استفاده از عدد پي در ساخت تخت جمشيد

RedWine
by RedWine
17-Dec-2007
 

مهندسان هخامنشي راز استفاده از عدد پي (۱۴/۳ ) را دو هزار و 500 سال پيش كشف كرده بودند. آنها در ساخت سازه هاي سنگي و ستون هاي مجموعه تخت جمشيد كه داراي اشكال مخروطي است، از اين عدد استفاده مي كردند.

عدد پي( ۳.۱۴)در علم رياضيات از مجموعه اعداد طبيعي محسوب مي شود. اين عدد از تقسيم محيط دايره بر قطر آن به دست مي آيد. كشف عدد پي جزو مهمترين كشفيات در رياضيات است. كارشناسان رياضي هنوز نتوانسته اند زمان مشخصي براي شروع استفاده از اين عدد پيش بيني كنند. عده زيادي، مصريان و برخي ديگر، يونانيان باستان را كاشفان اين عدد مي دانستند اما بررسي هاي جديد نشان مي دهد هخامنشيان هم با اين عدد آشنا بودند.

«عبدالعظيم شاه كرمي» متخصص سازه و ژئوفيزيك و مسئول بررسي هاي مهندسي در مجموعه تخت جمشيد در اين باره،‌ گفت: «بررسي هاي كارشناسي كه روي سازه هاي تخت جمشيد به ويژه روي ستون هاي تخت جمشيد و اشكال مخروطي انجام گرفته؛ نشان مي دهد كه هخامنشيان دو هزار و 500 سال پيش از دانشمندان رياضي دان استفاده مي كردند كه به خوبي با رياضيات محض و مهندسي آشنا بودند. آنان براي ساخت حجم هاي مخروطي راز عدد پي را شناسايي كرده بودند.»

دقت و ظرافت در ساخت ستون هاي دايره اي تخت جمشيد نشان مي دهد كه مهندسان اين سازه عدد پي را تا چندين رقم اعشار محاسبه كرده بودند. شاه كرمي در اين باره گفت: «مهندسان هخامنشي ابتدا مقاطع دايره اي را به چندين بخش مساوي تقسيم مي كردند.

سپس در داخل هر قسمت تقسيم شده، هلالي معكوس را رسم مي كردند. اين كار آنها را قادر مي ساخت كه مقاطع بسيار دقيق ستون هاي دايره اي را به دست بياورند. محاسبات اخير، مهندسان سازه تخت جمشيد را در محاسبه ارتفاع ستون ها، نحوه ساخت آنها،‌ فشاري كه بايد ستون ها تحمل كنند و توزيع تنش در مقاطع ستون ها ياري مي كرد. اين مهندسان براي به دست آوردن مقاطع دقيق ستون ها مجبور بودند عدد پي را تا چند رقم اعشار محاسبه كنند.»

هم اكنون دانشمندان در بزرگ ترين مراكز علمي و مهندسي جهان چون «ناسا» براي ساخت فضاپيماها و استفاده از اشكال مخروطي توانسته اند عدد پي را تا چند صد رقم اعشار حساب كنند. بر اساس متون تاريخ و رياضيات نخستين كسي كه توانست به طور دقيق عدد پي را محاسبه كند، «غياث الدين محمد كاشاني» بود.

اين دانشمند ايراني عدد پي را تا چند رقم اعشاري محاسبه كرد. پس از او دانشمنداني چون پاسكال به محاسبه دقيق تر اين عدد پرداختند. هم اكنون دانشمندان با استفاده از رايانه هاي بسيار پيشرفته به محاسبه اين عدد مي پردازند.

شاه كرمي با اشاره به اين موضوع كه در بخش هاي مختلف سازه تخت جمشيد، مقاطع مخروطي شامل دايره، بيضي، و سهمي ديده مي شود، گفت: «به دست آوردن مساحت، محيط و ساخت سازه هايي با اين اشكال هندسي بدون شناسايي راز عدد پي و طرز استفاده از آن غيرممكن است.»

داريوش هخامنشي بنيان گذار تخت جمشيد در سال 521 پيش از ميلاد دستور ساخت تخت جمشيد را مي دهد و تا سال 486 بسياري از بناهاي تخت جمشيد را طرح ريزي يا بنيان گذاري مي كند. اين مجموعه باستاني شامل حصارها، كاخ ها،‌ بخش هاي خدماتي و مسكوني، نظام هاي مختلف آبرساني و بخش هاي مختلف ديگري است.

مجموعه تخت جمشيد مهمترين پايتخت مقاومت هخامنشي در استان فارس و در نزديكي شهر شيراز جاي گرفته است.

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Recommendation

by A Persian (not verified) on

For all who are interested in an unbiased description about the Achaemenid Dynasty and the people of Achaemenid Persia, I recommend that you read the following book: "A History of Ancient Persia", by Robert William Rogers, Published by Charles Scribner’s Sons, New York, 1929. It’s an old book, but it is a very good, objective summary of the Achaemenid era. What is also nice about this book is that it has a couple of chapters on the society and the lifestyle of ancient Persians. It shows that early Persians were simple, modest, poor and mainly mountain dwelling people who did not have much. It shows that the greatness of the Achaemenid Empire was that it arose of those conditions. It is fantasy for us to think that ancient Persians were somehow geniuses who were born into a great culture that went on to dominate the world. What the book shows and what one should be proud of as a descendant of those people is their determination and their ability to rise to the occasion, and to be able to go on from those humble beginnings to establish what was perhaps the greatest empire of the antiquity. What is also significant about the Achaemenids and the Persians of that time was their willingness to incorporate other, more advanced, cultures into their own and to learn from them. That is what contributed to the cultural advancement of the Iranian society in later stages of its evolution and that is what sets them apart from other invaders in history who, instead of being open minded and accepting of other cultures, tried to impose their own upon the conquered nations.


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To Teach, RE: Pre-Islamic Iran

by A Persian (not verified) on

Absolutely. There was considerable artistic, technological and scientific advances in Pre-Islamic Iran, but most of it flourished under the Sassanid Empire. And you are right about the destruction of the Royal Library at Ctesiphone. It was ordered by Omar. There is an accounting of it in Ibn Khaldoon's book. This is not to say that Achamenids were devoid of culture. It is just that they were more interested in military conquests and expansion of their empire. There was also considerable technological evidence from the Achamenid period (such as seige weapons), but a lot of that was done with the help of foreign speciliasts in thier fields, who were far more experienced than the Persians. And really, there is nothing wrong with that!!!


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History of Pi

by moaleme tarikh (not verified) on

π is a lot older
The earliest known approximations date from around 1900 BC; they are Babylonian and Egyptian, both within 1% of the true value. The Indian text Shatapatha Brahmana gives π as 3.139. The Books of Kings (600 BC) appears to suggest π = 3 . Archimedes was the first to estimate π rigorously.


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To Irooni

by Teach (not verified) on

I disagree with you to some extent. We know VERY little about our pre-islamic history, many thanks to well-documented contribution of ancestors of Khomeini, Omar-Ibn-Al-khattab et al., who ordered destruction of library of Ctesiphon with some 60,000 skin books - similar to what khomeini's followers tried to do right after the revolution. What we know is almost completely from Greek and islamic sources or based on excavations in the last century. So, we simply do not know. However, there are recent research by Maria something et al. [from Univ of London? - I can find her complete name and affiliation if necessitates] that disputes that and presents evidence that pre-islamic persian empire has also been a power-house in science and technology as well. I believe judging iran based on today - a low point in her 7000-year of written history - is misleading. Maybe we should also take the success of so many iranians in the fertile west today into account as well.


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Konj - Kav --Your Education?!!!

by A Persian (not verified) on

Your “education”?!!! If you were educated you would know that borrowing architectural designs is something that all successful cultures do (i.e., Parthian arches in European designs). If you were educated you would know that the use of Egyptian engineers in not only designing Takht-e-Jamshid, but also in building bridges, etc. in battles with Greeks was a sign of Persian Empire’s reach and power, which showed that they used talent from all over their conquered territories (including Egypt) in achieving their goals. If you were educated, you would know that Persians made a point of incorporating symbolism from conquered territories in order to show that reigned over those cultures. If you were educated, you would know that all of this was a sign of the Achaemenid’s power and tolerance, and not any type of a weakness that should warrant a nasty response. If you were educated, you would know that agreeing with someone is not reason enough to accept his / her word as true and not ask that person for his / her sources. Lastly, if you were educated, you would know where to use quotation marks and capital letters!!!!

I am not going to spend any more energy on arguing with an ignorant person like you. As I mentioned earlier, I will also not enable and reward your laziness and lack of intellectual curiosity. So, I am not going to do your research for you. I will also not allow you to put the burden of research on me with a one line unintelligible sentence. Here's the deal: I have prepared my source. If you cite your sources, I will cite you mine. I will be patiently waiting for your citations!


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To: A Persian

by Irooni (not verified) on

I forgot to mention that discoverer or inventor of PI is Archimedes, ancient Greek mathematician, a phenomenon in ancient time. Did we have any from that ear? What’s his name? Huh?


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To: A Persian

by Irooni (not verified) on

I totally agree with you. We never had anything significant to be ours. Even now we copy everything. I don't think we have any creativity in us. Everything is borrowed or stolen from other cultures or civilizations. Sorry guys for bursting your bubbles.


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Pi or π

by YO (not verified) on

In a nutshell, if you measure distance using any mechanism that uses a wheel, you are automatically incorporating Pi (π) in that measurement, there is a good documentary on this produced by National Geography. If you need to know more please continue to read (I hate long Comments)
The original argument was that Egyptians new about (Pi) and used it in the construction of great pyramids, but to measure strait line they must have used rope (or similar objects), well using rope to measure long distances would give inaccurate reading (the measurements will not be the same) and the pyramids measurement would be off by a few meter. On the contrary the pyramids measurements are extremely accurate (to many decimal places). The only accurate system to measure striate line is using a wheel,
Japanese discovered this in a bicycle race (very recently!!!!)
Some British scientist wasted a lifetime supporting the argument for the Egyptian cause but of no evil. Now the latecomer to the game is the Iranian archaeologist arguing the same thing over Takhte Jamshid. Well more power to them they can compete with John Taylor the British guy. Who knows may be ET constructed the whole thong -). Need more
http://www.world-mysteries.com/mpl_2.htm
http://www.math.washington.edu/~greenber/PiPyr.htm...


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To "A Persian" (Again)

by Konj Kav (not verified) on

For your information, the reason that I "Did Not" question the author is because I Tend to "agree" with him. I remember "distinctly" that in my History Lessons That I took during my education, the "Statement" that the author has made was repeatedly confirmed by "Evidence". Forgive me for putting it this way, but I believe that Your Statement (or better put, "Opinion") is nothing but Just "Pure" garbage :)


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To Konj Kav

by A Persian (not verified) on

Yes. I do have sources. They are called "my eyes"!!! I am not giving a history presentation here. I simply made a comment in response to an atricle which, incidentally, itself does not have any "links" to "references". I wonder why you did not ask the author of the article for references?!!!So, the readers can take it for whatever it's worth.

Lastly, I am not going to reward your apparent intellectual (and perhaps physical?) laziness by running around and finding books that I read almost two decades ago and providing the cites for you. Perhaps you can do some reading on your own...and not "links", but rather books!!!! Good luck!!


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To "A Persian"

by Konj Kav (not verified) on

Could you back your statement with "Links" to references that support your argument? I am "Serious" :)


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Egyptian Engineers

by A Persian (not verified) on

As much of a fan of Iran's history as I am, I have to point out a very important fact. Takht-e-Jamshid was designed by Egyptian Engineers, not Iranians. the obvious architectural clues that show the Egyptian design are as follows: 1) palm design columns (note the palm leaves on the top of the columns), and 2) roofs made out of wood, which actually contributed to its speedy destruction when Alexander set fire to it. Much of the other architectural design was foreign in origin as well, i,e., the winged bulls are Assyrian in origin and the winged lions are Babylonian. Persians were more of a military powerhouse rather than a cultural one during the Achaemenid period. Even the administration of the Empire was done by non-Iranians (Jews of Judea). That's why the language of the Persian Court was Aramaic....you have to give credit when credit is due!


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