مقاله فراکتال و هندسه فراکتال به همراه ترجمه انگلیسی 56 ص فرمت word
A History of Fractal Geometry
While the lion’s share of the credit for the development of fractal geometry goes to Benoît Mandelbrot, many other mathematicians in the century preceding him had laid the foundations for his work. Moreover, Mandelbrot owes a great deal of his advancements to his ability to use computer technology — an advantage that his predecessors distinctly lacked; however, this in no way detracts from his visionary achievements. Nevertheless, while acknowledging and understanding the accomplishments of Mandelbrot, it undoubtedly helps to have some familiarity with the relevant works of Karl Weierstrass, Georg Cantor, Felix Hausdorff, Gaston Julia, Pierre Fatou and Paul Lévy — not only to make Mandelbrot’s work clearer — but to see its connections to other branches of mathematics. Equally, while most authors will not fail to include at least brief discussion of Mandelbrot’s rather interesting and slightly unconventional (for a modern
.mathematician) life in their texts on fractals, it seems only fair to give some, if not equal, consideration to his predecessors.
ترجمه
تاریخچه هندسه فرکتال
در حالی که سهم عمده ای از اعتبار برای هندسه فرکتال به بنوا مندلبروت بر می گردد، بسیاری از ریاضیدانان دیگر در قرن پیش از او ،پایه ها را برای کار خود پی ریزی کرده بودند.علاوه بر این مندلبروت مقدار زیادی از پیشرفت های خودش را به توانایی خود به استفاده از تکنولوژی کامپیوتر مدیون است،مزیتی که پیشینیان او بطور واضحی فاقد آن بودند،اما این به هیچ وجه از دستاوردهای نظری او نمی کاهد.با این وجود،در حالی که تصدیق و درک موفقیت مندلبروت،آن را بدون شک به کمک آشنایی با برخی از آثار مربوط به کارل وایرشتراس،گئورگ کانتور،فیلیکس هاسدروف،گاستون جولیا،پیرفاتو و پل لویی،نه فقط به روشن شدن آثار مندلبروت، بلکه برای دیدن ارتباطات به دیگر شاخه های ریاضی نیز کمک می کند.به همان شکل،گرچه بیشتر نویسندگان موفق نخواهند شد تا حد اقل بحث مختصری از زندگی نسبتاً جذاب و اندکی غیر متعارف مندلبروت را در متون خود روی فراکتال ها بر شمارند،این مقدار متوجه به پیشینیان او تنها عادلانه به نظر می رسد؛اگرچه برابر نیستند.
A History of Fractal Geometry
While the lion’s share of the credit for the development of fractal geometry goes to Benoît Mandelbrot, many other mathematicians in the century preceding him had laid the foundations for his work. Moreover, Mandelbrot owes a great deal of his advancements to his ability to use computer technology — an advantage that his predecessors distinctly lacked; however, this in no way detracts from his visionary achievements. Nevertheless, while acknowledging and understanding the accomplishments of Mandelbrot, it undoubtedly helps to have some familiarity with the relevant works of Karl Weierstrass, Georg Cantor, Felix Hausdorff, Gaston Julia, Pierre Fatou and Paul Lévy — not only to make Mandelbrot’s work clearer — but to see its connections to other branches of mathematics. Equally, while most authors will not fail to include at least brief discussion of Mandelbrot’s rather interesting and slightly unconventional (for a modern mathematician) life in their texts on fractals, it seems only fair to give some, if not equal, consideration to his predecessors.