1.
Archimedes was born in Syracuse, in the early 3rd century BCE, on the island of Sicily. He was probably not fluent in Greek at birth. (Then again, who knows?)
2.
He assembled one of the wildest and most impressive careers in mathematics, ancient or otherwise. My favorite work of his: “Sand Reckoner,” an estimate of how many grains of sand it would take to fill the universe.
3.
Archimedes mastered the “method of exhaustion,” which smells an awful lot like what we today call “calculus.” He used this technique to deduce the circumference of circles, the volume of spheres, and the area enclosed by parabolas.
4.
I’ve heard several historians (namely Viktor Blasjo and Chris Rorres) hail Archimedes’ analysis of floating bodies as one of the great achievements in math. It was a systematic analysis of a chaotic system, more than 20 centuries before chaos theory.
5.
Legend has it that Archimedes refused to yield when a Roman soldier ordered him to stop drawing diagrams in the dirt. Classic mathematician.
(By the way, I recommend the Twitter thread in which historians Alberto Martinez and Viktor Blasjo debate the plausibility of this tale.)
6.
The soldier, not knowing who Archimedes was, attacked him.
(And by the way, he really did view the sphere volume proof – that a sphere, fit snugly inside a cylinder, will fill 2/3 of its container – as his masterwork. Cicero tells us that its image appeared on his tombstone.)
7.
I imagine Archimedes departed our mortal plane beneath a fitting piece of geometry: a parabolic arch.
8.
(Not depicted: sphere volume proof.)
Rest in peace, Archimedes!
I think (6) should be “will fill 2/3 of its container” instead of “will fit 2/3 of its container”
I think it is true that Archimedes knew that if a sphere is fit snugly in a cylinder then the volume of the sphere is 2/3 the volume of the cylinder AND the surface area is 2/3 of the cylinder.
Yes, good call! Not sure what it would mean for a figure to “fit” some fraction of its container.
And interesting point about the surface area! It is a very pleasing fact that both are 2/3. I have a vague memory that surface area was better studied before Archimedes, and volume was his novel contribution? I have a copy of Lockhart’s “Measurement” somewhere, which I think lays out the surface area argument…
An alternative telling of the death, that I heard from my history of mathematics lecturer, has Archimedes on the beach drawing away at his diagrams as the Romans land an invasion force; he objected to them getting in the way of his work, saying “get out of my light” and was struck down.
Then again, the Romans may well have had a particular interest in killing him off, since their previous attempt at taking Syracuse had been thwarted by fearsome mechanisms (using levers and lots of folk pulling on ropes) that picked up their ships from the bay and dashed them against the rocks. One guess who designed those – famous also for “give me a lever long enough and a pivot to balance it on and I’ll move the world”. Again, how historical this is may be subject to debate !
Archimedes is responsible for the results about both the surface area and volume. Neither was known before him. The legend about the Roman soldier etc. is oft-told and fun but highly doubtful; we should all stop telling it from now on (though it made for some great anagrams and cartoons here!) For a convincing and thorough debunking, see The Cult of Pythagoras, by Alberto Martinez. He traces how this tall tale grew over the centuries.
Thanks, Steve! I’ve edited the text from merely saying “legend has it,” in order to accentuate the falseness.
I’m quite guilty of passing along bits of apocrypha like this while merely tagging them as “uncertain” or “folkloric”… but I’m sure you’re right that mathematics history is better served by exercising more prudence.
sounds like the sort of thing Thony Christie @rmathematicus (on Twitter) may have covered at some point too
You’ve given me a delicious social-media serendipity to add to my collection: Earlier today, I saw Anu Garg’s email announcing the 25th anniversary of his wildly popular A Word A Day mailing list. The email describes 4 contests themed on the 4 branches of his lexicographical service: Limericks, Pan-Grams, Coin-a-Word, and yes, Anagrams! Your nicely executed post would not qualify for the contest sadly (great prizes!) because it’s not about an event from the last 25 years, but I encourage you to send it to Anu, as he will undoubtedly enjoy it, and you might get some kind of honorable mention! http://wordsmith.org/25years/contests.html
Wonderful! The proof of the volume of the sphere and the cylinder is gorgeous: my favourite application of the Pythagorean theorem:-)
‘Died as he lived: doing math’ – this should be included in the hall of fame epitaphs.
Indeed!
Wow, such a novel way to tell an important tale. Kudos 👏