Return to my Most Pleasing Rectangle Web Poll
Go to my home page
dimensions in pixels: 27x33, 28x35, 28x37, 28x39, 28x41, 28x45, 28x49, 28x55
Most pleasing rectangle: 1 (843) 7% 2 (423) 4% 3 (1310) 12% 4 (2302) 20% 5 (2784) 24% 6 golden rectangle (2101) 18% 7 (801) 7% 8 (806) 7% total (11370) 99%
Above is the WWW's most pleasing histogram. If you just chose a rectangle, your choice has been sent to me by email, and I will be updating the graph in a day or so. Please be patient. Over the months, several people submitted without choosing a rectangle; those have been ignored. Today, six fives were obviously from the same person, seconds apart, and I ignored five of them.
Rectangle #6 is the golden rectangle (1x1.61803...), discovered by the ancient Greeks, and thought to be especially pleasing. Down through the ages, aesthetics, the philosophical study of what is pleasing, has been divided between two competing views. The first is that certain things have intrinsic beauty (such as the golden rectangle). The second is that beauty is in the eye of the beholder, that it is personal or is culturally determined. As a pragmatic person, I believe that the truth is somewhere in between, that the golden rectangle is indeed pleasing on some basic level, but I prefer other rectangles. I guess the whole idea of this poll is to gain some insight into the idea of basic beauty vs. personal beauty.
Another thought, rectangle #1 is very nearly a square (maybe moreso on your screen, if it is out of adjustment). And we see that it is somewhat more popular than rectangle #2. A square would suggest a different kind of perfection, from a perfect golden rectangle. If we had actually drawn a square above, I suspect that it would be even more popular.
A few people seem to have the need to change their votes, once they see which one is the golden rectangle, the "theoretically" ideal choice. There is no correct choice. We did not ask you to guess which one is the golden rectangle; we asked which rectangle looked most pleasing to you. And thank you for your honest answer.
Previous comments (the dates are mm/dd/yy):
- 06/16/05 - [Jim: I neglected to upload these results for about eight months, sorry about that]
- 06/15/05 - Jim, try moving the golden rectangle to a new position, or change display to avoid symmetry bias.4 and 5 are the middle positions. Perhaps some sort of symmetry aspect has biased results.
- 06/01/05 - I would be curious to see if the results were different if there was no background image behind the rectangles. I'm sure you are aware of the illusions that a background can create.
- 05/28/05 - Maybe if the set is not graduated from small to large the result would be different.
- 05/25/05 - It would be better if the rectangles were not shown together or in increasing order. I found my eye going towards the centre without reference to the attractiveness of the rectangle. BTW I knew about the golden ratio.
- 05/20/05 - I chose #7 but had clicked on #6 then changed my vote as I thought that 7 looked maybe prettier...I was quite undecided though between the two. Interesting.
- 05/10/05 - My favorite rectangle is the black one!! Thanks for entertaining my Math-overloaded brain!
- 05/07/05 - I chose number one because I thought it was a square, but after finding out it wasn't I feel betrayed...
- 05/03/05 - I think golden rectangle is really attractive but i yet believe the true meaning of rectangle. So, i wo'nt take much of my attraction to golden rectangles.
- 04/30/05 - The answer may differ between poll no1 and poll no 2. Have you tried to correllate these? For instance how many people do not choose the same rectangle? Will this corrlelate with the number of the rectangle (are you more likely to chose a different one when it is nearly square?)
- 04/14/05 - I think many people may have chosen 4 or 5 because they are in the middle. They look perfect because they aren't small or large
- 04/10/05 - I to have dificulty to choose between 5 and 6 somhow I choose 5 suprisingly when I clik on the result to see majority voter they also see number 5 as the most plesent rectangle Hm.
- 04/02/05 - I picked rect 8 then rect 7 I feel dirty.....ImmutableDark
- 03/26/05 - Whoa! This site IS gay!
- 03/22/05 - "If you arranged them randomly, it would be more scientific. People may have tendancy to exclude the extremes." < I agree with her>
- 03/22/05 - Wow neat idea
- 02/19/05 - Now I just need to get my saw and ill take care of this ugly front door who is a little bit too much 8 and not enough 6...
- 02/19/05 - I feel safe with the golden rectangle, I can recognize him many times
- 02/17/05 - Omar: I belive most people tends to guess which is the golden rectangle
- 02/15/05 - maybe i liked the tall thin rectangle because I aspire to be taller and thinner. Fat chance of that becoming reality! I don't think the rectangles should be presented individually as one might easily forget which one was best, as they are all so similar. sheela
- 01/28/05 - Hey Mr Loy, great site! I wonder, based on the results of your two polls, do you think the ancient greeks looked at their rectangles a certain way? It has been established that the golden rectangle has certain dimensions but it was only identified by the polls in poll 2... this leads me to think that the Ancient Greeks looked at their rectangles horizontally. This would make sense architecturally, as it would have been much easier in that age to construct a beautful rectangular structure horizontally as opposed to vertically. That said, perhaps our society finds beauty in vertical rectangles? I suppose it would be easy enough to test by showing polls a vertical and a horizontal rectangle and asking, which one is prettier? With that result one could go on to conclude, with some doubt mind you, that the preference for rectangles has changed.
- 01/12/05 - I chose #4. I was drawn to the middle, though. I tried to mentally isolate each because of the optical illusions resulting when ANY shape is placed near ANY other shape. I don't think the use of TV, paper, or other common media rectangles has any effect. These are only borders around the true objects of our attention. When I watch TV or read a book or credit card I don't notice the border. But when I look at a TV, book, or credit card (without watching or reading it) I may prefer a certain shape.
- 01/04/05 - Interestingly, I chose 6 for both orientations. Now, I must confess that I do know what the "Golden Rectangle" is, but I can't say that I would recognize it visually. There is one thing that you have not discussed (and I didn't see it below, although I didn't read all carefully): how these rectangles appear to the various observers in the experiment may differ! In fact, the actual ration of the two side lengths will depend on factors such as the aspect ration of the monitor, as well as the aspect ration of the resolution. Thus, if I put my monitor on 1280x960 resolution, they will appear differently than on 1280x1024, and they will appear differently depending on how I adjust my horizontal and vertical sizes for each resolution as well. And lastly, a triangle with a fixed "pixel" ratio of side lengths may appear at different actual side length ratios depending on it's orientation. That is to say, if the number of pixels per actual inch vertically is different from the number of pixels per inch horizontally, then a given rectangle will be rendered at different actual ratios depending on its orientation. Though I am sure you know this, you might point it out to your readers.
- 01/01/05 - the rectangles are too close together to appreciate their differences
- 12/21/04 - It appears the golden rectangle is not so "golden" when presented vertically.
- 12/15/04 - i still don't see what's pleasing about a stupid rectangle, it's just a stupid shape that we use in geometry class, what is the pleasance?
- 12/14/04 - What is wrong with all you people?!? are all of you on crack?? you guys are [deleted] stupid!
- 12/13/04 - I actually find number 3 from the first poll more attractive than the golden rectangle, figure that sincerly, Swenson
- 12/09/04 - BBB: Jim and I have the same preference on both polls! (determined by the last entry on 04/30/04)
- 12/08/04 - i took both polls, it seems the way the rectangles are displayed also play a roll in choice. maybe they should be in a random order not size order
- 12/05/04 - I'm supposed to be researching the Golden Rectangle for art class, so why am I here taking this poll? To tell you the truth, none look more pleasing then the other to me.
- 11/23/04 - the first rectangle looked like those rice sashimi rolled and convered in .. seaweed? now, i am hungry.
- 10/15/04 - [Jim: I neglected to upload these results for about three months, sorry about that]
- 10/12/04 - I like number seven because it is most anthropomorphically proportioned...or so it seems to me. Awesome idea, by the way. Thanks! 8}
- 09/30/04 - I had great difficulty choosing between #3 and #5, ultimately going with the majority (i.e. #5).... Do many people report having a difficult time deciding?
- 09/20/04 - The golden one rokzzzzzz
- 09/10/04 - I liked 8 but was surprised to find that when on their sides I preferred 7 as then 8 looked somehow to long. And hey, Jim. I miss that hieroglyph stuff MK
- 09/02/04 - Interesting. I've done this experiment many times with my statistics classes as a one sample t test. The results ususlly are significantly lower than the golden ratio. Some students have suggested that A4 paper 1.4 or TV screens 1.25 are influencing our judgment.
- 08/17/04 - Two of us Hugh and Cindy separately prefer 4. 08/17/2004 Very interesting as we were discussing the rare use of the golden triangle
- 08/13/04 - I think you need to present the rectangles to people one at a time. They are in relationship to one another and therefore affect preferences. Try using a flash card, where the image is central and the rectangles are shown in random order. The viewer clicks on the one they prefer. No numbers & no relationship to another rectangle would give you a less bias result. You must be having fun with this?
- 08/09/04 - Hany: Rectangle 6 is really beautiful, and when i choose it, i had no doubt about it that i really like it. But I am surprised that's a known fact that this rectangle/ratio is beautiful!! And Thank you for your great website btw ;)
- 07/29/04 - I thought 6 was pleasing, and was amused to find it was actually the 'golden' one. Though it's actually black, of course... a colour that reminds me of the darkness that occasionally envelops my soul. Hmm, now that I notice it the rectangles... they all are black! Cold, sunless, endless black! BLACK! Aaaaaaa
- 07/22/04 - It would be interesting to find out the percentages broken down by sex.
- 06/14/04 - neat page man, thanks. doing reasearch for a bookcase I'm
- 06/11/04 - I couldn't decide between 4 & 5. I found 4 has a ratio of root 2, and seems like a more balanced rectangle to me.
- 06/10/04 - Fascinating that the golden rectangle is not the most pleasing to the eye. Could it be that the polled population could have a different opinion from the "norm"?
- 05/28/04 - You are sort of wierd, but I enjoy your webpage
- 05/25/04 - Number 6 is, quite clearly, exceptionally sexy.
- 05/17/04 - BTW you might have influenced the results by placing the rectangles in order. May be people naturally vote for the middle ones? You should have chosen a different strategy - may be presenting the users with randomly selected 6 rectangles in random order.
- 05/14/04 - AHH RECTANGLE 1 MAKES ME WANT TO THROW UP FOR SOME REASON, WHILE 3 AND 6 MAKE ME FEEL ORGANIZED. WOAH [Jim: By the way, typing all caps is known as "shouting"]
- 05/10/04 - All I know is that the first one is quite possible the ugliest rectangle I have ever seen. Yes, you should do a poll on the ugliest rectangle and I think that one would win.
- 04/30/04 - Jim, which rectangle is most pleasing to you? [Jim: 7 in this poll, and 8 in poll #2]
- 04/30/04 - Jim im disappointed number seven should be the golden rectangle. I just got jiped!
- 04/30/04 - Jim, I wish I would have picked the golden rectangle.
- 04/30/04 - this really [deleted].....people have no life...you have no life...if you have any comment [deleted] and contact [email address deleted]
- 04/27/04 - I liked the seventh triangle just because.
- 04/27/04 - I liked the first rectangle because it is almost square and that is more even and visually pleasing to my eye.
- 04/26/04 - 6 rules
- 04/24/04 - I think that one rectangle's votes will stabalized over time to represent roughtly 8.723%, making the bar chart rendering (above) a golden rectangle, regardless of if it was, itself, golden.
- 04/09/04 - I wasn't trying to pick "The Golden" rectangle. I was only picking out the rectangle that was most pleasing to me. I missed by a mile by picking number 8.
- 04/09/04 - I wonder the effect of displaying the rectangles randomly side-by-side rather than the progression short to tall they are in your exhibit.
- 04/08/04 - i like the skirt joke hahaha
- 04/02/04 - This is ****ing retarded, you're all losers that need lives. [Jim: my censoring]
- 03/30/04 - Hi, I'm Deryck from Hong Kong, aged 13. When I saw that 8 rectangles, I thought I chose a special rectangle which was extraodinary... But when I revealed the results---- oh my god, that 'strange thing' that I chose was the golden rectangle!!!! Jim, I GIVE UP!!!
- 03/28/04 - as an artist in iron, I have often referred to the 'golden mean.' However, it often runs into other architectureal concerns and most often into building codes (read insurance company demands).
- 03/27/04 - If you look back over the time trend of the results of your poll is there a shift as more people move to wide screen TV? [Jim: I don't know]
- 03/26/04 - [Jim's comment: I don't think we tend to judge the dimensions of a computer monitor, a TV screen, a picture frame, a movie screen, or a piece of paper as pleasing or not; it is the artwork (rectangular or otherwise) on those rectangles that we judge]
- 03/26/04 - [Jim's comment: The question is, "Which is the most pleasing rectangle?" How is it possible to answer that without comparing them side by side? Looking at one rectangle at a time will not answer the question, they must be side by side. Don't you think?]
- 03/22/04 - great fun. wouldnt it be convenient to add a program or a way to automatically adjust the dimensions of a perfect square in my monitor to the ideal perfect square? i think its a valid question. [Jim's comment: I'll work on that]
- 03/17/04 - funny. after doing a graphical layout for a flyer (in the proportions of the golden rectangle) half of the night i stumbled across this poll and instantly chose the sixth shape. seems it's kinda stuck in me head.
- 03/17/04 - Never heard of the golden rectangle until now, but I picked it. PROOF that the ancient Greeks were RIGHT!
- 03/16/04 - I think that the rectangles are so close together that judgements about what is most pleasing will be affected by their neighbors; probably a good scientific study would display only one at a time, or only pairs. Also the issue of screen resolution is a serious one; on the Mac, pixels are square, but on most Windows systems, they are not. All that said, it's an interesting study; thanks for putting it up.
- 03/10/04 - I chose rectangle 1 which appeared like almost a perfect square. Also, the poll'll be more effective had you drawn the rectangles apart.
- 03/09/04 - I think the poll is a spoiled a little by showing all the rectangles side-by-side. In this way, I felt drawn to pick one of the shapes in the middle of the range. Perhaps it might be better to show each shape individually.
- 03/08/04 - The high selection of 4 and 5 does not suprise me. I think most people will pick one of the two centre rectangles simply because they are in the middle of the screen. Must remember that 'most' people (I'm not one of them) prefer symetry and may feel awkward picking from one side or the other.
- 03/04/04 - I think that the presentation creates a bias. Some people may be influenced topick 5 because it is near the center. This could be avoided if the order of display of the rectangles was randomly picked each time, or if one at a time were displayed. Alternatively, what if the user simply dragndropped a corner to set up the rectangle that the user considered most pleasing?
- 03/01/04 - [Jim: Sorry I neglected to upload data for almost a whole month]
- 02/26/04 - Amazing. The mind that craves determining the most pleasing rectangle. Outstanding.
- 02/26/04 - Interesting, if not scientific poll. The golden rectangle in ancient art is pure myth. Whenever anyone measures the art, they use the rectangles that match the thoery rather than the many that don't. As your informal poll and the dimensions of most rectangles around us indicate, the golden rectangle is especially beautiful only as a mathematical construct. (No, not even the Monolith. Much too long.)
- 02/18/04 - 16 x 9 is the most common screen ratio these days, which comes out to 1x1.777 what is the dimension of #7?
- 02/13/04 - FYI... The monolith in 2001 is 1 x 4 x 9
- 01/28/04 - Interesting poll. Wasn't the monolith in 2001 supposed to be based on the Golden Rectangle? [see next message (above)]
- 01/13/04 - [I suffered two computer crashes, and I lost about three weeks worth of data, including several reader comments. Sorry about that. By the way, someone has been flooding my email with rectangle poll choices. Most of that got deleted.]
- 12/23/03 - baa humbug ect,ect. 12/23/03
- 12/03/03 - Cool poll. =) //MackanZoor. PS! Your link leading to "Probability 101" further down this page is broken.
- 11/30/03 - Simple integer ratios come up in music, too. I remember reading that images can be treated like sounds for some transformations; is this another parallel? Does the human mind handle sound and visual input in a similar manner?
- 11/23/03 - Why do people make sarcastic comments in here? It is so rude!!!!!!!!!!!!!
- 11/23/03 - I don't judge rectangle by their outsides, I think it is what's inside that counts
- 11/23/03 - Pleasing rectangles. GIVE ME A BREAK. Rectangles are rectangles are rectangles. None are more pleasing than others. They are all the same. Actually I think they are all different in their own special way. :~) (Notice the sarcasm, hint, hint.
- 11/23/03 - Rectangle 4 definately was most apealing to me, I don't know why. Did you know credit cards are golden rectangles so people will use them more?
- 11/07/03 - I thought that the rectangle #3 looked nice because it looked like the standard piece of printer paper or book, you know, about half again as tall as it is wide. Books do have a rather standard shape to their pages and covers, usually. Is this because people prefer that shape of a book? Is it because it is easier to hold or because it looks better, or both? It is wider than the Golden Rectangle, though.
- 10/24/03 - so why 5 on poll 1?
- 10/22/03 - secks?
- 10/21/03 - I am currently writing a book on aesthetics including a chapter on the golden section. I have come to the general conclusion that simple integer ratios like 1:1 2:1 2:3 3:4 are aesthetically more pleasing than the golden section. Your poll results are very interesting! m.simmonds@... [I don't publish email addresses] Dept of Psychology, University of Canterbury,Christchurch, NZ
- 10/15/03 - i was playing checkers on yahoo games this evening. a fellow named 'Reenforce' passed your website URL along to me. The first thing I looked at was the menu of links. I briefly looked to see your biology links and intend to go back there. I then looked at your biography page to find out who 's business I am snooping through. Somehow I ended up at a page that I thought odd - pleasing rectangles? lol
- 10/01/03 - Are you doing this all manually? No wonder you couldnt figure out Access... [It is mostly automated, now]
- 09/21/03 - I think that I might have to agree that presenting the rectangles in a random order would be a better method. I think that it would be interesting to see if the results are the same. I also might have been influenced by the fact that I knew that one of the rectangles was a golden rectangle. What I'm not sure of is whether I gravitated toward the one which I thought was the golden rectangle or whether I subconciously tried to pick a different rectangle.
- 09/13/03 - perhaps the reason that number 5 is the most pleasing is because it is in the middle. most of the people dont like extremes, so they'd choose something which is closer to the middle.
- 09/12/03 - To the person worried about resolutions (who mentioned 1024x768 specifically): All common resolutions for standard computer displays are 4:3. The notable exception is 1280x1024, for which the standard (assuming horizontal resolution is fixed) should be 1280x960.
- 08/07/03 - This is the most *random* web poll i have EVER participated in, and very interesting it is too. :)
- 08/05/03 - If you arranged them randomly, it would be more scientific. People may have tendancy to exclude the extremes.
- 07/30/03 - Jim's comment: People have favorite numbers. That should complicate the results of any poll. Luckily, mine is off the scale of this poll.
- 07/28/03 - I purposely didn't take much time to ponder the aesthetics of the rectangles. I just let my eyes get drawn to one. And lo and behold it was the golden rectangle. Go figure!
- 07/15/03 - What are the ratios of the most popular shapes. I bet its about 1:1.5 for fig 5 and 1:1.35.. for fig 4.
- 07/14/03 - Perhaps the reason why people choose different rectangles in the horizontal and vertical orientations has to do with peoples preception of horizontal and vertical sizes. Like the optical illusion with the top hat whose brim is in reality as wide as the hat is tall, perhaps rectangle number five is percieved as taller when in the vertical position, and is thus fooling us into thinking it's a golden rectangle... [Jim's response: I thought the same myself, however we are not identifying rectangles, but choosing one over its neighbor. I suspect that this doesn't have much to do with optical illusions?]
- 06/12/03 - My opinion is that a more pleasing proportion for a rectangle can be formed by extending the square to the length of its diagonal. The Golden Mean approach makes a rectangle look uncomfortably long and lanky to me.
- 06/12/03 - I found it difficult to disentangle the rectangles from their numbering as I prefer some to others; and I agree with other comments about the juxtaposition of the rectangles causing the test to measure something other than desired. Perhaps the best way to present the test is to view the rectangles separately and in random order and have the rectangle-rater assign aesthetic appeal on scale of 1-10.
- 06/07/03 - Maybe people don't change their answer, but different people on the same computer choose different rectangles.
- 06/02/03 - It depends what's in the rectangle. I also think that it is the set of proportions -- one rectangle within another -- where esthetics kick in.
- 06/01/03 - Can I also tell you that I think your site rocks somewhat. :-))
- 06/01/03 - I think you need to compare the results of the "perfect" rectangle and those of one's body shape. I might have chosen "4" for a reason. ;-D
- 05/24/03 - I learned about the golden rectangle in high school, about 30 years ago. Thought I'd look it up on the www. Interesting poll! However, it will depend on how a person's PC display is set up. My video card can produce many height/width ratios. currently it's set for 1024 X 768 pixels. This is then adjusted to fill the monitor screen. So a square might not look like a square, either! Just a comment. Interesting poll.
- 05/15/03 - The Classic greek thinkers had a particularly abstract idea of beauty: the exactness of mathematics and the possibility of both simplicity and complexity had a peculiar appeal. Similarly, they often described human beauty in terms of symmetry and fitness to a particular task. Their view of the Golden Ratio was probably more like what we would call an intellectual appreciation. For me, the Golden Rectangle IS somehow satisfying but other, less well-ordered rectangles are pleasing for other reasons: their asymmetry seem dynamic or more interesting. I find, for example, tall, narrow windows architecturally exciting.
- 05/09/03 - [Jim says: Today someone submitted rectangle #6 65 times. I'm counting that as one vote]
- 05/05/03 - I believe you should randomly position the rectangles as it seems the centrally positioned ones are being favoured merely for being central. [Jim's response - There are a lot of possible variations here. I could change the color (I might do that in a later poll), texture, background color, spacing, overall size, triangles, etc.]
- 05/05/03 - My initial reaction was to choose 4 but I went for 5 as it is a little taller. I do not like my rectangles to skinny as it implies weakness. i do not like them to fat as it implies squareness. I agree with the first comment about the A4 Paper size.
- 05/02/03 - What is the more aesthetic is the "bell" curve of your statistics, thus a "normal" distribution.
- 05/01/03 - maybe positioning between 5 and 7 slants 6's golden attraction... i felt my selection drawn to the right, but, as it seems, not close enough to the edge. do you think that a random arrangement each time would skew your findings?
- 04/29/03 - I'm very fond of the oblong, both for its shape and its sound. 8 most resembles an oblong to my eye. therefore, 8.
- 03/17/03 - It looks like the ratio of the square root of two to one
- 02/21/03 - looks like a triangle of rectangles... sorry!
- 12/28/02 - My choices did not include a 5
- 12/28/02 - the entire web is out of sync with me!
- 12/13/02 - hmm
- 09/16/02 - please tell me why you are asking?
- 09/12/02 - What's the deal with 'pleasing rectangles'?
- 06/21/02 - Voted for 5 as the most pleasing to me, but actually imagined that the golden one was 6!
- 06/21/02 - comment below should read similar not sislar!!
- 06/21/02 - i think the number 4 which I voted for is very sislar to an A4 page which I am conditioned to like by constant exposure
About the normal curve, this is from my page Probability 101:
On the left, we have three graphs. The first represents the probabilities of each possible number of heads, when we flip six coins (or one coin six times). Zero heads or six heads are the least likely (the shortest rectangles), and three heads is the most likely (the tallest rectangle). The second graph is the same for 12 coins. Here 6 heads is the most likely outcome, but that outcome is not likely (much less than 0.5). And the third is the famous normal curve, which is the limit of infinitely many coins, and has the equation: y = (1/sqrt(2pi))e^((-x^2)/2) (where a^b means a to the b power). The total green area under each graph has an area of 1, as the total probability must be 1. And so, you can see where the normal curve comes from.
Return to my Most Pleasing Rectangle Web Poll
Go to my home page