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History of Science and Engineering

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THE DEVELOPMENT OF METHODS CONSTRUCTIONS MAGIC KONFIGURATIONS
А.Е. Malykh

The article contains historical mathematical analysis of the valuable contribution of scholars in creation of studies about magic figures (circles, polygons, crosses, stars and so on). Many famous and unknown scientists from different times and nationalities are fulfilled their investigations in this direction. Material of paper contains a sketch about early methods of constructions and then – short survey of further development this object of study. Origin of these figures was ancients China and India. Then knowledge little by little penetrated in other countries. They not only adopted methods of construction, but enriched, developed them: new magic figures were constructed, their structure learned; properties came to light and different applications were discovered.
Gradually three types of magic squares were distinguished. Methods of construction them were different. Moreover such squares had own structure: perfect, composite, bordered, simples and so on. Each of theirs had also own methods of receiving. Magic squares constructed not only from n2 successive natural numbers, but from odd, even, simple, polygonal numbers, successive natural degrees of numbers and others.
Scientific legacy of scholars also is shown in article. Among them were mathematicians of China, India, countries of Islam, medieval Western Europe, Japan. A process of formation studies about magic constructions is including period from ancient sources up to beginning of XVIII century.
Key words: magic figures (circles, polygons, crosses, stars); magic squares (perfect, combined, bordered and others); types, composi-tions; construction.


Contacts: E-mail: malych@pspu.ru

Pp. 03-13.

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