#archimedes — Public Fediverse posts on home.social

scinexx - das wissensmagazin @[email protected] · 2026-03-11 · 07:34 UTC

Seite des Archimedes-Palimpsests wiederentdeckt. Historiker spürt lange verschollenes Blatt der spätantiken Abschrift in Frankreich auf. #Archimedes #ArchimedesPalimpsest #Antike #Manuskript #Geometrie
https://www.scinexx.de/news/archaeologie/seite-des-archimedes-palimpsests-wiederentdeckt/

#archimedes #archimedespalimpsest #antike #manuskript #geometrie

Alan J. Cain @[email protected] · 2026-02-24 · 11:50 UTC

Friedrich Schiller's (1759–1805) poem ‘Archimedes and the Student’ (see 1st attached image for typeset text):

To Archimedes came an inquisitive youth
“Initiate me,” he said to him, “into the divine science,
That bore such splendid fruit for the nation
And shielded the walls of the city from the sambuca!”
“Divine you call the science? It is,” replied the sage,
“But it was so, my son, even before it served the state.
If you want only fruit from her, even mortals can provide it;
Who courts the goddess, seeks not in her the woman.”

(The sambuca was a ship-mounted siege engine; see 2nd attached image. During the Roman siege of Syracuse, it failed in the face of the war-machines designed by Archimedes.)

In 1808, Carl Friedrich Gauss (1777–1855) became director of the observatory at Göttingen and in his inaugural lecture declared that mathematics in general and astronomy in particular had a value — at least in part aesthetic — that was prior to and independent of any utility:

‘The happy great minds who created and expanded astronomy as well as the other beautiful parts of mathematics were certainly not inspired by the prospect of future use: they searched the truth for its own sake and found in the very success of their efforts their reward and their happiness. I cannot avoid at this point reminding you of ARCHIMEDES […]. You must all know the beautiful poem by SCHILLER.’

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[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

#Archimedes #Schiller #Gauss #poetry #HistMath

#histmath #poetry #gauss #schiller #archimedes

Alan J. Cain @[email protected] · 2026-02-13 · 13:10 UTC

The thirteen archimedean solids are the polyhedra (other than the five regular solids) all the faces of which are regular polygons and where for each pair of vertices some symmetry transformation carries one vertex to the other (see 1st attached image).

According to Pappus (fl. c.300–c.350 CE), who wrote a half-millennium later, Archimedes discovered them. The context of Pappus' report suggests that Archimedes was seeking polyhedra inscribable in spheres.

Archimedes excluded the infinite classes of prisms and anti-prisms, in which two n-gons are joined by squares or equilateral triangles (2nd attached image). Although they satisfy the definition, and are technically inscribable in spheres, they are somehow not ‘sphere-like’.

This suggests that Archimedes may have been influenced by the aesthetic preference for circles and spheres that descended from Pythagoras.

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#ArchimedeanSolids #RegularSolids #polyhedra #Archimedes #Pappus #HistMath

#histmath #pappus #archimedes #polyhedra #regularsolids #archimedeansolids

Alan J. Cain @[email protected] · 2026-02-07 · 11:32 UTC

Leonardo Pisano (c.1170–after 1240), dubbed ‘Fibonacci’, thought that Archimedes' proof that π was between $3\frac{10}{71}$ and $3\frac{1}{7}$ was beautiful [pulcra].

Archimedes' proof proceeds by calculating approximate ratios of the perimeters of 96-gons circumscribed about and inscribed in a circle to the diameter of that circle, implicitly starting with dodecagons and repeatedly bisecting edges to obtain 24-, 48-, and then 96-gons (see attached image).

Fibonacci’s judgement seems to be the earliest extant description of a *proof* as beautiful in the European tradition. [Al-Nasawī (fl. 1029–44) had earlier described a proof as beautiful.]

But there is a twist in the story...

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#MathematicalBeauty #BeautifulProof #HistMath #Fibonacci #Archimedes #Pi

#pi #archimedes #fibonacci #histmath #beautifulproof #mathematicalbeauty

Alan J. Cain @[email protected] · 2026-02-04 · 18:02 UTC

As noted in a previous post, Archimedes thought highly of the result that the ratio of either the volumes or surface areas of a cone, a sphere, and a cylinder exactly circumscribing them is $1:2:3$.

So did others: three centuries later, the architect Nicon (d.149/50 CE), father of the philosopher and physician Galen (129–c.210/217 CE), thought it fitting to point out the ratio of the configuration in a public inscription in his city, Pergamon:

‘the cone, the sphere, the cylinder.
If a cylinder encloses the other two shapes,
[...]
Competition the principle and in solids
the progression $1 ∶ 2 ∶ 3$,
a noble, divine equalization,
but also mutual interdependence
of the solids, always in the ratio $1 ∶ 2 ∶ 3$.
They should be beautiful and wonderful,
the three solid shapes’

Nicon doubtless admired these ratios as an architect: a sphere inside a cylinder brings to mind the Pantheon at Rome, of which the Temple of Zeus Asclepius Soter in Pergamon was a half-scale copy. These buildings were designed so that a basically cylindrical rotunda was crowned with a hemispherical dome under which a sphere would fit (see attached image).

[Each day of February, I am posting a story/image/fact/anecdote related to the aesthetics of mathematics.]

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#MathematicalBeauty #HistMath #Archimedes #geometry #architecture #aesthetics

#aesthetics #architecture #geometry #archimedes #histmath #mathematicalbeauty

Alan J. Cain @[email protected] · 2026-02-03 · 08:38 UTC

Max Dehn (1878–1952) said that Archimedes’ (c.287–212 BCE) discovery that the surface area of a sphere was four times its great circle was the one of the most beautiful results of Greek mathematics.

Archimedes himself had a high opinion of this result and two others in his two books ‘On the Sphere and the Cylinder’: that the volume and surface area of a sphere and a cylinder exactly circumscribing it are in the ratio $2 : 3$. One can add a cone fitting inside the cylinder to have ratios $1 : 2 : 3$ (see 1st attached image).

It has been suggested that Archimedes’ conjectures for these ratios may have been guided by a conscious or unconscious search for beautiful integer ratios between geometric configurations. There is no direct evidence for this motivation, but Archimedes’ work seems to exhibit a preference for small integer ratios.

According to Plutarch, Archimedes desired that his tomb should be marked by a cylinder enclosing a sphere and an inscription of the ratio of the one to the other; Cicero related how he had sought out Archimedes’ tomb and found a column just so inscribed (see 2nd attached image).

[Each day of February, I intend to post an interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

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#MathematicalBeauty #HistMath #Archimedes #Plutarch #Cicero #geometry #aesthetics