The story of William Rowan Hamilton’s discovery of new four-dimensional numbers called quaternions is familiar. The solution of a problem that had bothered him for years occurred to him in a flash of insight as he walked along the Royal Canal in Dublin. But this Eureka moment did not arise spontaneously: it was the result of years of intense effort. The great French mathematician Henri Poincaré also described how sudden inspiration occurs unexpectedly, but always following a period of concentrated research [TM148, or search for “thatsmaths” at irishtimes.com].
Posts Tagged 'Algebra'
The Many Modern Uses of Quaternions
Published October 4, 2018 Irish Times 1 CommentTags: Algebra, Hamilton
The Flight of the Bumble Bee
Published August 23, 2018 Occasional Leave a CommentTags: Algebra, Puzzles
Alice and Bob, initially a distance l apart, walk towards each other, each at a speed w. A bumble bee flies from the nose of one to the nose of the other and back again, repeating this zig-zag flight at speed f until Alice and Bob meet. How far does the bumble bee fly?
Although polynomial equations have been studied for centuries, even millennia, surprising new results continue to emerge. Marden’s Theorem, published in 1945, is one such — delightful — result.
Cubic with roots at x=1, x=2 and x=3.
“It is difficult to imagine modern mathematics without the concept of a Lie group.” (Ioan James, 2002).
Sophus Lie (1842-1899)
Sophus Lie grew up in the town of Moss, south of Oslo. He was a powerful man, tall and strong with a booming voice and imposing presence. He was an accomplished sportsman, most notably in gymnastics. It was no hardship for Lie to walk the 60 km from Oslo to Moss at the weekend to visit his parents. At school, Lie was a good all-rounder, though his mathematics teacher, Ludvig Sylow, a pioneer of group theory, did not suspect his great potential or anticipate his remarkable achievements in that field.
Cubic Skulduggery & Intrigue
Published March 15, 2018 Irish Times Leave a CommentTags: Algebra, History
Solution of a cubic equation, usually called Cardano’s formula.
Babylonian mathematicians knew how to solve simple polynomial equations, in which the unknown quantity that we like to call x enters in the form of powers, that is, x multiplied repeatedly by itself. When only x appears, we have a linear equation. If x-squared enters, we have a quadratic. The third power of x yields a cubic equation, the fourth power a quartic and so on [TM135 or search for “thatsmaths” at irishtimes.com].
Metallic Means
Published February 9, 2017 Occasional Leave a CommentTags: Algebra, Arithmetic, Recreational Maths
The golden mean occurs repeatedly in the pentagram [image Wikimedia Commons]
and is the positive root of the quadratic equation
with the value
There is no doubt that
The Beginning of Modern Mathematics
Published January 26, 2017 Occasional Leave a CommentTags: Algebra, History
The late fifteenth century was an exciting time in Europe. Western civilization woke with a start after the slumbers of the medieval age. Johannes Gutenberg’s printing press arrived in 1450 and changed everything. Universities in Bologna, Oxford, Salamanca, Paris and elsewhere began to flourish. Leonardo da Vinci was in his prime and Christopher Columbus was discovering a new world.
Illustrations by Leonardo da Vinci in Pacioli’s De Divina Proportione.
