Lesson Six – The Golden Ratio in Art and Corporate Logos
The first act of this lesson has the whole class examining works of art for examples of the Golden Ratio in use. The focus then changes to modern corporate logos. Several of these are studied and seen to demonstrate the purposeful use of the Golden Ratio. The attached PowerPoint file may be used to facilitate this part of the lesson. In it, two famous artworks (the Mona Lisa by Da Vinci and Drunkenness of Noah by Michelangelo) and four logos are presented. Teachers may add other pieces to this presentation or use other means and images altogether. The prompt at the end of the presentation signals the beginning of the main action of the lesson. Students are instructed to investigate other modern logos for usage of the Divine Proportion. Intrinsic aesthetic appeal should be the main factor used to select logos for investigation. This follows the working theory that images that use the Golden Ratio are more aesthetically appealing. If this is true, it should follow that the logos that impact the students the most should contain some manifestation of the Golden Ratio. |
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Students will need access to technology for this purpose. Although traditional tools (e.g., rulers, pencils, etc.) are perfectly suitable for finding golden relationships, many barriers may prevent students from being able to print found images onto paper. For this reason, students should have access to and previous training in programs that allow for measurement and calculation on the screen (for example, Geometer’s Sketchpad, Geogebra, etc.).
The lesson should finish with a whole-class discussion about the students’ findings. It is important to highlight logos in which the Divine Proportion was found as well as images in which it was suspected but is ultimately absent. Pieces from this latter group add an interesting element to the ongoing discussion: If the Golden Ratio is as compelling as we have been told, then why are we attracted to these images that do not appear to follow it? Is our theory flawed, or have we missed something?
Interesting debates may develop if multiple groups of students investigate the same logo but come up with different results. This provides opportunities for students to use mathematical understanding to defend their positions on art.
The lesson should finish with a whole-class discussion about the students’ findings. It is important to highlight logos in which the Divine Proportion was found as well as images in which it was suspected but is ultimately absent. Pieces from this latter group add an interesting element to the ongoing discussion: If the Golden Ratio is as compelling as we have been told, then why are we attracted to these images that do not appear to follow it? Is our theory flawed, or have we missed something?
Interesting debates may develop if multiple groups of students investigate the same logo but come up with different results. This provides opportunities for students to use mathematical understanding to defend their positions on art.
References
Buonarroti, M. (circa 1508-12). Drunkenness of Noah [Electronic image). Retrieved from http://www.michelangelo-gallery.com/the-drunkenness-of-noah.aspx
Da Vinci, L. (circa 1503-06). Mona Lisa [Electronic image]. Retrieved from https://en.wikipedia.org/wiki/Mona_Lisa
Hart, G. (2015, March 27). Mathematical impressions: The golden ratio. [Video File]. Retrieved from
https://www.simonsfoundation.org/multimedia/mathematical-impressions-multimedia/
mathematical-impressions-the-golden-ratio/
Meisner, G. (2014). Da Vinci and the divine proportion in art composition. Retrieved from https://www.goldennumber.net/leonardo-da-vinci-golden-ratio-art/
Meisner, G. (2016). Michelangelo and the art of the golden ratio in art and composition.
Retrieved from https://www.goldennumber.net/michelangelo-sistine-chapel-golden-ratio-art-design/
Buonarroti, M. (circa 1508-12). Drunkenness of Noah [Electronic image). Retrieved from http://www.michelangelo-gallery.com/the-drunkenness-of-noah.aspx
Da Vinci, L. (circa 1503-06). Mona Lisa [Electronic image]. Retrieved from https://en.wikipedia.org/wiki/Mona_Lisa
Hart, G. (2015, March 27). Mathematical impressions: The golden ratio. [Video File]. Retrieved from
https://www.simonsfoundation.org/multimedia/mathematical-impressions-multimedia/
mathematical-impressions-the-golden-ratio/
Meisner, G. (2014). Da Vinci and the divine proportion in art composition. Retrieved from https://www.goldennumber.net/leonardo-da-vinci-golden-ratio-art/
Meisner, G. (2016). Michelangelo and the art of the golden ratio in art and composition.
Retrieved from https://www.goldennumber.net/michelangelo-sistine-chapel-golden-ratio-art-design/