Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner

Being a physical science major, it is extremely fascinating to explore the connections between mathematics, science, and art. I know that a lot of modern art has begun to use advanced technology, but I had no idea that even Leonardo DaVinci integrated mathematics into his art. One mathematical term in familiar is very fascinating to me: psi. Psi, also known as the golden ratio, is a number encountered when taking ratios of distances in simple geometric figure. The number turns out to be 1.618034…. At first glance, this would appear to be irrelevant in art, but it can actually be found in architectural masterpieces created in Ancient Greece. The Parthenon is famous for its use of the golden ratio in its construction; even the Greeks knew that the golden ratio was visually pleasing. Another ancient example of the use of the Golden ratio is the Great Pyramid of Giza.

This pyramid was built circa 2560 BC and the length of the base divided by the height is very near the Golden Ratio (1.5717…). Euclid also speaks of the Golden Ratio; Plato dabbled in the area as well. Plato philosophized that if a line were divided into two equal segments so that each would be related to the whole in the same way, then a special proportional relationship would result. Plato, as we know now, was quite correct.
So how, exactly, is the golden ratio derived? It turns out that there are multiple ways to do so. One is the Fibonacci sequence.
Here is a ‘Fibonacci series’.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ..
If we take the ratio of two successive numbers in this series and divide each by the number before it, we will find the following series of numbers.
1/1 = 1

2/1 = 2

3/2 = 1.5

5/3 = 1.6666…

8/5 = 1.6

13/8 = 1.625

21/13 = 1.61538…

34/21 = 1.61904…
The ratio seems to be settling down to a particular value, which we call the golden ratio(Phi=1.618..). (http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html)
The Fibonacci Sequence is even more intimately related to the Golden Ratio: shapes exist such as the Golden Rectangle and the Golden Spiral which combine these two concepts in different ways. The Golden Rectangle is a shape formed using proportions that are two sequential numbers in the Fibonacci Sequence. It has been theorized that this shape is one of the most appealing shapes to the eye. It seems like no large coincidence then that it is precisely this shape that Leonardo DaVinci used in his very famous Mona Lisa.
The Golden Ratio is also found in more modern artwork. The Sacrament of the Last Supper, by Salvadore Dali, is actually painted on a canvas matching the proportions of the Golden Rectangle.

Clearly, the Golden Ratio has stood the test of time. Its usage has spanned centuries upon centuries, and it has been utilized by dozens of artists and architects. Personally, I think this is a part of its appeal. The Golden Ratio and the Fibonacci sequence are found so often, in both math, art, and nature, but both concepts still remain largely a mystery. Why are shapes created by these mathematical concepts so visually pleasing? Did the ancient architects realize the aesthetics of these ratios and implement them on purpose, or was it just a coincidence? Personally, I think there is still a lot to learn about the use of the Golden ratio in history, but the ratio does serve one very important purpose: it shows another way that math and art are intimately connected.

http://www.youtube.com/watch?v=fmaVqkR0ZXg

P.S.–sorry this is late, I didn’t join the class until 3rd week so I had some catching up to do.

43 Responses to “Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner”

  1. modern art says:

    modern art…

    Oil painting is both classic and modern style of art….

  2. gothiphop says:

    gothiphop…

    [...]Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC[...]…

  3. Homepage says:

    … [Trackback] …

    [...] Read More: classes.design.ucla.edu/Winter09/9-1/blog/c/?p=882 [...] …

  4. Sam Davis says:

    There are some interesting time limits on this article but I don’t know if I see all of them middle to heart. There’s some validity however I will take maintain opinion till I look into it further. Good article , thanks and we wish more! Added to F…

    Amazing. Never discovered this has been possible through doing it this specific style. Nevertheless, it’s actually a really refreshing take on stuff! Just what are your thinking on swapping regions around nevertheless?…

  5. TERRENCE says:


    Buy Viagra

    Buy Cheap Generic.Drugs Today!…

  6. click this link to go to their website…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  7. Wow, fantastic blog layout! How long have you been blogging for? you made blogging look easy. The overall look of your site is wonderful, as well as the content!. Thanks For Your article about Taking the GOLD! ….

    Wow, wonderful blog layout! How long have you been blogging for? you made blogging look easy. The overall look of your site is fantastic, let alone the content!. Thanks For Your article about Taking the GOLD! ….

  8. Ready, Set, Go | 6th Sense Solutions I was suggested this web site by my cousin. I am not sure whether this post is written by him as no one else know such detailed about my difficulty. You’re wonderful! Thanks! your article about Ready, Set, Go | 6…

    Very nice style and design and wonderful subject matter, hardly anything else we require : D….

  9. Well Hatched says:

    Hmm is anyone else having problems with the images on this blog loading? I’m trying to determine if its a problem on my end or if it’s the blog. Any responses would be greatly appreciated….

    Hey! I’m at work browsing your blog from my new iphone! Just wanted to say I love reading through your blog and look forward to all your posts! Carry on the fantastic work!…

  10. symptom says:

    An engrossing speech is designer observe. I conceive that you should indite much on this topic, it power not be a sacred matter but generally group are not enough to verbalize on specified topics. To the next. Cheers like your Ready, Set, Go | 6th Se…

    An absorbing communicating is couturier interpret. I cerebrate that you should compose more on this message, it might not be a bias issue but mostly grouping are not sufficiency to communicate on much topics. To the succeeding. Cheers like your Ready, …

  11. I do agree with all the concepts you’ve offered on your post. They’re very convincing and can certainly work. Nonetheless, the posts are very quick for starters. May you please prolong them a little from subsequent time? Thanks for the post….

    Thanks for your post on the traveling industry. I would also like to include that if you are a senior taking into account traveling, it truly is absolutely imperative that you buy travel cover for senior citizens. When traveling, retirees are at bigges…

  12. student jobs says:

    This continually is amazing to me how blog owners such as your self can find some time along with the dedication to keep on producing remarkable content. Your blog isterrific and one of my own have to read websites. I simply want to thank you….

    I loved as much as you’ll receive carried out right here. The sketch is attractive, your authored subject matter stylish. nonetheless, you command get got an nervousness over that you wish be delivering the following. unwell unquestionably come more f…

  13. Online Casinos…

    Online Casino games reviews discussion and more, only at online casino cash net…

  14. Great weblog right here, added to my bookmarks!…

    Howdy! Do you know if they make any plugins to safeguard against hackers? I’m kinda paranoid about losing everything I’ve worked hard on. Any suggestions?…

  15. student jobs says:

    Thanks , I have recently been looking for info about this subject for ages and yours is the best I’ve discovered so far. But, what about the conclusion? Are you sure about the source?…

    The Zune concentrates on being a Portable Media Player. Not a web browser. Not a game machine. Maybe in the future it’ll do even better in those areas, but for now it’s a fantastic way to organize and listen to your music and videos, and is without p…

  16. Free Ipad says:

    Swift Products Of buy ipad - An Introduction…

    An Analysis Of Easy Methods In buy ipad…

  17. Ipad Review says:

    Easy Secrets In buy ipad Around The UK…

    Choosing Convenient Products In buy ipad…

  18. Win Ipad says:

    Simple Products In buy ipad - Where To Go…

    Compared - Straightforward buy ipad Secrets…

  19. Ipad Review says:

    Thinking About Realistic Plans In buy ipad…

    Significant Details In buy ipad Revealed…

  20. phen 375 says:

    phen 375…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  21. Phen375 video…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  22. simply click the up coming internet page…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  23. Visit onlinecasino2013.blogspot.co.uk…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  24. Blogspot.com says:

    Blogspot.com…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  25. Christa says:

    Christa…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  26. casino online spielen kostenlos…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  27. Recommended Internet site…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  28. casino online for real money…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  29. Francisca says:

    Francisca…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  30. Highly recommended Reading…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  31. visit the up coming internet site…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  32. Immediate Loans For individuals on Advantages - Pay back On Time and steer clear of Of Additional Rates of interest…

    Pay Day Loans Immediate Lender Guidance - Get the best Direct Payday Lenders…

  33. click here says:

    online payday loan…

    payday loans online…

  34. payday loans…

    internet payday loans…

  35. quick payday loans…

    pay day loan online…

  36. Inexpensive Loans United kingdom: Instant Cash Without Any Individual Pledging…

    Run after Bank Mortgage loan Modification with regard to Chase Clients…

  37. animal insurance…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  38. payday loans online payday loans online payday loans online payday loans online payday loans online payday loans online payday loans online payday loans online payday loans online payday loans online…

    payday loans online payday loans online payday loans online payday loans online payday loans online payday loans online payday loans online payday loans online payday loans online payday loans online…

  39. Bad Bank loan Quick Payday advances…

    Get yourself a Loan nowadays: Common Blunders and How to Prevent them…

  40. blackjackonlinecasinos.co.uk…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…

  41. ppi claims says:

    ppi claim…

    click here…

  42. phen375 review…

    Week 2: The Golden Ratio’s Place in Art, by Sarah Lechner « DESMA9_sectionC…