Institute for the History of Science

Geometrical/ artful patterns are valuable in visualization and understanding geometrical/ mathematical concepts. In this paper, I explain some patterns and methods of dividing and composing squares, based on Abu'l- Wafa Buzdjani's book (4th Hejira/ AD 10th century). In addition, I applied activities as a workshop format in high school geometry classroom. Participants were 14 students grade 11 at a High school in Isfahan.  They cut and assembled squares by scissor and painted them. Then they found some applied patterns in geometrical based tiling in Islamic constructions in Isfahan. Finally, they presented their works in power point format to others. Notation to such patterns and arts helped them to better understanding geometrical concepts such as rotation, symmetry, reflection, transformation, mapping, translation and dilation.

In this paper has illustrated some word problems. These problems are valuable from three view: 1- riddle representation of these problems is very attractive for students; 2- since these problems gathered from source belongs to 5th, 6th Hegira century, we can review historical culture and math history in Iran; 3- Educationally, students learn translate the word problems to math symbols and apply appropriate methods to solve them.

This Persian manuscript was compiled in the 6th Hejira (AD 12th century) by Ali ibn Yusuf ibn Ali Munshi. The book contains 274 pages and is held in the central library of Teheran University. It is written in Persian but has never been translated into modern Persian. The following is a summary of its contents

The history of Islamic geometry is interwoven with the history and cultural traditions of the regions in which it flourished. There is a rich variety of distinctive and different styles.  Many designs reappear over the ages in different parts of the world.

Dividing a right angle into five equal angles only with a straightedge and a compass used to construct a particular tiling patterns in Islamic arts which one of those patterns presented at figure1 (10 petal rose construction). The methods and ideas which I explain in this paper has obtained from Iranian math history . All figures have been created by the author using the Geometer's Sketchpad (GSP) software program. These samples has applied at Isfahan Math House as workshops for teaching math history to secondary students and math teachers.

‫علم‬ ‫تاریخ‬ ‫دورۀ‬ ، 18 ‫شمارۀ‬ ، 2 ‫زمستان‬ ‫و‬ ‫پاییز‬ ، 1399 ‫ص‬ ، 447-485 ‫بارۀ‬ ‫در‬ ‫شمارۀ‬ ‫خطی‬ ‫مجموعۀ‬ ‫از‬ ‫فارسی‬ ‫هندسی‬ ‫رسالۀ‬ ‫سه‬ 772 ‫پاریس‬ ‫ملی‬ ‫کتابخانۀ‬ ‫عصارزادگان‬ ‫نرگس‬ ‫تهران‬ ‫دانشگاه‬ ‫علم‬ ‫تاریخ‬ ‫پژوهشکدۀ‬ ‫علم،‬ ‫تاریخ‬ ‫ارشد‬ ‫کارشناس‬ [email protected] ‫امینی‬ ‫حسن‬ ‫٭‬ ‫علم)‬ ‫تاریخ‬ ‫(پژوهشکدۀ‬ ‫اسالمی‬ ‫ملل‬ ‫تمدن‬ ‫و‬ ‫تاریخ‬ ‫گروه‬ ‫استادیار،‬ ‫تهران‬ ‫دانشگاه‬ ‫اسالمی،‬ ‫معارف‬ ‫و‬ ‫الهیات‬ ‫دانشکدۀ‬ [email protected] ‫(دریافت:‬ 27 / 09 / 1399 ‫پذیرش:‬ ، 24 / 12 / 1399) ‫چکیده‬ ‫شمارۀ‬ ‫خطی‬ ‫نسخه‬ ‫مجموعٔە‬ 772 ‫رساله‬ ‫حاوی‬ ‫پاریس‬ ‫ملی‬ ‫کتابخانٔە‬ ‫متعدد‬ ‫های‬ ‫رساله‬ ‫میان‬ ‫از‬ ‫برخوردارند.‬ ‫خاصی‬ ‫ارزش‬ ‫از‬ ‫کدام‬ ‫هر‬ ‫که‬ ‫است‬ ‫علمی‬ ‫این‬ ‫های‬ ‫رسالٔە‬ ‫فارسی‬ ‫ترجمٔە‬ ‫مجموعه،‬ ‫العمال‬ ‫من‬ ‫الصناع‬ ‫الیها‬ ‫مایحتاج‬ ‫الهندسیة‬ ‫یا‬ ‫النجارة‬ ‫کتاب‬ ‫و‬ ‫بوزجانی‬ ‫از‬ ‫والمتوافقة‬ ‫المتشابهة‬ ‫الشکال‬ ‫تداخل‬ ‫فی‬ ‫رسالٔە‬ ‫ا‬ ‫ز‬ ‫بوده‬ ‫اسالمی‬ ‫دورۀ‬ ‫علم‬ ‫تاریخ‬ ‫پژوهشگران‬ ‫توجه‬ ‫مورد‬ ‫ناشناخته،‬ ‫مؤلفی‬ ‫اند.‬ ‫به‬ ‫می‬ ‫نظر‬ ‫رساله‬ ‫تمامی‬ ‫رسد‬ ّ ‫عبدالل‬ ‫بن‬ ‫ابواسحاق‬ ‫کتابت‬ ‫به‬ ‫مجموعه‬ ‫این‬ ‫های‬ ‫ه‬ ‫ترجمه‬ ‫نیز‬ ‫برخی‬ ‫و‬ ‫یزدی‬ ‫کوبنانی‬ ‫کوبنانی‬ ‫آثار‬ ‫به‬ ‫توجه‬ ‫با‬ ‫باشد.‬ ‫او‬ ‫تألیف‬ ‫یا‬ ‫سال‬ ‫بین‬ ‫او‬ ‫علمی‬ ‫فعالیت‬ ‫تاریخ‬ ‫های‬ 845 ‫تا‬ 886 ‫زده‬ ‫تخمین‬ ‫قمری‬ ‫هجری‬ ‫می‬ ‫وجود‬ ‫مجموعه‬ ‫این‬ ‫شدن‬ ‫نوشته‬ ‫زمان‬ ‫بارۀ‬ ‫در‬ ‫متعددی‬ ‫آراء‬ ‫حال‬ ‫این‬ ‫با‬ ‫شود،‬ ‫آن‬ ‫به‬ ‫مقاله‬ ‫در‬ ‫که‬ ‫دارد‬ ‫رساله‬ ‫اهمیت‬ ‫است.‬ ‫شده‬ ‫اشاره‬ ‫ها‬ ‫این‬ ‫ریاضی‬ ‫های‬ ‫ای‬ ‫از‬ ‫مجموعه‬ ‫یا‬ ‫شده‬ ‫تألیف‬ ‫فارسی‬ ‫ریاضی‬ ‫رساالت‬ ‫از‬ ‫گزارشی‬ ‫که‬ ‫است‬ ‫نظر‬ ‫ن‬ ‫می‬ ‫دست‬ ‫به‬ ‫دوران‬ ‫آن‬ ‫تا‬ ‫عربی‬ ‫از‬ ‫شده‬ ‫ترجمه‬ ‫سه‬ ‫محتوای‬ ‫رو‬ ‫پیش‬ ‫مقالٔە‬ ‫در‬ ‫دهد.‬ ‫می‬ ‫بررسی‬ ‫مجموعه‬ ‫این‬ ‫از‬ ‫فارسی‬ ‫هندسی‬ ‫رسالٔە‬ ‫تاریخ‬ ‫مطالعٔە‬ ‫لحاظ‬ ‫از‬ ‫که‬ ‫شود‬ ‫رساله‬ ‫موضو‬ ‫با‬ ‫متوالی‬ ‫رسالٔە‬ ‫سه‬ ‫دارد.‬ ‫اهمیت‬ ‫فارسی‬ ‫هندسی‬ ‫های‬ ‫در‬ ‫هندسه‬ ‫ع‬ ‫گونه‬ ‫به‬ ‫آنها‬ ‫نگارش‬ ‫نحوۀ‬ ‫که‬ ‫دارد‬ ‫وجود‬ ‫مجموعه‬ ‫این‬ ‫نظر‬ ‫به‬ ‫مستقل‬ ‫که‬ ‫است‬ ‫ای‬ ‫می‬ ‫عنوان‬ ‫فاقد‬ ‫پیاپی‬ ‫رسالٔە‬ ‫سه‬ ‫این‬ ‫رسند.‬ ‫معرفی‬ ‫عناوین‬ ‫این‬ ‫با‬ ‫مقاله‬ ‫این‬ ‫در‬ ‫و‬ ‫اند‬ ‫می‬ ‫(برگ‬ ‫مساحت‬ ‫علم‬ ‫در‬ ‫مختصر‬ ‫شوند:‬ ‫های‬ 65 ‫پ‬-69 ‫مساحت‬ ‫کتاب‬ ‫پ)؛‬ ‫(برگ‬ ‫های‬ 70 ‫پ‬-89 ‫اه‬ ‫اصالح‬ ‫در‬ ‫رساله‬ ‫پ)؛‬ ‫(برگ‬ ‫مساحت‬ ‫ل‬ ‫های‬ 90 ‫پ‬-100 ‫عنوان‬ ‫با‬ ‫اول‬ ‫رسالٔە‬ ‫َح‬ ‫َح‬ ‫مص‬ ‫متن‬ ‫ر).‬ « ‫مساحت‬ ‫در‬ ‫مختصر‬ » ‫است‬ ‫شده‬ ‫ارائه‬ ‫دشواری‬ ‫و‬ ‫اصل‬ ‫کردن‬ ‫پیدا‬ ‫برای‬ ‫نویسندگان‬ ‫تالش‬ ‫است.‬ ‫شده‬ ‫بیان‬ ‫او‬ ‫ریاضی‬ ‫های‬

Geometrical/ artful patterns are valuable in visualization and understanding geometrical/ mathematicalconcepts. In this article, I explain some patterns and methods of dividing and composing squares, based on Abu'l-Wafa Buzdjani's book (4 th Hejira/ AD 10 th century). In addition, I applied activities as a workshop format in high school geometry classroom. Participants were 14 students grade 11 at a High school in Isfahan. They cut and assembled squares by scissor and painted them. Then they found some applied patterns in geometrical based tiling in Islamic constructions in Isfahan. Finally, they presented their works in power point format to others. Notation to such patterns and arts helped them to better understanding geometrical concepts such as rotation, symmetry, reflection, transformation, mapping, translation and dilation.

Activities concerning history of mathematics have been a part of ICMEs since ICME2 in Exeter in 1972. They are now regular features of ICMEs, organized by the HPM (International Study Group on Relations between History and Pedagogy of Mathematics). The premise of this discussion group was that research on history of mathematics in education tends to have older pupils and students in mind, and that there is a lack of both research and resources on how to include a historical perspective when teaching younger pupils. Three key questions were pointed out in the invitation to the discussion group: Organizers Co-chairs: Bjørn Smestad (Norway), Funda Gonulates (USA)

مطالعۀ تاریخ علم نشانگر راه و روش کاشفان علم و عناصر مؤثر در توفیق یا ناکامی دانشمندان
است. انتظار می رود در کتاب های درسی به عنوان سند مکتوب فرهنگ جامعه که در اختیار
دانش آموزان قرار می گیرد، به روندهای تکامل و کشف موضوعات علمی اشاره شود. مطالعۀ
تاریخ ریاضیات به ویژه، می تواند نقش به سزایی در بهبود کیفیت آموزش ریاضی داشته باشد.
در این نوشته، حاشیه های افزوده شده به متن کتاب های درسی ریاضی نونگاشت با عنوان
»خواندنی،« شامل اشاره های تاریخی، مورد بررسی انتقادی قرار گرفته و شماری از اشتباهات
مشهود در این بخش ها، مطرح و پیشنهادهایی برای اصلاح آنها ارائه شده است

Qāsim ʿAlī Qāʾinī is an Iranian astronomer and mathematician (?-alive in 1099 AH). His works have been left behind. A number of his treatises have been listed under the name of Astrolabe, which has completely different contents. In this article, while introducing a number of his works that are listed in the lists and the new works that were found, the differences and distinctions of the treatises that are recorded in the lists with the name of Astrolabe are stated. Qāʾinī was one of the students of Mullā Muḥammad Ḥusayn, the son of Mullā Muḥammad Bāqir Yazdī, and he learned the science of astrolabe from him. Qāʾinī was living in the reign of Shāh Sulaymān, the 8 th king of the Safavid dynasty, and was alive in 1099 AH.

An enameled ceramic qibla-finder bowl exists in Damascus museum (cover page of 4th issue of Miras-e Elmi). Magnetic needle could float on the water in the bowl and establish cardinal directions. The circular table drawn in the bowl gives the deviation of the direction of qibla in 40 localities. The localities are in the eastern part of the Muslim world, from Syria to India including some holy places specifically for Shiites. The information is provided by Abjad letters and there is some confusion in the information given in the list. For example, the qibla deviation of Mashhad is written 45  ̊E, while its true value is 54  ̊W. According to the inscription on its center, it was made in Damascus by a certain Seyed Thābit. On the outer edge, inscription indicates: “made for the king, the winner, the victorious, the just, Khāqān, son of Khāqān, king of the two lands and two seas and servant of the two noble sanctuaries, Sultan
Selim, may God perpetuate his reign; amen!”. This refers to the Ottoman Sultan Selim who reigned in Syria from 1516 to 1520 AD.