Robert Baldwin Hayward (7 March 1829 – 2 February 1903) was an English educator and mathematician.

Life

Born on 7 March 1829, at

Bocking, Essex Bocking is an area of Braintree, Essex, England, which was a former village and civil parish. In 1934 it became part of the civil parish of Braintree and Bocking, which is now within Braintree District. It forms an electoral division for Essex Co ...

, he was son of Robert Hayward by his wife Ann Baldwin; his father, from an old

Quaker Quakers are people who belong to a historically Protestant Christian set of Christian denomination, denominations known formally as the Religious Society of Friends. Members of these movements ("theFriends") are generally united by a belie ...

family, withdrew from the Quaker community on his marriage. Educated at

University College, London , mottoeng = Let all come who by merit deserve the most reward , established = , type = Public research university , endowment = £143 million (2020) , budget = � ...

, entered

St John's College, Cambridge St John's College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge founded by the House of Tudor, Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corpo ...

, in 1846, graduating as fourth wrangler in 1850. He was fellow from 30 March 1852 till 27 March 1860, and from 1852 till 1855 assistant tutor. From 1855 Baldwin was mathematical tutor and reader in natural philosophy at

Durham University , mottoeng = Her foundations are upon the holy hills (Psalm 87:1) , established = (university status) , type = Public , academic_staff = 1,830 (2020) , administrative_staff = 2,640 (2018/19) , chancellor = Sir Thomas Allen , vice_chan ...

, leaving in 1859 to become a mathematical master at

Harrow School (The Faithful Dispensation of the Gifts of God) , established = (Royal Charter) , closed = , type = Public schoolIndependent schoolBoarding school , religion = Church of E ...

. Hayward remained at Harrow till 1893, a period of 35 years. He reformed mathematics teaching there. He was president (1878–89) of the Association for the Improvement of Geometrical Teaching (afterwards the

Mathematical Association The Mathematical Association is a professional society concerned with mathematics education in the UK. History It was founded in 1871 as the Association for the Improvement of Geometrical Teaching and renamed to the Mathematical Association in ...

). Hayward was a mountain climber and an original member of the

Alpine Club The first alpine club, the Alpine Club, based in the United Kingdom, was founded in London in 1857 as a gentlemen's club. It was once described as: :"a club of English gentlemen devoted to mountaineering, first of all in the Alps, members of which ...

from its foundation in 1858, withdrawing in 1865. He died at

Shanklin Shanklin () is a seaside resort and civil parishes in England, civil parish on the Isle of Wight, England, located on Sandown Bay. Shanklin is the southernmost of three settlements which occupy the bay, and is close to Lake, Isle of Wight, Lake ...

Isle of Wight The Isle of Wight ( ) is a county in the English Channel, off the coast of Hampshire, from which it is separated by the Solent. It is the largest and second-most populous island of England. Referred to as 'The Island' by residents, the Isle of ...

, on 2 February 1903.

Works

* 1884: "Proportional Representation", ''

The Nineteenth Century ''The Nineteenth Century'' was a British monthly literary magazine founded in 1877 by James Knowles. It is regarded by historians as 'one of the most important and distinguished monthlies of serious thought in the last quarter of the nineteent ...

'' (February) * 1895: "Hints on Teaching Arithmetic (pamphlet) Two of Robert Baldwin Hayward's works are available at

Internet Archive The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...

: * 1890
''The Elements of Solid Geometry''
* 1892
''The Algebra of Coplanar Vectors and Trigonometry''
In pure mathematics he published papers in the ''Transactions'' of the

Cambridge Philosophical Society The Cambridge Philosophical Society (CPS) is a scientific society at the University of Cambridge. It was founded in 1819. The name derives from the medieval use of the word philosophy to denote any research undertaken outside the fields of law ...

and the ''

Quarterly Journal of Mathematics The ''Quarterly Journal of Mathematics'' is a quarterly peer-reviewed mathematics journal established in 1930 from the merger of ''The Quarterly Journal of Pure and Applied Mathematics'' and the ''Messenger of Mathematics''. According to the ''Jou ...

''. He was elected

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

on 1 June 1876, in recognition of his work on the method of moving axes.

Unified angles

Hayward called a hyperbola an ''excircle'' in his ''Algebra of Coplanar Vectors and Trigonomety''. Chapter 6 considered "Excircular or hyperbolic trigonometry" where

hyperbolic function In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the u ...

s are described. He was taken by the analogy of

circular sector A circular sector, also known as circle sector or disk sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, where the smaller area is known as the ''minor sector'' and the large ...

s and

hyperbolic sector A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points and on the rectangular hyperbola , or the corresponding region when this hyperbola is re-scaled and i ...

s. This insight was cited by

Alexander Macfarlane Alexander Macfarlane FRSE LLD (21 April 1851 – 28 August 1913) was a Scottish logician, physicist, and mathematician. Life Macfarlane was born in Blairgowrie, Scotland, to Daniel MacFarlane (Shoemaker, Blairgowire) and Ann Small. He s ...

in his essay "Definitions of the Trigonometric Functions".

Family

Hayward married in 1860 Marianne, daughter of Henry Rowe, of Cambridge; his wife's sister married

Henry William Watson Rev. Henry William Watson Fellow of the Royal Society, FRS (25 February 1827, Marylebone, London11 January 1903, Berkswell near Coventry) was a mathematician and author of a number of mathematics books. He was an ordained priest and Cambridge Apo ...

. He had issue two sons and four daughters, including Sir Maurice Henry Weston Hayward, K.C.S.I., colonial administrator in India.

Notes

Attribution {{DEFAULTSORT:Hayward, Robert Baldwin 1829 births 1903 deaths 19th-century English mathematicians Alumni of St John's College, Cambridge Fellows of St John's College, Cambridge Fellows of the Royal Society People from Bocking, Essex Academics of Durham University