Forwarded from دستیار زیر نویس و هایپر لینک
This media is not supported in your browser
VIEW IN TELEGRAM
بازتاب مراسم گرامیداشت روز ملی ریاضیات (29 اردیبهشت 95) و تجلیل از پروفسور بهمن مهری در خبر شبانگاهی گیلان
@GuilanMath
💢💢💢💢💢💢💢
📡 @infinitymath
@GuilanMath
💢💢💢💢💢💢💢
📡 @infinitymath
Forwarded from Deleted Account
➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰
📡 @infinitymath
➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰
🔳 پرونده ویژه : کاشیکاری اشر
موریس اشر، هنرمند و معمار هلندی بود که با کمک گرفتن از مفاهیم ریاضیاتی و هندسی توانست طرح های هندسی خارق العاده زیادی خلق کند و روشی برای کاشیکایی صفحه معرفی کند که امروزه به روش اشر معروف است، در مقاله زیر به طور مختصر به کاشیکاری و روش هندسی اشر برای آن اشاره شده است. به طور ساده میتوان گفت اساس این روش بر کاشیکاری صفحه بوسیله چند ضلعی ها و حرکات صلب صفحه مانند انتقال، دوران و تقارن استوار است، برای مروری کوتاه بر این موضوع مقالات خواندنی به علاوه تصاویر جذاب و معروف از کاشیکاری های اشر در ادامه برای اولین بار در کانال بی نهایت ارائه میشوند. تصاویر مربوط به معروفترین طرح ها و کاشیکاری های اشر است که نام هر کدام برای پیگیری بیشتر ذکر شده است. مطالعه مقاله زیر و مرور تصاویر و همچنین پیگیری این موضوع جذاب و شگفت انگیز را به علاقه مندان ریاضی توصیه میکنیم.
💢💢💢💢💢💢
📡 @infinitymath
💢💢💢💢💢💢
Creating tessellations of the plane by recognizable figures was Escher's first groundbreaking artistic technique. He called it the regular subdivision of the plane, or regelmatige vlakverdeling in his native Dutch. Escher's works feature complex and whimsical figures, mostly animals, which magically interlock to cover the printed page. Creating these mathematically constrained outlines is no easy process, and Escher was unquestionably the master. His technique was to start with a simple tessellation by geometric shapes, and then evolve it into a recognizable figure. Escher writes[1]:
📡 @infinitymath
One can divide a plane into geometric shapes according to certain systems; these forms can become infinitely varied and very complex and still meet the requirement of filling the plane with congruent forms in rhythmic repetition without leaving any 'void.' If one then tries to mold the form so as to evoke an association with something familiar to the viewer - an object, an animal, or whatever it might be - it becomes a compelling game in view of the infinite possibilities offered as well as the rigourous restrictions imposed by the rules. It is a painstaking process of groping and fumbling about. Sometimes not a single one of the patterns that appear at the end were consciously sought at the start. It dawns on you slowly. Then comes the moment when you recognize it when you suddenly realize - and here we shift from a general impression to a specific one -: it is a man on a horse! After this, he develops rapidly under the impact of certainty.
@infinitymath
Here, Escher lays out his methods for creating tessellations:
Begin with a tessellation by geometric shapes.
"Mold the form". Here, he bends and manipulates the straight lines of the geometric scaffolding.
Look at the resulting pattern and attempt to recognize a figure.
Push the pattern towards the desired shape. @infinitymath
Not only was this Escher's process for creating tessellations, but also the theme of many of his artworks. Escher wants his audience to see and understand the process behind the patterns, and often presents prints with story like transitions from geometric to recognizable tessellations. You can investigate the passage from geometry to art in Metamorphosis Exploration.
@infinitymath
What makes the creation of tessellations a "compelling game" is the interplay between "molding a form" and attempting to recognize a figure in it. We shall see that it is quite difficult to create a tessellation with a preconceived subject or motif, but easy to make interesting looking shapes that, after the fact, can be decorated and enhanced to look like something.
@infinitymath
Several techniques explaining how to create the Escehr like tessellations will be covered in the section Tessellations by Recognizable Figures. As a first step, however, we must learn more about Tessellations by Polygons.
Web address: euler.slu.edu
〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰
📡 @infinitymath
〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰
📡 @infinitymath
➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰➰
🔳 پرونده ویژه : کاشیکاری اشر
موریس اشر، هنرمند و معمار هلندی بود که با کمک گرفتن از مفاهیم ریاضیاتی و هندسی توانست طرح های هندسی خارق العاده زیادی خلق کند و روشی برای کاشیکایی صفحه معرفی کند که امروزه به روش اشر معروف است، در مقاله زیر به طور مختصر به کاشیکاری و روش هندسی اشر برای آن اشاره شده است. به طور ساده میتوان گفت اساس این روش بر کاشیکاری صفحه بوسیله چند ضلعی ها و حرکات صلب صفحه مانند انتقال، دوران و تقارن استوار است، برای مروری کوتاه بر این موضوع مقالات خواندنی به علاوه تصاویر جذاب و معروف از کاشیکاری های اشر در ادامه برای اولین بار در کانال بی نهایت ارائه میشوند. تصاویر مربوط به معروفترین طرح ها و کاشیکاری های اشر است که نام هر کدام برای پیگیری بیشتر ذکر شده است. مطالعه مقاله زیر و مرور تصاویر و همچنین پیگیری این موضوع جذاب و شگفت انگیز را به علاقه مندان ریاضی توصیه میکنیم.
💢💢💢💢💢💢
📡 @infinitymath
💢💢💢💢💢💢
Creating tessellations of the plane by recognizable figures was Escher's first groundbreaking artistic technique. He called it the regular subdivision of the plane, or regelmatige vlakverdeling in his native Dutch. Escher's works feature complex and whimsical figures, mostly animals, which magically interlock to cover the printed page. Creating these mathematically constrained outlines is no easy process, and Escher was unquestionably the master. His technique was to start with a simple tessellation by geometric shapes, and then evolve it into a recognizable figure. Escher writes[1]:
📡 @infinitymath
One can divide a plane into geometric shapes according to certain systems; these forms can become infinitely varied and very complex and still meet the requirement of filling the plane with congruent forms in rhythmic repetition without leaving any 'void.' If one then tries to mold the form so as to evoke an association with something familiar to the viewer - an object, an animal, or whatever it might be - it becomes a compelling game in view of the infinite possibilities offered as well as the rigourous restrictions imposed by the rules. It is a painstaking process of groping and fumbling about. Sometimes not a single one of the patterns that appear at the end were consciously sought at the start. It dawns on you slowly. Then comes the moment when you recognize it when you suddenly realize - and here we shift from a general impression to a specific one -: it is a man on a horse! After this, he develops rapidly under the impact of certainty.
@infinitymath
Here, Escher lays out his methods for creating tessellations:
Begin with a tessellation by geometric shapes.
"Mold the form". Here, he bends and manipulates the straight lines of the geometric scaffolding.
Look at the resulting pattern and attempt to recognize a figure.
Push the pattern towards the desired shape. @infinitymath
Not only was this Escher's process for creating tessellations, but also the theme of many of his artworks. Escher wants his audience to see and understand the process behind the patterns, and often presents prints with story like transitions from geometric to recognizable tessellations. You can investigate the passage from geometry to art in Metamorphosis Exploration.
@infinitymath
What makes the creation of tessellations a "compelling game" is the interplay between "molding a form" and attempting to recognize a figure in it. We shall see that it is quite difficult to create a tessellation with a preconceived subject or motif, but easy to make interesting looking shapes that, after the fact, can be decorated and enhanced to look like something.
@infinitymath
Several techniques explaining how to create the Escehr like tessellations will be covered in the section Tessellations by Recognizable Figures. As a first step, however, we must learn more about Tessellations by Polygons.
Web address: euler.slu.edu
〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰
📡 @infinitymath
〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰〰
👍1
Forwarded from Deleted Account
طرح های هنرمند، نقاش و معمار هلندی موریس اشر با الهام از مفاهیم ریاضی
نام اثر:
Day and night
روز و شب
📡 @infinitymath
نام اثر:
Day and night
روز و شب
📡 @infinitymath
Forwarded from Deleted Account
طرح های هنرمند، نقاش و معمار هلندی موریس اشر با الهام از مفاهیم ریاضی
نام اثر:
Eight heads
هشت سر
📡 @infinitymath
نام اثر:
Eight heads
هشت سر
📡 @infinitymath
Forwarded from Deleted Account
طرح های هنرمند، نقاش و معمار هلندی موریس اشر با الهام از مفاهیم ریاضی
نام اثر:
Metamorphosi I
دگردیسی 1
📡 @infinitymath
نام اثر:
Metamorphosi I
دگردیسی 1
📡 @infinitymath
Forwarded from Deleted Account
طرح های هنرمند، نقاش و معمار هلندی موریس اشر با الهام از مفاهیم ریاضی
نام اثر:
Metamorphosi II
دگردیسی 2
📡 @infinitymath
نام اثر:
Metamorphosi II
دگردیسی 2
📡 @infinitymath
Forwarded from Deleted Account
طرح های هنرمند، نقاش و معمار هلندی موریس اشر با الهام از مفاهیم ریاضی
نام اثر:
Metamorphosi III
دگردیسی 3
📡 @infinitymath
نام اثر:
Metamorphosi III
دگردیسی 3
📡 @infinitymath
Forwarded from Deleted Account
طرح های هنرمند، نقاش و معمار هلندی موریس اشر با الهام از مفاهیم ریاضی
نام اثر:
Mobius strip
📡 @infinitymath
نام اثر:
Mobius strip
📡 @infinitymath
Forwarded from Deleted Account
طرح های هنرمند، نقاش و معمار هلندی موریس اشر با الهام از مفاهیم ریاضی
نام اثر:
Three world
📡 @infinitymath
نام اثر:
Three world
📡 @infinitymath
Forwarded from Deleted Account
کاشیکاری دایره به روش موریس اشر با الهام از هندسه هذلولوی
نام اثر:
Circle limit
📡 @infinitymath
📡 @infinitymath
نام اثر:
Circle limit
📡 @infinitymath
📡 @infinitymath