The Golden Ratio
Apple's logo artists have infused the iCloud logo with some mathematical elegance. In this case, the golden ratio or φ.

The circles in the 'puffs' of the iCloud are sized in a ratio of 1:1.6, an approximation of golden ratio, as discovered by Australian designer Alan van Roemburg. It seems unlikely the proportion was unintentional; Apple's artists simply have an acute sense of the history of design and mathematics.

The golden ratio has been around since at least Euclid and Pythagoras. Fans of the Da Vinci Code should know it too, as Dan Brown has referenced φ several times in his books. No wonder iCloud seems so elegant and aesthetically pleasing.

Hat tip to John Gruber

Update: The original source of the image appears to have been Takamasa Matsumoto.

Top Rated Comments

emaja Avatar
181 months ago
So, how long before Apple gets sued by these Euclid and Pythagoras guys - whoever they are - for using their proprietary ratios?

...and yes, this is a poor attempt at humor.
Score: 9 Votes (Like | Disagree)
Hellhammer Avatar
181 months ago
I highly doubt this was intentional. They probably created a set of circles, copied and pasted them, rotated them, and there's your 'golden' ratio.

Giving them too much credit.

You would be surprised to see how widely the Golden Ratio is used.

//www.youtube.com/watch?v=fmaVqkR0ZXg&feature=related
Score: 5 Votes (Like | Disagree)
Consultant Avatar
180 months ago
This is by far the Best MacRumors article ever!
Except that Alan (June 15) is not the one who discovered it (http://stam-design-stam.blogspot.com/2011/06/icloud.html) (on June 9). Alan seems to be intentionally shady too.

Explained in the second part of the article: http://obamapacman.com/2011/06/icloud-logo-designed-with-triple-golden-ratio/

After iCloud was announced, I found their icon to be eerily similar to the CloudApp that's been on the app store for quite awhile..the only difference is one additional circle on the left. getcloudapp.com/[/URL] hasn't anyone else noticed this?
MobileMe was established before getcloudapp.

It's like that MobileMe had the icon before this other company did.
Score: 4 Votes (Like | Disagree)
nagromme Avatar
181 months ago
Giving them too much credit. They don't care about the minor details that much.

Image (http://i.imgur.com/74B5Z.png3)
I agree with that -- but you'd also be surprised how widely the Golden Ratio is used, unintentionally :)
Exactly. The mystique of the Golden Ratio is fun, but reality is more boring :)

I know the iCloud post was just for fun, so I’m not slamming it. But as a matter of interest: the Golden Ratio has NOT been intentionally used by great artists through history. You can find something “close” to that ratio in any image if you look for it. It’s like finding faces in clouds (no pun).

You could pick ANY ratio, say, 11-to-17, and find something very close to it somewhere in just about any image.

In modern times, the ratio is better-known and some certainly do use it. Apple may have too... but it’s a little off (thanks, stewart) and given that it was designed on a computer, I think the golden ratio in the logo is nothing intentional.

Read Mario Livio’s book, The Golden Ratio: The Story of Phi. And you won’t be disappointed: for every myth about The Golden Ratio that he dismantles on solid historical research, there’s some other thing you never knew about the number that’s even cooler, AND true. (Like the ways that numbers related to it appear in nature.)
Score: 4 Votes (Like | Disagree)
Gav2k Avatar
181 months ago
Very apple like
Score: 3 Votes (Like | Disagree)
luke.mac1 Avatar
180 months ago
I can't believe I'm the first to post this...

I guess every iCloud has a golden lining...
(p.s. i know it's supposed to be silver lol)
Score: 2 Votes (Like | Disagree)

Popular Stories

iPhone 17 Pro 3 4ths Perspective Aluminum Camera Module 1

iPhone 17 Pro Launching Later This Year With These 12 New Features

Sunday April 13, 2025 7:52 am PDT by
While the iPhone 17 Pro and iPhone 17 Pro Max are not expected to launch until September, there are already plenty of rumors about the devices. Below, we recap key changes rumored for the iPhone 17 Pro models as of April 2025: Aluminum frame: iPhone 17 Pro models are rumored to have an aluminum frame, whereas the iPhone 15 Pro and iPhone 16 Pro models have a titanium frame, and the iPhone ...
Apple 2025 Thumb 1

10 Products Still Coming From Apple in 2025

Friday April 11, 2025 4:14 pm PDT by
Apple may have updated several iPads and Macs late last year and early this year, but there are still multiple new devices that we're looking forward to seeing in 2025. Most will come in September or October, but there could be a few surprises before then. We've rounded up a list of everything that we're still waiting to see from Apple in 2025. iPhone 17, 17 Air, and 17 Pro - We get...
iPad Pro iPadOS

iPadOS 19 Will Be 'More Like macOS' in Three Ways

Sunday April 13, 2025 6:43 am PDT by
A common complaint about the iPad Pro is that the iPadOS software platform fails to fully take advantage of the device's powerful hardware. That could soon change. Bloomberg's Mark Gurman today said that iPadOS 19 will be "more like macOS." Gurman said that iPadOS 19 will be "more like a Mac" in three ways:Improved productivity Improved multitasking Improved app window management...
Foldable iPhone 2023 Feature Homescreen

Foldable iPhone Resolutions Leak With Under-Screen Camera Tipped

Monday April 14, 2025 3:12 am PDT by
Apple's upcoming foldable iPhone (or "iPhone Fold") will feature two screens as part of its book-style design, and a Chinese leaker claims to know the resolutions for both of them. According to the Weibo-based account Digital Chat Station, the inner display, which is approximately 7.76 inches, will use a 2,713 x 1,920 resolution and feature "under-screen camera technology." Meanwhile, the...
M6 MacBook Pro Feature 1

Waiting for the Perfect MacBook Pro? 2026 Might Be the Year

Thursday April 10, 2025 4:19 am PDT by
Apple in October 2024 overhauled its 14-inch and 16-inch MacBook Pro models, adding M4, M4 Pro, and M4 Max chips, Thunderbolt 5 ports on higher-end models, display changes, and more. That's quite a lot of updates in one go, but if you think this means a further major refresh for the MacBook Pro is now several years away, think again. Bloomberg's Mark Gurman has said he expects only a small...
Apple Vision Pro with battery Feature Blue Magenta

Vision Pro 2 Rumored to Have Two Key Advantages Over Current Model

Sunday April 13, 2025 7:15 am PDT by
Apple is working on a new version of the Vision Pro with two key advantages over the current model, according to Bloomberg's Mark Gurman. Specifically, in his Power On newsletter today, Gurman said Apple is developing a new headset that is both lighter and less expensive than the current Vision Pro, which starts at $3,499 in the U.S. and weighs up to 1.5 pounds. Gurman said Apple is also...
maxresdefault

The MacRumors Show: New iOS 19, iPhone 17, and Apple Watch Ultra 3 Leaks

Friday April 11, 2025 7:13 am PDT by
On this week's episode of The MacRumors Show, we catch up on the latest iOS 19 and watchOS 12 rumors, upcoming devices, and more. Subscribe to The MacRumors Show YouTube channel for more videos Detailed new renders from leaker Jon Prosser claim to provide the best look yet at the complete redesign rumored to arrive in iOS 19, showing more rounded elements, lighting effects, translucency, and...
top stories 2025 04 12

Top Stories: iOS 19 and iPhone 17 Pro Rumors, Siri Revamp Turmoil, and More

Saturday April 12, 2025 6:00 am PDT by
It was a big week for leaks and rumors in the Apple world, with fresh claims about iOS 19, the iPhone 17 Pro, and even the 20th anniversary iPhone coming a couple of years from now. Sources also spilled the tea on the inner turmoil at Apple around the Apple Intelligence-driven Siri revamp that has seen significant delays, so read on below for all the details on these stories and more! iOS ...
iPhone 16e Feature

iPhones, Macs, and Other Apple Devices Exempted From Trump Tariffs

Saturday April 12, 2025 9:44 am PDT by
Apple and other electronics manufacturers have received a break from Trump's reciprocal tariffs, with the U.S. Customs and Border Protection agency sharing a long list of products excluded from the levies last night. iPhones, Macs, iPads, Apple Watch, and other Apple devices will not be subject to the 125 percent tariffs that have been put in place on imported Chinese goods, nor will Apple...