The precision of mathematical reasoning,the abstractness of mathematical language,the profundity of mathematical thought and method,as well as the excessive formalization of mathematics teaching have formed an impassa...The precision of mathematical reasoning,the abstractness of mathematical language,the profundity of mathematical thought and method,as well as the excessive formalization of mathematics teaching have formed an impassable gap,hindering students in approaching mathematics.This has concealed the beauty of mathematics and the light of mathematical culture.However,if students are able to cross this gap,they would find that mathematics is a vast world full of vitality,imagination,wisdom,poetry,and beauty.The pursuit of mathematical beauty is one of the motivations for scientists to research this field.Experiencing mathematical beauty is of great significance to students'learning and growth.In teaching,the value of mathematical beauty is explored,such as stimulating emotions,opening up to the truth,and cultivating goodness.Several effective ways are suggested in this article to guide students to discover the mathematical beauty in life while finding it in problem-solving methods and exploring it in knowledge systems.展开更多
Palladio’s design principles,including proportion and harmony,have often been associated with mathematical definitions of beauty.However,the geometric and semantic properties of his fac¸ades have rarely been ana...Palladio’s design principles,including proportion and harmony,have often been associated with mathematical definitions of beauty.However,the geometric and semantic properties of his fac¸ades have rarely been analysed in a holistic manner.There is little evidence of how mathematical beauty may be embodied in his architecture.This research investigates complexity(fractal dimension or D)and diversity(perplexity or PP)as aesthetic indices,aiming to capture distinct characteristics of Palladian architecture.The D and PP values of 22 Palladian villa fac¸ades are measured and analysed,before being compared with those of three Renaissance facades by Sebastiano Serlio.The combination of D and PP captures the geometric and semantic aesthetic qualities of architectural compositions.Importantly,the developed scatter plot of D and PP results supports the identification of four distinct aesthetic types of Palladian fac¸ade designs.The novel combination of D and PP measures contributes to a better understanding of one definition of the mathematical beauty of architecture,wherein“the whole is other than the sum of the parts”in compositional terms(a famous Gestalt principle).Specifically,this research provides new mathematical insights into the visual character of Palladian architecture and compares two important measures thereof.展开更多
基金the 2020 Qilu University of Technology(Shandong Academy of Sciences)Teaching Research Project-Theoretical and Practical Research of Higher Mathematics Curriculum Ideological Politics(2020szzx23).
文摘The precision of mathematical reasoning,the abstractness of mathematical language,the profundity of mathematical thought and method,as well as the excessive formalization of mathematics teaching have formed an impassable gap,hindering students in approaching mathematics.This has concealed the beauty of mathematics and the light of mathematical culture.However,if students are able to cross this gap,they would find that mathematics is a vast world full of vitality,imagination,wisdom,poetry,and beauty.The pursuit of mathematical beauty is one of the motivations for scientists to research this field.Experiencing mathematical beauty is of great significance to students'learning and growth.In teaching,the value of mathematical beauty is explored,such as stimulating emotions,opening up to the truth,and cultivating goodness.Several effective ways are suggested in this article to guide students to discover the mathematical beauty in life while finding it in problem-solving methods and exploring it in knowledge systems.
基金supported by the ARC(DP220101598)UNSW Scientia program.
文摘Palladio’s design principles,including proportion and harmony,have often been associated with mathematical definitions of beauty.However,the geometric and semantic properties of his fac¸ades have rarely been analysed in a holistic manner.There is little evidence of how mathematical beauty may be embodied in his architecture.This research investigates complexity(fractal dimension or D)and diversity(perplexity or PP)as aesthetic indices,aiming to capture distinct characteristics of Palladian architecture.The D and PP values of 22 Palladian villa fac¸ades are measured and analysed,before being compared with those of three Renaissance facades by Sebastiano Serlio.The combination of D and PP captures the geometric and semantic aesthetic qualities of architectural compositions.Importantly,the developed scatter plot of D and PP results supports the identification of four distinct aesthetic types of Palladian fac¸ade designs.The novel combination of D and PP measures contributes to a better understanding of one definition of the mathematical beauty of architecture,wherein“the whole is other than the sum of the parts”in compositional terms(a famous Gestalt principle).Specifically,this research provides new mathematical insights into the visual character of Palladian architecture and compares two important measures thereof.
