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Measurement of a Circle
- GenresScience
Hardcover
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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 - 2 of 2 reviews
April 10, 2022
The Birth of Pi
9 April 2022
This is a rather short text, though that might have something to do with most of it being missing, however it is a very significant work namely because it introduces the concept of pi, that being the ratio between the diameter of a circle, and it’s circumference. The interesting thing is that ratio basically never changes, and for those who don’t know, the number of diameters that will fit around the circumference of the circle is roughly 3.14. I say roughly because the number is actually irrational.
Mind you, it isn’t as if Archimedes came up with the concept, it had been known for quite a long time before then, namely because it has been used in architecture. Also, he doesn’t actually give it a name, he just outlines what it happens to be. However, what this text does is that it provides us with proof as to what the ratio is mathematically, to as close as it is possible (though he uses a fraction to describe it here, possibly because they didn’t have a decimal point - which came from the Arabs, as quite a lot of our maths did).
The thing is that this text is pretty heavy on the maths, which probably shouldn’t be surprising because this seems to be the case with a lot of Archimedes’ writing. In fact, it can be rather difficult to follow for the uninitiated (such as myself). Okay, I don’t mind maths, and have played around with it in the past, but there is basically a limit that I reached when my brain started to explode – and that limit was basically my computer science degree. Sure, I could probably work things out if I really needed to, but fortunately these days I don’t.
Honestly, one of the good things that arose out of the covid pandemic was that I didn’t have to take exams at university, which meant that I was actually able to pass these subjects as opposed to facing an exam that could quite easily drag my marks down significantly, if I didn’t end up failing that is. Anyway, this probably isn’t the type of tract for anybody to read, and I only read it because I wanted to see how the Ancients approached maths.
9 April 2022
This is a rather short text, though that might have something to do with most of it being missing, however it is a very significant work namely because it introduces the concept of pi, that being the ratio between the diameter of a circle, and it’s circumference. The interesting thing is that ratio basically never changes, and for those who don’t know, the number of diameters that will fit around the circumference of the circle is roughly 3.14. I say roughly because the number is actually irrational.
Mind you, it isn’t as if Archimedes came up with the concept, it had been known for quite a long time before then, namely because it has been used in architecture. Also, he doesn’t actually give it a name, he just outlines what it happens to be. However, what this text does is that it provides us with proof as to what the ratio is mathematically, to as close as it is possible (though he uses a fraction to describe it here, possibly because they didn’t have a decimal point - which came from the Arabs, as quite a lot of our maths did).
The thing is that this text is pretty heavy on the maths, which probably shouldn’t be surprising because this seems to be the case with a lot of Archimedes’ writing. In fact, it can be rather difficult to follow for the uninitiated (such as myself). Okay, I don’t mind maths, and have played around with it in the past, but there is basically a limit that I reached when my brain started to explode – and that limit was basically my computer science degree. Sure, I could probably work things out if I really needed to, but fortunately these days I don’t.
Honestly, one of the good things that arose out of the covid pandemic was that I didn’t have to take exams at university, which meant that I was actually able to pass these subjects as opposed to facing an exam that could quite easily drag my marks down significantly, if I didn’t end up failing that is. Anyway, this probably isn’t the type of tract for anybody to read, and I only read it because I wanted to see how the Ancients approached maths.
October 2, 2016
I was a Math & Physics major. Archimedes impressed me with his remarkable abilities applied to logical proofs relating sizes of circles and triangles, as well as approximating a domain for pi between 3 1/7 and 3 10/71. Gratefully, this is pretty straightforward. But not everyone would find it interesting.
Displaying 1 - 2 of 2 reviews