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On Spirals
This is the second volume of the first fully-fledged English translation of the works of Archimedes - antiquity's greatest scientist and one of the most important scientific figures in history. It covers On Spirals and is based on a reconsideration of the Greek text and diagrams, now made possible through new discoveries from the Archimedes Palimpsest. On Spirals is one of Archimedes' most dazzling geometrical tours de force, suggesting a manner of 'squaring the circle' and, along the way, introducing the attractive geometrical object of the spiral. The form of argument, no less than the results themselves, is striking, and Reviel Netz contributes extensive and insightful comments that focus on Archimedes' scientific style, making this volume indispensable for scholars of classics and the history of science, and of great interest for the scientists and mathematicians of today.
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About the author
Archimedes
158 books125 followersborn perhaps 287 BC
died 212 BC
Greek mathematician, engineer, and physicist Archimedes among the most important intellectuals of antiquity discovered the principle of buoyancy and formulae for the area and volume of various figures, applied geometry to hydrostatics and mechanics, and devised the numerous ingenious screw.
Archimedean screw, an ancient apparatus, consisted of a spiral tube around an inclined axis and raised water, or inclined tube contained a tight-fitting, broad-threaded screw.
Archimides first described faces, regular polygons of at least two different types, and identical vertices of Archimedean solid, a polyhedron.
Archimedes, an astronomer of Syracuse, invented.
Although a few details of his life are known, he is regarded as one of the leading classical scientists. Among his advances are the foundations and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege machines and the pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.
People generally consider Archimedes among the greatest of all time. He used the method of exhaustion to calculate under the arc of a parabola with the summation of an infinite series and gave a remarkably accurate approximation of pi. He also defined the spiral that bears his name, surfaces of revolution, and a system for expressing very large numbers.
He proved the relation between the sphere and surface, including the bases, of the cylinder and regarded this greatest achievement. Despite orders not to harm Archimedes, a Roman soldier killed him during the siege of Syracuse, and he then died. Marcus Tullius Cicero describes visiting a sphere, inscribed within a cylinder, which surmounts tomb of Archimedes.
People little knew the writings unlike inventions of Archimedes. From Alexandria, people read and quoted him, but Isidore of Miletus made the first comprehensive compilation not until 530; Eutocius in the sixth century wrote commentaries that opened the works of Archimedes to wider readership for the first time. The relatively few copies of written work of Archimedes survived through the Middle Ages, but this source of ideas influenced scientists during the Renaissance. In 1906, previously unknown works in the Archimedes Palimpsest provided new insights into obtaining his results.
died 212 BC
Greek mathematician, engineer, and physicist Archimedes among the most important intellectuals of antiquity discovered the principle of buoyancy and formulae for the area and volume of various figures, applied geometry to hydrostatics and mechanics, and devised the numerous ingenious screw.
Archimedean screw, an ancient apparatus, consisted of a spiral tube around an inclined axis and raised water, or inclined tube contained a tight-fitting, broad-threaded screw.
Archimides first described faces, regular polygons of at least two different types, and identical vertices of Archimedean solid, a polyhedron.
Archimedes, an astronomer of Syracuse, invented.
Although a few details of his life are known, he is regarded as one of the leading classical scientists. Among his advances are the foundations and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege machines and the pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.
People generally consider Archimedes among the greatest of all time. He used the method of exhaustion to calculate under the arc of a parabola with the summation of an infinite series and gave a remarkably accurate approximation of pi. He also defined the spiral that bears his name, surfaces of revolution, and a system for expressing very large numbers.
He proved the relation between the sphere and surface, including the bases, of the cylinder and regarded this greatest achievement. Despite orders not to harm Archimedes, a Roman soldier killed him during the siege of Syracuse, and he then died. Marcus Tullius Cicero describes visiting a sphere, inscribed within a cylinder, which surmounts tomb of Archimedes.
People little knew the writings unlike inventions of Archimedes. From Alexandria, people read and quoted him, but Isidore of Miletus made the first comprehensive compilation not until 530; Eutocius in the sixth century wrote commentaries that opened the works of Archimedes to wider readership for the first time. The relatively few copies of written work of Archimedes survived through the Middle Ages, but this source of ideas influenced scientists during the Renaissance. In 1906, previously unknown works in the Archimedes Palimpsest provided new insights into obtaining his results.
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Displaying 1 of 1 review
January 20, 2023
An Ancient Peer Review
20 January 2023 - Paddington
There were a couple of interesting things in this letter, and yes it was a letter because the opening is Archimedes addressing it to somebody else. The interesting thing is that he is apologising for not writing sooner because he had to send the proof to other people – yeah, this seems to be an ancient version of getting your work peer reviewed, not that it needed to be peer reviewed, but then again I suspect that half the reason we have his writings is because of this peer review process.
Mind you, it certainly wasn’t like what we have today, namely where we can send a bulk email, or even photo copy a bunch of them, they all had to be written out by hand. Well, sort of because I suspect that they would have had slaves to do that, and all Archemides would have done is simply attached a cover letter, like what has been done with this one.
The other thing is that a formula is mentioned that I remember from computer science, and suddenly, looking at it, I realised that it represented a spiral. Unfortunately I can’t format the formula on goodreads (and I can’t be bothered finding an image that is a copy of the formula since I am writing this during my lunch break, which sitting in the attic of an Air BnB in Paddington). But yeah, looking at the formula when it was just numbers, and simply using it out of context pretty much made no sense, but seeing it in the context of the spiral I pretty much had an Archimedes moment myself (though I didn’t jump out of the bath and run down Oxford street crying out ‘Eureka’).
Well, there is what Wikipedia says but that isn’t quite what I was thinking of.
Yeah, it’s interesting, but like the other ones, my eyes tend to glaze over when I hit the mathematical formula, probably because while I don’t mind maths, I have a lot of other things these days to keep my mind active (like getting AI to write my performance reviews).
20 January 2023 - Paddington
There were a couple of interesting things in this letter, and yes it was a letter because the opening is Archimedes addressing it to somebody else. The interesting thing is that he is apologising for not writing sooner because he had to send the proof to other people – yeah, this seems to be an ancient version of getting your work peer reviewed, not that it needed to be peer reviewed, but then again I suspect that half the reason we have his writings is because of this peer review process.
Mind you, it certainly wasn’t like what we have today, namely where we can send a bulk email, or even photo copy a bunch of them, they all had to be written out by hand. Well, sort of because I suspect that they would have had slaves to do that, and all Archemides would have done is simply attached a cover letter, like what has been done with this one.
The other thing is that a formula is mentioned that I remember from computer science, and suddenly, looking at it, I realised that it represented a spiral. Unfortunately I can’t format the formula on goodreads (and I can’t be bothered finding an image that is a copy of the formula since I am writing this during my lunch break, which sitting in the attic of an Air BnB in Paddington). But yeah, looking at the formula when it was just numbers, and simply using it out of context pretty much made no sense, but seeing it in the context of the spiral I pretty much had an Archimedes moment myself (though I didn’t jump out of the bath and run down Oxford street crying out ‘Eureka’).
Well, there is what Wikipedia says but that isn’t quite what I was thinking of.
Yeah, it’s interesting, but like the other ones, my eyes tend to glaze over when I hit the mathematical formula, probably because while I don’t mind maths, I have a lot of other things these days to keep my mind active (like getting AI to write my performance reviews).
Displaying 1 of 1 review