One of the most remarkable and important mathematical results obtained by Archimedes was the determination of the volume of a sphere. Archimedes used a technique of sub-dividing the volume into slices of known cross-sectional area and adding up, or integrating, the volumes of the slices. This was essentially an application of a technique that was … Continue reading Archimedes and the Volume of a Sphere
Tag: Archimedes
It’s as Easy as Pi
Every circle has the property that the distance around it is just over three times the distance across. This has been known since the earliest times [see TM120 or search for “thatsmaths” at irishtimes.com]. The constant ratio of the circumference to the diameter, denoted by the Greek letter pi, is familiar to every school-child. You … Continue reading It’s as Easy as Pi
Who First Proved that C / D is Constant?
Every circle has the property that the distance around it is just over three times the distance across. This has been “common knowledge” since the earliest times. But mathematicians do not trust common knowledge; they demand proof. Who was first to prove that all circles are similar, in the sense that the ratio of circumference … Continue reading Who First Proved that C / D is Constant?
Mowing the Lawn in Spirals
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 … Continue reading Mowing the Lawn in Spirals
The Antikythera Mechanism
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 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. … Continue reading The Antikythera Mechanism
The remarkable BBP Formula
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 … Continue reading The remarkable BBP Formula
Happy Pi Day 2013
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 … Continue reading Happy Pi Day 2013
Archimedes uncovered
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 … Continue reading Archimedes uncovered
Sharing a Pint
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. … Continue reading Sharing a Pint
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