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On Conoids and Spheroids
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Archimedes
153Ìýbooks123Ìýfollowersborn 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
June 16, 2022
More Maths Problems
15 June 2022
This is definitely not the type of book that you casually read in the way that I’m casually reading it, but then again I’m not that much of a math nerd that I will read it line by line to make sure that I understand how Archimedes is formulating his proofs. Sure, this is something that I would do at university (though I have to admit that half the time I simply ended up bluffing my way through the problems, particularly with Computing Theory, where you needed to be some sort of genius to actually understand how to formulate half the proofs that were put to you � well that, or that you simply just loved the subject, as our tutor happened to do).
Anyway, I’m not really sure what to say about this book. Yes, it’s ancient, though I’m not sure if Archimedes is simply reciting stuff that had been around for centuries beforehand. In fact, I sort of get the impression that while Euclid was pretty much codifying a lot of stuff that had already been around (the Babylonians understood Pythaogras� Therom), Archimedes is moving off into new directions.
Actually, the interesting thing is that a lot of this stuff was done for fun, but then again people would be doing complex maths problems in the 1700s and 1800s � it was sort of the thing to do. Then again, it was pretty much like the modern crossword, or even sudoku, though there does tend to be some method in the madness that happens to be sudoku, and as for crosswords, some of them are pretty ridiculous. I have some friends who actually have a cryptic crossword club, where they sit in a coffee shop and attempt to solve cryptic crosswords.
I guess the problem is that you need to really focus pretty deeply to understand Archimedes� proofs, and there of course are a lot of propositions that need to be set out for the proof to work. Mind you, some of them are probably not listed in this work because they are what is known as assumed knowledge � namely that the author assumes that you already know this stuff. Actually, that is pretty much the same as a lot of the science textbooks that are floating around today, but then again these aren’t the type of books that you would find in your typical bookshop (if they still happen to exist).
Well, okay, you also have the internet, which means that you can hyperlink your work to the point where it looks like it is just one long hyperlink, but it also means that you don’t need to create a ridiculously long document by repeating all of the assumed knowledge, but can refer the reader to where that assumed knowledge is located � that is of course that it doesn’t turn out to be some circular referencing.
In the end though, while it is interesting to see how maths developed, and while the statement that Pythogoras� Therom isn’t used in everyday life (friends of mine who knit tell me that they use it all the time) is rather false, this probably isn’t the type of book to casually read on the train (which is basically what I did anyway).
15 June 2022
This is definitely not the type of book that you casually read in the way that I’m casually reading it, but then again I’m not that much of a math nerd that I will read it line by line to make sure that I understand how Archimedes is formulating his proofs. Sure, this is something that I would do at university (though I have to admit that half the time I simply ended up bluffing my way through the problems, particularly with Computing Theory, where you needed to be some sort of genius to actually understand how to formulate half the proofs that were put to you � well that, or that you simply just loved the subject, as our tutor happened to do).
Anyway, I’m not really sure what to say about this book. Yes, it’s ancient, though I’m not sure if Archimedes is simply reciting stuff that had been around for centuries beforehand. In fact, I sort of get the impression that while Euclid was pretty much codifying a lot of stuff that had already been around (the Babylonians understood Pythaogras� Therom), Archimedes is moving off into new directions.
Actually, the interesting thing is that a lot of this stuff was done for fun, but then again people would be doing complex maths problems in the 1700s and 1800s � it was sort of the thing to do. Then again, it was pretty much like the modern crossword, or even sudoku, though there does tend to be some method in the madness that happens to be sudoku, and as for crosswords, some of them are pretty ridiculous. I have some friends who actually have a cryptic crossword club, where they sit in a coffee shop and attempt to solve cryptic crosswords.
I guess the problem is that you need to really focus pretty deeply to understand Archimedes� proofs, and there of course are a lot of propositions that need to be set out for the proof to work. Mind you, some of them are probably not listed in this work because they are what is known as assumed knowledge � namely that the author assumes that you already know this stuff. Actually, that is pretty much the same as a lot of the science textbooks that are floating around today, but then again these aren’t the type of books that you would find in your typical bookshop (if they still happen to exist).
Well, okay, you also have the internet, which means that you can hyperlink your work to the point where it looks like it is just one long hyperlink, but it also means that you don’t need to create a ridiculously long document by repeating all of the assumed knowledge, but can refer the reader to where that assumed knowledge is located � that is of course that it doesn’t turn out to be some circular referencing.
In the end though, while it is interesting to see how maths developed, and while the statement that Pythogoras� Therom isn’t used in everyday life (friends of mine who knit tell me that they use it all the time) is rather false, this probably isn’t the type of book to casually read on the train (which is basically what I did anyway).
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