Misconceptions about the Golden Ratio

Markowsky, George

doi:10.1080/07468342.1992.11973428

Cited by 84 publications

(73 citation statements)

References 7 publications

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“…[26][27][28] Ne verthe less, the re are many stu di es that con tra dict the re se arch abo ut the gol den ra ti o and Fi bo nac ci se quen ce. 29 Du ring a re vi ew of the li te ra tu re, we ca me across many stu di es on the lengths of hand bo nes, rati os among the fin gers and the fac tors af fec ting the se ra ti os. We we re ab le to find two ar tic les in which the Fi bo nac ci se qu en ce and the gol den ra tio of the length of fin gers we re dis cus sed.…”

Section: Discussionmentioning

confidence: 99%

Radiological Analysis of Human Hand in Terms of Artistic Anatomy

Yılmaz¹,

Alıcıoğlu²,

Süt³

et al. 2010

Turkiye Klinikleri J Med Sci

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Section: Discussionmentioning

confidence: 99%

Radiological Analysis of Human Hand in Terms of Artistic Anatomy

Yılmaz¹,

Alıcıoğlu²,

Süt³

et al. 2010

Turkiye Klinikleri J Med Sci

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“…On the other hand, Kajander and Lovric [31] found that reader-friendly language, incorrect generalizations, oversimplifications, illustrations and diagrams in mathematics textbooks may lead to misconceptions. Likewise, Markowsky [32] investigated that many high school geometry textbooks consisted of incorrect statements about the golden ratio. Similarly, Luneta [33] claimed that even though there are two squares in Figure 1, many students would only classify the shape on the right as a square because the shape on the left is the prototype of a rhombus in mathematics textbooks.…”

Section: The Potential Role Of Mathematics Textbooks In Supporting MImentioning

confidence: 99%

Exploring high-achieving sixth grade students’ erroneous answers and misconceptions on the angle concept

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Filiz

2016

International Journal of Mathematical Education in Science and

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The aim of this research was to investigate high achievers' erroneous answers and misconceptions on the angle concept. The participants consisted of 233 grade 6 students drawn from eight classes in two well-established elementary schools of Trabzon, Turkey. All participants were considered to be current achievers in mathematics, graded 4 or 5 out of 5, and selected via a purposive sampling method. Data were collected through six questions reflecting the learning competencies set out in the grade 6 curriculum in Turkey and the findings of previous studies that aimed to identify students' misconceptions of the angle concept. This questionnaire was then applied over a 40 minute period in each class. The findings were analyzed by two researchers whose inter-rater agreement was computed as 0.97, or almost perfect. Thereafter, coding discrepancies were resolved, and consensus was established. We found that although the participants in this study were high achievers, they still held several misconceptions on the angle concept such as recognizing a straight angle or a right angle in different orientations. We also show how some of these misconceptions could have arisen due to the definitions or representations used in the textbook, and offer suggestions concerning their content in the future.

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“…Indeed, it is easy to find art examples that match e.g. the golden ratio, but such an example does not in itself constitute proof of the concept (Gardner 1952), and many claims about golden ratios found in art has also been refuted (Markowsky 1992). Still, art is being made with proportions of which many found some more beautiful than others.…”

Section: Introductionmentioning

confidence: 99%

Large-Scale Analysis of Art Proportions

Jensen

2015

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Abstract. While literature often tries to impute mathematical constants into art, this large-scale study (11 databases of paintings and photos, around 200.000 items) shows a different truth. The analysis, consisting of the width/height proportions, shows a value of rarely if ever one (square) and with majority of images having a proportion larger than one, but less than e.g. the golden ratio. Furthermore, more images have the inversed proportion, meaning that portrait paintings are more common than landscape paintings. The inverse is true for photographs, i.e. more landscape than portrait format photographs has been found in the databases.

show abstract

Misconceptions about the Golden Ratio

Cited by 84 publications

References 7 publications

Radiological Analysis of Human Hand in Terms of Artistic Anatomy

Radiological Analysis of Human Hand in Terms of Artistic Anatomy

Exploring high-achieving sixth grade students’ erroneous answers and misconceptions on the angle concept

Large-Scale Analysis of Art Proportions

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