### Thomas Harriot: Mathematician, Astronomer and Navigator

Sir Walter Raleigh, adventurer, explorer and privateer, was among most colourful characters of Tudor times. He acquired extensive estates in Waterford and Cork, including Molana Abbey near Youghal, which he gave to his friend and advisor, the brilliant mathematician and astronomer Thomas Harriot.

Left: Sir Walter Raleigh (1552-1618). Right: Thomas Harriot (1560?-1621)

Raleigh needed an excellent navigator on his transatlantic voyages, and he brought along Harriot, who had earlier been his mathematics tutor. Harriot had written a text, Archicon, on navigation after graduating from Oxford.

Harriot accompanied Raleigh on his expedition to Virginia in 1585, and carried out surveys and studies of local Indian languages while there. In preparation for the voyage, Rayleigh asked him about the most efficient means of stacking cannon balls on a ship deck. Harriot came up with the solution known to all grocers used to stacking oranges. He later corresponded with famed astronomer Johannes Kepler, who conjectured that the usual packing method was the most efficient. It was some four centuries before a rigorous proof of Kepler’s conjecture was produced in 1998.

Harriot’s main contribution to navigation was in finding a mathematical formula for drawing lines of latitude on a chart so that a route with constant compass bearing would be a straignt line on the map. The resulting map is the projection discovered earlier by the Flemish cartographer Gerardus Mercator.

Harriot also discovered an important result for geometry on the sphere. The sum of the angles of a spherical triangle is always larger than two right angles. The amount E by which it exceeds 180° is called the spherical excess. The 16th century French mathematician Albert Girard showed that this excess determines the surface area of the triangle: the radius squared by the excees gives the area (in symbols, A=R²E). This result was discovered earlier, but not published, by Harriot.

In 1607 Harriot observed and sketched what was later called Halley’s Comet, using an early telescope. In addition, he is credited with producing the first map of the Moon. His only published work is a text in algebra, which includes a treatment of negative and complex roots of polynomial equations. In his writing on algebra, Harriot introduced several novel symbols, some of which, like “<” and “>” for ‘less than’ and ‘greater than’, are still in use today.

In his report on the Virginia expedition, Harriot described how Indians dried and shredded tobacco leaves and smoked them in pipes. He recommended smoking as medicinally beneficial, ideal for ‘purging superfluous phlegm and other gross humours’. His own end came as a result of a cancerous tumour of the nose, probably resulting from his use of tobacco.