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
187 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
187 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
187 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
187 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
187 months ago
Very apple like
Score: 3 Votes (Like | Disagree)
luke.mac1 Avatar
186 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

Tim Cook Rainbow

Apple Event in October? Here's What to Expect

Monday September 29, 2025 9:31 am PDT by
Apple's annual iPhone event is in the rearview mirror, but rumors suggest the company plans to release a handful of additional products before the year ends. Will there be another Apple event this October? We discuss the possibility below. Apple in October Apple's most recent October events were in 2021 and 2023. In 2022 and 2024, Apple did not host an October event. Instead, it...
apple wallet drivers license feature iPhone 15 pro teal 1

Apple's iPhone Driver's License Feature Now Available in 11 U.S. States

Tuesday September 30, 2025 6:40 am PDT by
In select U.S. states, residents can add their driver's license or state ID to the Wallet app on the iPhone and Apple Watch, providing a convenient and contactless way to display proof of identity or age at select airports and businesses, and in select apps. Apple recently revealed that the feature would soon be available in North Dakota, and starting today, the feature has officially gone...
maxresdefault

New iPad Pro With M5 Chip Leaked in Unboxing Video

Tuesday September 30, 2025 8:39 am PDT by
An apparent unboxing video for an unannounced iPad Pro with the M5 chip was uploaded to YouTube today by Russian channel Wylsacom. The same YouTube account leaked the 14-inch MacBook Pro with the M4 chip before it was announced by Apple last year, so this is likely a legitimate leak. Based on the box shown in the video, this appears to be a 13-inch iPad Pro with an M5 chip, 256GB of...
fcc vision pro leak

FCC Accidentally Leaks Apple's Next Vision Pro

Tuesday September 30, 2025 3:48 pm PDT by
The United States Federal Communications Commission (FCC) has seemingly confirmed Apple's work on an updated version of the Vision Pro headset. One of several documents the FCC shared today references an Apple-designed "Head Mounted Device" with a model number of A3416. An included image confirms the device is a Vision Pro. The FCC's uploads are transmission tests, SAR test reports, and...
iOS 26

Apple Releases iOS 26.0.1 With Fixes for Wi-Fi, Cellular, and Camera Issues on iPhone 17 Models

Monday September 29, 2025 10:12 am PDT by
Apple today released iOS 26.0.1 and iPadOS 26.0.1, the first updates to the iOS 26 and iPadOS 26 operating systems that came out earlier this week. The new software can be downloaded on eligible iPhones and iPads over-the-air by going to Settings > General > Software Update. According to Apple's release notes for the update, iOS 26.0.1 addresses a bug that could cause aberrations in...
macbook pro prime day 2025

FCC Leaks Upcoming MacBook Pro and More

Tuesday September 30, 2025 1:58 pm PDT by
The United States Federal Communications Commission has confirmed Apple's work on a new version of the MacBook Pro and several other products, leaking details on the devices ahead of launch. The FCC published documents that reference model numbers that do not correspond with existing devices. A3434, for example, references an unreleased MacBook Pro, while other numbers are likely for...
space black mbp

Here's Every New Apple Product That Leaked Yesterday

Wednesday October 1, 2025 8:27 am PDT by
A handful of upcoming Apple products leaked yesterday, through a combination of YouTube videos out of Russia and U.S. Federal Communications Commission (FCC) documents that were released, despite Apple's confidentiality requests. The leaked products include an iPad Pro with an M5 chip, as well as updated MacBook Pro and Apple Vision Pro models. All of these devices had already been rumored...
Apple MacBook Pro M4 hero

New MacBook Pro Nears Mass Production, But Four Bigger Upgrades Expected Next Year

Sunday September 28, 2025 2:08 pm PDT by
Apple's next MacBook Pro models will enter mass production soon, according to the latest information shared by Bloomberg's Mark Gurman. In his Power On newsletter today, Gurman said he continues to believe the new MacBook Pro models will be released at some point between late 2025 and the first quarter of 2026, meaning they should be available to order by March at the latest. Apple often...
iOS 26

Apple Continues to Prepare iOS 26.0.1 With Multiple Bug Fixes Expected

Sunday September 28, 2025 1:30 pm PDT by
Apple is preparing to release iOS 26.0.1, according to a private account on X with a proven track record of sharing information about future iOS versions. The account initially said iOS 26.0.1 would have a build number of 23A350, but they now expect the update to have a build number of 23A355. This suggests that the software update will include more bug fixes or changes than initially...
Home Hub Command Center with Dome Base Feature

Apple Working on All-New Operating System

Thursday September 25, 2025 1:11 pm PDT by
Apple is developing an all-new operating system codenamed "Charismatic," according to Bloomberg's Mark Gurman. Apple smart home hub concept based on rumors This is likely Apple's long-rumored "homeOS" operating system. In a report last month, Gurman said both Apple's rumored smart home hub in 2026 and tabletop robot in 2027 will run the new operating system. He said the software platform ...