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 — close to two thousand years later — formulated as integral calculus.

Continue reading ‘Archimedes and the Volume of a Sphere’## Posts Tagged 'Archimedes'

### Archimedes and the Volume of a Sphere

Published November 28, 2019 Occasional ClosedTags: Archimedes, Geometry

### It’s as Easy as Pi

Published August 3, 2017 Irish Times ClosedTags: Archimedes, Geometry, Number Theory, 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 might expect to find a proof in Euclid’s *Elements of Geometry*, he could not prove it, and he made no mention of the ratio (see last week’s post).

### Who First Proved that C / D is Constant?

Published July 27, 2017 Occasional ClosedTags: Archimedes, Geometry, Pi

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 *C* to diameter *D* has the same value for all?

*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.

### The Antikythera Mechanism

Published November 21, 2013 Irish Times ClosedTags: Archimedes, Mechanics, Time measurement

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. 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’

### The remarkable BBP Formula

Published August 8, 2013 Occasional ClosedTags: Archimedes, Computer Science, History, Number Theory, Pi

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’

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’

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’

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’