All iPads Golden Ratio as perfect spacing between phone, tablet, and laptop

Discussion in 'iPad' started by samiznaetekto, Dec 12, 2013.

  1. samiznaetekto, Dec 12, 2013
    Last edited: Dec 12, 2013

    samiznaetekto macrumors 65816

    Dec 26, 2009
    I currently have iPhone 5, rMini, MBA 11", and MBP 17":

    - 17" as desktop replacement, for programming, video and photo editing, iTunes library, and other desktop-class tasks
    - 11" for programming on the go, fits in my Scottevest jackets, or carry it in a shoulder bag for iPad
    - rMini as a wearable computer, fits all my cargo/hiking pants and shorts, goes with me everywhere (taken to the mountains already!)
    - iPhone, well, is a phone + WiFi hotspot for whatever other devices I have with me, email on the go, Yelp, navigation and various other small tasks

    After retina MBP 13" introduction, I'm thinking about replacing 17"+11" with 13", since maintaining and syncing 2 computers is too much. And I hope that iPhone 6 will be 5". I think, I'll feel complete with 5", 7.9", 13.3" range - it covers everything I need without gaps too big or too small.

    So, this and the endless debates "Air or Mini?" here got me thinking about ideal screen size "spacing". And sure enough, the ratio 13.3/7.9 equals 1.68 - very close to 1.618, the golden ratio (within 4%). And by this theory, the ideal size below 7.9 would be 7.9/1.618 = 4.9", or exactly what thinks will be the size of iPhone 6, since it's the same sheet as Air (254ppi) cut at 1136x640 resolution.


    If you prefer Air, the harmonious step up would be 9.7*1.618 = 15.7" (15.4" rMBP), down 9.7/1.618 = 6" (iPhablet rumors, anyone? :D)

    But having both Air and Mini is too redundant (a mere 1.23 ratio), and 13" MBA or MBP with Air is only 1.37 step, let alone 11" MBA: only 18% from Air.

    Anyway, thought I'd share my thoughts on how to cover the range of screen sizes in a way that feels complete and satisfying without redundancy.
  2. PatrickNSF macrumors 6502


    Jan 24, 2011
    Interesting analysis. I have an iPhone 5S, rMini, 13 rMBP and 27" iMac. Seems to cover the bases for me.
  3. jimsowden macrumors 68000


    Sep 6, 2003
    Dude, this is a very smart connection, much better than the "will my iPhone float" type questions MacRumors has degraded into. You should pitch the article to The Verge or the like.

    I'd read it.
  4. nStyle macrumors 65816

    Dec 6, 2009
    Sorry...There isn't a connection. The figures you're using are diagonal measurements and mean nothing next to each other, unless you're going to use them as a dual monitor in which case they still wouldn't be anywhere close to the golden ratio or a golden rectangle when placed side by side.

    You're comparing individual screen sizes here. The golden ratio makes no difference. What does make a difference would be having a far enough gap between screen sizes to make owning each device make sense to you.
  5. samiznaetekto thread starter macrumors 65816

    Dec 26, 2009
    I'm not talking about golden ratio as a perfect aspect ratio for a screen, I'm talking about...

    ...the gap should be geometric factor (multiplier - each size some X times bigger than previous), not additive factor (each size X inches bigger than previous).
  6. nStyle macrumors 65816

    Dec 6, 2009
    Yeah but I'm saying the ratio in which you multiply is arbitrary since 1.618 actually means nothing in this scenario since you're comparing apples (no pun intended) to oranges. The golden ratio is calculated using widths and heights, not diagonals.

    If Apple were truly concerned about using this arbitrary (in this case) 1.618 multiplier to separate their device sizes, they would have already done it.
  7. tobeornottobe macrumors regular

    Nov 4, 2013
    You might have to recalculate your ratios with the new bigger iPad coming out next year. ;)
  8. smoking monkey macrumors 65816

    smoking monkey

    Mar 5, 2008
    You Only Live Twice
    Personally I'd like
    Phone: 4.5 inch
    ipad: 11 inch
    laptop: 16 inch
    Desktop: 27 inch

    The iPad and the Laptop could probably have a bigger screen with no increase in actual body size. That would be a great outcome.

    I would imagine there isn't a big enough difference between a 5 inch phone and a 7 inch mini. But assume Apple will release a 4.5 or 5 inch phone next year.
  9. rkuo macrumors 6502a

    Sep 25, 2010
    The use case is what really matters, not the gap between sizes.

    Here are some breakpoints.

    Wristwatch sized
    One-handed use
    Two handed use
    View from couch
  10. samiznaetekto thread starter macrumors 65816

    Dec 26, 2009
    Golden ratio is not only harmonic aspect ratio, but also harmonic multiplication factor in natural fractals, e.g.


    Sizes that increase geometrically by the same, golden ratio, multiplier feel most aesthetically filling the range of sizes from small to large.

    And yes, the aspect ratios of iPhone, iPad, and Macbooks are different, so their widths or heights do not increase in the same progression as diagonals, but it's the diagonals that hint us of overall device dimensions.

    Well, it looks they already did: 15.4/9.7, 13.3/7.9, 21.5/13.3, and 27/15.4 are all very close to Phi. The only thing not fitting into this harmonious sequence is iPhone, and two versions - 4.9" and 6" - will fit it perfectly. There will be two lines of harmonious sequences:

    "junior": 4.9, 7.9, 13.3, 21.5
    "senior": 6, 9.7, 15.4, 27

    Your choice - some people prefer more compact devices, some pefer more real estate.


    The difference between a 4.9" phone and mini (7.9") is exactly the magic Phi factor. :rolleyes:
  11. samiznaetekto thread starter macrumors 65816

    Dec 26, 2009
    This should clarify things for you:


  12. adamj575 macrumors 6502


    May 17, 2011
    Way above my head here, all I know is I like what I like. If it makes me happy then it's "golden".
  13. JoeRito, Dec 13, 2013
    Last edited: Dec 13, 2013

    JoeRito macrumors 6502a


    Apr 12, 2012
    New England, USA
    Shouldn't we be applying the golden ratio/rectangle to the length/width of an individual screen instead of comparing the diagonals of multiple devices to each other?

    Therefore, looking at one device at a time, we can check to see if it meets the golden ratio or not. So the iPad Air is 7 3/4 divided by 5 3/4 or 1.35 (approx 4/3rds) not the golden ratio. So, (a+b)/a = 1.35. Likewise, we can measure all other devices this way.

    By comparison, the Surface Pro would be 1.78 (approx 16:9). The 16:10 screens have the aspect ratio closest to the Golden Ratio (really Golden Rectangle) at 1.60. This discussion is distinctly different than considering what the ideal screen size, or diagonal, should be.

    From wiki:
    Two quantities a and b are said to be in the golden ratio φ if:
    (A+B)/A = A/B

Share This Page