Published October 29, 2015
Tags: Archimedes, Geometry
Like a circle in a spiral / Like a wheel within a wheel / Never ending or beginning / On an ever-spinning reel. The Windmills Of Your Mind
Broadly speaking, a spiral curve originates at a central point and gets further away (or closer) as it revolves around the point. Spirals abound in nature, being found at all scales from the whorls at our finger-tips to vast rotating spiral galaxies. The seeds in a sunflower are arranged in spiral segments. In the technical world, the grooves of a gramophone record and the coils of a watch balance-spring are spiral in form.
Left: Archimedean spiral. Centre: Fermat spiral. Right: Hyperbolic spiral.
Continue reading ‘Mowing the Lawn in Spirals’
The article in this week’s That’s Maths column in the Irish Times ( TM033 ) is about the Antikythera Mechanism, which might be called the First Computer.
Two storms, separated by 2000 years, resulted in the loss and the recovery of one of the most amazing mechanical devices made in the ancient world. The first storm, around 65 BC, wrecked a Roman vessel bringing home loot from Asia Minor. The ship went down near the island of Antikythera, between the Greek mainland and Crete. Continue reading ‘The Antikythera Mechanism’
Information that is declared to be forever inaccessible is sometimes revealed within a short period. Until recently, it seemed impossible that we would ever know the value of the quintillionth decimal digit of pi. But a remarkable formula has been found that allows the computation of binary digits starting from an arbitrary position without the need to compute earlier digits. This is known as the BBP formula.
Continue reading ‘The remarkable BBP Formula’
Published March 14, 2013
Tags: Archimedes, Number Theory, Pi
Today, 14th March, is Pi Day. In the month/day format it is 3/14, corresponding to 3.14, the first three digits of π. So, have a Happy Pi Day. Larry Shaw of San Francisco’s Exploratorium came up with the Pi Day idea in 1988. About ten years later, the U.S. House of Representatives passed a resolution recognizing March 14 as National Pi Day.
Today is also the birthday anniversary of Albert Einstein, giving us another reason to celebrate. He was born on 14 March 1879, just 134 years ago today.
Continue reading ‘Happy Pi Day 2013’
Published January 3, 2013
Tags: Archimedes, History, Pi
The That’s Maths column in this week’s Irish Times ( TM012 ) describes the analysis of the ancient codex known as the Archimedes Palimpsest.
Archimedes of Syracuse
Archimedes (Ἀρχιμήδης, 287-212 BC) was a brilliant physicist, engineer and astronomer, and the greatest mathematician of antiquity. He is famed for founding hydrostatics, for formulating the law of the lever, for designing the helical pump that bears his name, for devising engines of war, and for much more. Continue reading ‘Archimedes uncovered’
Published December 13, 2012
Tags: Analysis, Archimedes, Puzzles
Four friends, exhausted after a long hike, stagger into a pub to slake their thirst. But, pooling their funds, they have enough money for only one pint.
Annie drinks first, until the surface of the beer is half way down the side (Fig. 1(A)). Then Barry drinks until the surface touches the bottom corner (Fig. 1(B)). Cathy then takes a sup, leaving the level as in Fig. 1(C), with the surface through the centre of the bottom. Finally, Danny empties the glass.
Question: Do all four friends drink the same amount? If not, who gets most and who gets least? Continue reading ‘Sharing a Pint’