini. He worked alongside his father from an early age, succeeded him as director of the Paris Observatory in 1712, and continued the family's work in astronomy and geodesy. He took part in numerous observing expeditions and resumed the measurement of the Observatory's meridian arc, which he completed in 1718. From this measurement, he concluded that the Earth is elongated at the poles, a position consistent with Cartesian physics, of which he was an ardent defender, and which placed him in direct opposition to Newton's supporters, for whom the Earth is flattened at the poles. This major scientific controversy of the 18th century would not be settled until the measurements made by his son César-François. Realizing around 1740 that his arguments could no longer withstand the new data, he abandoned his scientific activities and handed over the directorship of the Observatory to his son. Besides his work as a geodesist, Jacques Cassini distinguished himself through his astronomical observations of planets and their satellites, which he used to determine orbital inclinations, and through his detection of the proper motion of stars in 1738. He wrote a Traité de la grandeur et de la figure de la Terre (Treatise on the Size and Shape of the Earth), published in 1720. He died in 1756 following a carriage accident. The asteroid (24102) Jacquescassini was named in his honour.

Jean-Dominique Cassini de Thury

Jean-Dominique Cassini de Thury (1748–1845), known as Cassini IV or the Count of Cassini, was the great-grandson of Giovanni Domenico Cassini and the son of César-François Cassini. He was the last representative of the Cassini line of astronomers to head the Paris Observatory. In 1768, he was sent on a mission to the Atlantic as a commissioner responsible for testing the marine clocks designed by Pierre Le Roy to determine longitude at sea. He gradually took over the running of the Observatory from his ailing father and officially became its director in 1784. He completed publication of the map of France begun by his father and took part in the geodetic operations linking the Paris and Greenwich meridians. At the beginning of the Revolution, he briefly accepted several political responsibilities and collaborated for a few months on the work of the commission responsible for developing the metric system. Deeply attached to the monarchy, he resigned from his duties in September 1793, shortly after the plates for the map of France had been transferred to the War Depot. Imprisoned and then released, he retired to his château at Thury, resigned from the Bureau des longitudes and the new Institut national, but was elected to the Académie des sciences in 1799. He devoted his final years to defending his family's scientific prestige and published in 1810 the Mémoires pour servir à l'histoire des sciences et à celle de l'Observatoire royal de Paris. His son Alexandre-Henri (1781–1832), sometimes referred to as Cassini V, was a botanist, thereby definitively ending the family's astronomical tradition.

César-François Cassini

César-François Cassini (1714–1784), known as Cassini de Thury or Cassini III, was a French astronomer and geodesist, the son of Jacques Cassini. He belonged to the celebrated Cassini dynasty of astronomers, which directed the Paris Observatory for more than a century. His scientific career began at the height of the debate between Cartesians and Newtonians over the shape of the Earth. He took part in the geodetic operations conducted by his father in 1733–1734, then carried out a new measurement of the Paris meridian between 1739 and 1740, reaching the opposite conclusion to Jacques Cassini's: the Earth is flattened at the poles, in accordance with Newtonian predictions. This correction paved the way for the cartographic undertaking that was his principal work: the production of the first general map of France, drawn up by systematic triangulation and covering the entire territory. More than an astronomer, Cassini III established himself above all as a great geodesist and a leading cartographer. In 1771, he was appointed Director General of the Paris Observatory, with hereditary entitlement to the official residence, a privilege that until then had not been transferable. He died of smallpox on 4 September 1784.

star puzzle

Star puzzles are three-dimensional puzzles made up of solid pieces that fit together to form regular or semiregular star polyhedra. These objects combine a test of manual skill with a mathematical aspect related to the geometry of star polyhedra—such as icosahedral or dodecahedral stars. They provide a playful introduction to the polyhedral structures of three-dimensional geometry.

Cassini family

A French family of astronomers, geodesists and cartographers of Italian origin whose members directed the Paris Observatory across successive generations for more than a century. Giovanni Domenico Cassini (1625–1712), known as Cassini I, an astronomer of Italian origin who was naturalized as a French citizen, was the first director of the Paris Observatory and the founder of the line. An exceptional observer, he discovered several of Saturn's satellites and the division in Saturn's rings that bears his name. His son Jacques Cassini (1677–1756), known as Cassini II, succeeded him as head of the Observatory and devoted himself chiefly to measuring the shape of the Earth, arguing, against Newton, that the Earth was elongated at the poles. César-François Cassini de Thury (1714–1784), known as Cassini III, Jacques's son, revised his father's conclusions on the Earth's shape and undertook the production of the first general map of France based on systematic triangulation, a work that remains his principal scientific legacy. Jean-Dominique, comte de Cassini (1748–1845), known as Cassini IV, César-François's son, completed the publication of this map and took part in surveying operations linking the Paris and Greenwich meridians, before withdrawing from scientific work after the Revolution. Alexandre-Henri (1781–1832), vicomte de Cassini, the latter's son, abandoned the family tradition to devote himself to the judiciary and botany, bringing the line of Cassini astronomers to an end.

Felice Casorati

Felice Casorati (1835–1890), an Italian mathematician. The son of a physiologist at the University of Pavia, he studied engineering and architecture there. In 1858, he undertook a scientific journey to Göttingen and Paris with Brioschi and Betti, which enabled him to meet the leading European mathematicians—notably Riemann and Weierstrass—and played a decisive role in the revival of Italian mathematical research. Appointed professor at the University of Pavia, he succeeded Mainardi there in the chair of infinitesimal calculus and also taught algebra, analytic geometry, geodesy and analysis. His work focused mainly on complex analysis: he wrote a foundational treatise, Teoria delle funzioni di variabili complesse (1868), which contains the result known as the Weierstrass-Casorati theorem. He maintained extensive correspondence with Beltrami, Hermite and Weierstrass, and received several scientific honours.

Mary Cartwright

Mary Lucy Cartwright (1900–1998), British mathematician. Born into a modest family—her father was a vicar—she was educated by governesses until the age of eleven, before attending a school where she first took an interest in history, then in mathematics. In 1919, she entered St Hugh's College, Oxford, among the very few women students. There she read Whittaker and Watson's Modern Analysis and joined G. H. Hardy's seminar. In 1923, she was the first woman to obtain a first-class degree. After a period of secondary-school teaching, she returned to Oxford, where, under the supervision of Hardy and Titchmarsh, she prepared a thesis on the zeros of entire functions of special types, defended in 1930. She pursued her career at Cambridge, where she taught function theory until her retirement in 1968, then helped edit Hardy's collected works. Her work covered a broad range: real and complex functions, holomorphic functions, topology, differential equations, nonlinear oscillations and dynamical systems. She is regarded as a pioneer of chaos theory. She received numerous honours.

control chart

A control chart is a graphical tool used in industrial statistics and quality management. On the chart, each point corresponds to the value of a statistic—mean, range, proportion of non-conforming items, etc.—calculated from a sample taken at a particular point during a manufacturing process. The x-coordinate of each point represents the sample number or date, and the y-coordinate the observed value of the statistic. Upper and lower control limits are drawn on the chart; when a point exceeds these limits, it signals a potential drift in the process, triggering corrective action.

Henri Cartan

Henri Cartan (1904–2008) was a French mathematician and the son of Élie Cartan. His body of work was substantial: he made major contributions to the theory of functions of several complex variables, homological algebra and algebraic topology. He also developed the concept of a filter in topology. He was one of the co-founders of the Bourbaki group, whose influence on 20th-century mathematics was profound. In 1980, he received the Wolf Prize, one of mathematics’ highest honors.

Hélène Cartan

Hélène Cartan (1917–1952) was a French mathematician, daughter of Élie Cartan and sister of Henri Cartan. In 1937, she entered the École Normale Supérieure on the rue d'Ulm, then in principle reserved for men, and passed the agrégation in 1940. After taking up a secondary-school teaching post, she conducted research in topology alongside her teaching and presented a paper to the Académie des Sciences in 1942. Her career was prematurely cut short by tuberculosis, which claimed her life in 1952. She was among the women scientists who paved the way for women's access to France's major higher-education institutions.

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