Magister Mathematicae (talk | contribs) explanation of revert [http://en.wikipedia.org/w/index.php?title=Unit_fraction&diff=prev&oldid=23140635] |
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Such image implictly states that egyptians were squaring circles, which accepted knowledge states as false. |
Such image implictly states that egyptians were squaring circles, which accepted knowledge states as false. |
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:: "One of the oldest surviving mathematical writings is the Rhind papyrus, named after the Scottish Egyptologist A Henry Rhind who purchased it in Luxor in 1858. It is a scroll about 6 metres long and 1/3 of a metre wide and was written around 1650 BC by the scribe Ahmes who copied a document which is 200 years older. This gives date for the original papyrus of about 1850 BC but some experts believe that '''the Rhind papyrus is based on a work going back to 3400 BC''' (the work of the Saqarra architect). You can see more about the Rhind papyrus in the History topic article Egyptian papyri. In the Rhind papyrus Ahmes gives a rule to construct a square of area nearly equal to that of a circle. The rule is to cut 1/9 off the circle's diameter and to construct a square on the remainder. Although this is not really a geometrical construction as such it does show that the problem of constructing a square of area equal to that of a circle goes back to the beginnings of mathematics. This is quite a good approximation, corresponding to a value of 3.1605, rather than 3.14159, for pi." |
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:: [[http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Squaring_the_circle.html rhind papyrus]] |
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:: user drini may not be very well informed on mathematics and the history of curves, but there is certainly no reason to suggest this is anything but the accepted mainstream position regarding Egyptian mathematics. It is well documented by Gillings in "Mathematics in the time of the Pharoahs" . |
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: ''There is a construction by an Egyptian architect which dates back to the 3rd millennium BC which attempts to solve the problem by the use of two different coordinate systems. It should be noted that it is the limitation to just [[compass (drafting)|compass]] and [[straightedge]] that makes the problem difficult.'' |
: ''There is a construction by an Egyptian architect which dates back to the 3rd millennium BC which attempts to solve the problem by the use of two different coordinate systems. It should be noted that it is the limitation to just [[compass (drafting)|compass]] and [[straightedge]] that makes the problem difficult.'' |
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: [[http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Trisecting_an_angle.html Trisection]] |
: [[http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Trisecting_an_angle.html Trisection]] |
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:[[http://www-groups.dcs.st and .ac.uk/~history/HistTopics/Doubling_the_cube.html Doubling a cube]] |
:[[http://www-groups.dcs.st and .ac.uk/~history/HistTopics/Doubling_the_cube.html Doubling a cube]] |
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:: The Greeks began visiting Egypt and picking up useful bits of mathematics in the time of Thales. Solon, Plato, Pythagorus and Herodotus all visited Egypt and over a period of three centuries wrote about their religion, philosophy, mathematics, science, history and geography. For another three centuries in the Ptolomaic period, a great library was established at Alexandria where Greeks and Romans from all over the Mediterranian world came to study and to copy and extrapolate on the Egyptians ideas. Well into the Medeival period Egyptian unit fractions were the standard mathematical notation. To just ignore that millenia of exploration of Egyptian mathematics like it didn't exist and to just attribute all of their ideas to the Greeks and Romans who wrote about them latter seems more than a bit ethocentric. |
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: ''The problem really dates back to the invention of [[geometry]] and has occupied mathematicians for millennia. Ancient geometers had a very good practical and intuitive grasp of the problems complexity.'' |
: ''The problem really dates back to the invention of [[geometry]] and has occupied mathematicians for millennia. Ancient geometers had a very good practical and intuitive grasp of the problems complexity.'' |
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No, the circle squaring problem does not dates as back as the earliest geometry problems, which were calculational, not constructional.'' |
No, the circle squaring problem does not dates as back as the earliest geometry problems, which were calculational, not constructional.'' |
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:: drini may wish to take that up with the other cited authors who disagree, but the earliest circle squaring problem I know of, the one refered to above, is indeed Egyptian and dated to its earliest dynasties. As to whether its calculational as opposed to constructional, a sketch of an arc is drawn, apparently with a compass and then its x and y coordinates are measured, there being no prohibition against the use of a ruler in the Egyptian history of the problem. |
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:''Still using Egyptian unit fractions for their calculations, Greeks such as [[Eratosthenes]] and [[Plato]] built machines to solve the problem of doubling the cube which is mathematically related to squaring the circle.'' |
:''Still using Egyptian unit fractions for their calculations, Greeks such as [[Eratosthenes]] and [[Plato]] built machines to solve the problem of doubling the cube which is mathematically related to squaring the circle.'' |
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No, greeks did not have a decimal system, but they weren't limited to suing Egyptian fractions, for they could use rations that had other demonimators than 1. Indeed, any positive rational number can be represented as a finite sum of unit fractions, but in practice this is not as easily doable without good arithmetic system: 2/17 decomposes as egyptian fractions as 1/9 + 1/153, and denominators can become ugly even for small fractions. Furthermore, the fact that greeks did use all rational numbers in their calculations is illustrated by the fact that they believed ANY number was indeed as rational number (ergo the shock with sqrt(2)) |
No, greeks did not have a decimal system, but they weren't limited to suing Egyptian fractions, for they could use rations that had other demonimators than 1. Indeed, any positive rational number can be represented as a finite sum of unit fractions, but in practice this is not as easily doable without good arithmetic system: 2/17 decomposes as egyptian fractions as 1/9 + 1/153, and denominators can become ugly even for small fractions. Furthermore, the fact that greeks did use all rational numbers in their calculations is illustrated by the fact that they believed ANY number was indeed as rational number (ergo the shock with sqrt(2)) |
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:: 1.) The Greeks did have a decimal system, many of their measures are decimal multiples. |
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:: 2.) They could use whatever notation they wanted but the fact is the use of Egyptian unit fractions is common in Greek mathematics |
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:: 3.) The Egyptians had a good aritmetic system |
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:: 4.) If you actually study unit fractions you will find that the Egyptians could and did find unit fraction equivalents using rulers as calculators, and there is nothing ugly about their mathematics. |
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:: 5.) [[http://sunsite.utk.edu/math_archives/.http/hypermail/historia/feb99/0103.html the contra argument]] [[http://sunsite.utk.edu/math_archives/.http/hypermail/historia/feb99/0108.html next in thread]] |
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: ''In recent years the analytic geometry of the Egyptians unit fraction algorythms have become interesting. The mathematics underlying the solutions of the Egyptians who first attacked the problem in the [[Rhind Papyrus]] are once again being studied because of their implications for continued fractions.'' |
: ''In recent years the analytic geometry of the Egyptians unit fraction algorythms have become interesting. The mathematics underlying the solutions of the Egyptians who first attacked the problem in the [[Rhind Papyrus]] are once again being studied because of their implications for continued fractions.'' |
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See comments in [[Talk:Squaring the circle]]. BAsically, it's only to Rktect and a small handful of people that believe that such think as egyptian analytic geometry existed. |
See comments in [[Talk:Squaring the circle]]. BAsically, it's only to Rktect and a small handful of people that believe that such think as egyptian analytic geometry existed. |
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:: Drini apparently found that it isn't just me (92,800 google hits for Egyptian analytic geometry) |
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:: "Engels, Hermann. Quadrature of the circle in ancient Egypt. Historia Math. 4 (1977), 137--140. (Reviewer: L. Guggenbuhl.) SC: 01A15, MR: 56 #5124. Explains the Egyptian formula for the area of a circle in terms of the practices of Egyptian stone masons. In order to form a relief, the stone masons covered their designs with a grid. The hypothesized construction involves an error which would confirm the now commonly held view that the ancient Egyptians did not properly understand the Pythagorean theorem. Closely related topics: Ancient Egypt, The Circle, Coordinates, and Pythagorean Triangles and Triples. " |
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::[[http://math.truman.edu/~thammond/history/AnalyticGeometry.html analytic geometry]] |
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As phrased, it sounds that it's indeed topic subject to research by many mathematicians and scientists, whereas it is not. Therefore, I reverted [http://en.wikipedia.org/w/index.php?title=Unit_fraction&diff=prev&oldid=23140635]. -- ([[User:Drini|☺drini♫]]|[[User talk:Drini|☎]]) 03:49, 13 September 2005 (UTC) |
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:: Mathematics is either a topic drini doesn't know much about or or a topic he can't be intellectually honest enough about to admit where he is wrong. [[User:Rktect|Rktect]] 14:54, 13 September 2005 (UTC) |
Revision as of 14:54, 13 September 2005
Explanation of revert
The revert I made it's because the content added by Rktect is a POV attempt to push his beliefs on egyptian world. Namely, that egyptians did knew how to square the circle.
- [[Image:egyptian circle.jpg|right|400px|The square and the circle have the same area]]
Such image implictly states that egyptians were squaring circles, which accepted knowledge states as false.
- "One of the oldest surviving mathematical writings is the Rhind papyrus, named after the Scottish Egyptologist A Henry Rhind who purchased it in Luxor in 1858. It is a scroll about 6 metres long and 1/3 of a metre wide and was written around 1650 BC by the scribe Ahmes who copied a document which is 200 years older. This gives date for the original papyrus of about 1850 BC but some experts believe that the Rhind papyrus is based on a work going back to 3400 BC (the work of the Saqarra architect). You can see more about the Rhind papyrus in the History topic article Egyptian papyri. In the Rhind papyrus Ahmes gives a rule to construct a square of area nearly equal to that of a circle. The rule is to cut 1/9 off the circle's diameter and to construct a square on the remainder. Although this is not really a geometrical construction as such it does show that the problem of constructing a square of area equal to that of a circle goes back to the beginnings of mathematics. This is quite a good approximation, corresponding to a value of 3.1605, rather than 3.14159, for pi."
- user drini may not be very well informed on mathematics and the history of curves, but there is certainly no reason to suggest this is anything but the accepted mainstream position regarding Egyptian mathematics. It is well documented by Gillings in "Mathematics in the time of the Pharoahs" .
- There is a construction by an Egyptian architect which dates back to the 3rd millennium BC which attempts to solve the problem by the use of two different coordinate systems. It should be noted that it is the limitation to just compass and straightedge that makes the problem difficult.
- The ancient Egyptians and later the Greeks, did not restrict themselves to attempting to find a plane solution but rather developed a great variety of methods using various curves invented specially for the purpose, or devised constructions based on some mechanical method." Many of these devices became common drafting aids in the offices of architects. Some of the dimensioned drawings of ancient Egyptian architects can be found in Somers Clarke and R. Englebacj "Ancient Egyptian Construction and Architecture", Dover 1990.
The discussion about the curves used by greeks on circle squaring are to be found at Talk:Squaring the circle where the three links mentioned below are analyzed and showing that they do not support a claim as strong as Rktect pretends
- [circle squarering]
- [Trisection]
- [and .ac.uk/~history/HistTopics/Doubling_the_cube.html Doubling a cube]
- The Greeks began visiting Egypt and picking up useful bits of mathematics in the time of Thales. Solon, Plato, Pythagorus and Herodotus all visited Egypt and over a period of three centuries wrote about their religion, philosophy, mathematics, science, history and geography. For another three centuries in the Ptolomaic period, a great library was established at Alexandria where Greeks and Romans from all over the Mediterranian world came to study and to copy and extrapolate on the Egyptians ideas. Well into the Medeival period Egyptian unit fractions were the standard mathematical notation. To just ignore that millenia of exploration of Egyptian mathematics like it didn't exist and to just attribute all of their ideas to the Greeks and Romans who wrote about them latter seems more than a bit ethocentric.
- The problem really dates back to the invention of geometry and has occupied mathematicians for millennia. Ancient geometers had a very good practical and intuitive grasp of the problems complexity.
No, the circle squaring problem does not dates as back as the earliest geometry problems, which were calculational, not constructional.
- drini may wish to take that up with the other cited authors who disagree, but the earliest circle squaring problem I know of, the one refered to above, is indeed Egyptian and dated to its earliest dynasties. As to whether its calculational as opposed to constructional, a sketch of an arc is drawn, apparently with a compass and then its x and y coordinates are measured, there being no prohibition against the use of a ruler in the Egyptian history of the problem.
- Still using Egyptian unit fractions for their calculations, Greeks such as Eratosthenes and Plato built machines to solve the problem of doubling the cube which is mathematically related to squaring the circle.
No, greeks did not have a decimal system, but they weren't limited to suing Egyptian fractions, for they could use rations that had other demonimators than 1. Indeed, any positive rational number can be represented as a finite sum of unit fractions, but in practice this is not as easily doable without good arithmetic system: 2/17 decomposes as egyptian fractions as 1/9 + 1/153, and denominators can become ugly even for small fractions. Furthermore, the fact that greeks did use all rational numbers in their calculations is illustrated by the fact that they believed ANY number was indeed as rational number (ergo the shock with sqrt(2))
- 1.) The Greeks did have a decimal system, many of their measures are decimal multiples.
- 2.) They could use whatever notation they wanted but the fact is the use of Egyptian unit fractions is common in Greek mathematics
- 3.) The Egyptians had a good aritmetic system
- 4.) If you actually study unit fractions you will find that the Egyptians could and did find unit fraction equivalents using rulers as calculators, and there is nothing ugly about their mathematics.
- 5.) [the contra argument] [next in thread]
- In recent years the analytic geometry of the Egyptians unit fraction algorythms have become interesting. The mathematics underlying the solutions of the Egyptians who first attacked the problem in the Rhind Papyrus are once again being studied because of their implications for continued fractions.
See comments in Talk:Squaring the circle. BAsically, it's only to Rktect and a small handful of people that believe that such think as egyptian analytic geometry existed.
- Drini apparently found that it isn't just me (92,800 google hits for Egyptian analytic geometry)
- "Engels, Hermann. Quadrature of the circle in ancient Egypt. Historia Math. 4 (1977), 137--140. (Reviewer: L. Guggenbuhl.) SC: 01A15, MR: 56 #5124. Explains the Egyptian formula for the area of a circle in terms of the practices of Egyptian stone masons. In order to form a relief, the stone masons covered their designs with a grid. The hypothesized construction involves an error which would confirm the now commonly held view that the ancient Egyptians did not properly understand the Pythagorean theorem. Closely related topics: Ancient Egypt, The Circle, Coordinates, and Pythagorean Triangles and Triples. "
As phrased, it sounds that it's indeed topic subject to research by many mathematicians and scientists, whereas it is not. Therefore, I reverted [1]. -- (☺drini♫|☎) 03:49, 13 September 2005 (UTC)
- Mathematics is either a topic drini doesn't know much about or or a topic he can't be intellectually honest enough about to admit where he is wrong. Rktect 14:54, 13 September 2005 (UTC)