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

samiznaetekto

macrumors 65816
Original poster
Dec 26, 2009
1,016
24
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 Tested.com 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.
 
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PatrickNSF

macrumors 6502
Jan 24, 2011
476
157
Interesting analysis. I have an iPhone 5S, rMini, 13 rMBP and 27" iMac. Seems to cover the bases for me.
 

jimsowden

macrumors 68000
Sep 6, 2003
1,766
16
NY
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.
 

nStyle

macrumors 65816
Dec 6, 2009
1,147
279
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.
 

samiznaetekto

macrumors 65816
Original poster
Dec 26, 2009
1,016
24
You're comparing individual screen sizes here. The golden ratio makes no difference.
I'm not talking about golden ratio as a perfect aspect ratio for a screen, I'm talking about...

What does make a difference would be having a far enough gap between screen sizes to make owning each device make sense to you.
...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).
 

nStyle

macrumors 65816
Dec 6, 2009
1,147
279
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.
 

smoking monkey

macrumors 65816
Mar 5, 2008
1,310
336
I HUNGER
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.
 

rkuo

macrumors 6502a
Sep 25, 2010
723
320
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).
The use case is what really matters, not the gap between sizes.

Here are some breakpoints.

Wristwatch sized
One-handed use
Pocketable
Purseable
Palmable
Two handed use
Backpackable
Desk
View from couch
 

samiznaetekto

macrumors 65816
Original poster
Dec 26, 2009
1,016
24
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.
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.

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.
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.

----------

I would imagine there isn't a big enough difference between a 5 inch phone and a 7 inch mini.
The difference between a 4.9" phone and mini (7.9") is exactly the magic Phi factor. :rolleyes:
 

JoeRito

macrumors 6502a
Apr 12, 2012
505
155
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
 
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