“The mathematical brilliance of A*”
The sqrt(2) aspect ratio allows a portrait full app to be scaled up to the exactly to the folded out screen. But does anyone want that? You probably want to fit more content on the bigger screen, so some layout necessarily changes.
Both sides have the same aspect ratio as the whole screen.
> this isn't great design, it's tautology. of course the phone open is twice the size of it closed.
Well, it sounds obvious now, but before Archimedes, ancient engineers split their screens 60-40, so the full screen wasn't twice the size of either side.
If the user isn't going to be multitasking, then the app needs to additionally support the widescreen dimensions of 2X by Y, and the portrait orientation of Y by 2X. Both of these are so drastically larger overall that aspect ratio is a barely-relevant part of the UI layout problem, because nobody wants every button and text label to be double the size (which would mostly defeat the benefits of having the larger screen for anything other than multitasking).
The issue of the internal screen being the same aspect ratio as the external when rotated is completely separate.
Here's just the screen sizes, not even taking into account actual resolution:
iPhone (2007) 3.5" 74.0 × 49.3 36 cm²
iPhone 5 4.0" 88.6 × 49.8 44 cm²
iPhone 12 mini 5.4" 124.5 × 57.5 72 cm²
iPhone Duo, cover 5.4" 113.4 × 77.2 88 cm²
iPhone 6 Plus 5.5" 121.8 × 68.5 83 cm²
iPhone X 5.8" 133.7 × 61.8 83 cm²
iPhone Air 6.5" 150.0 × 69.1 104 cm²
iPhone 18 Pro Max 6.9" 159.2 × 73.3 117 cm²
iPhone Duo, inner 7.6" 157.6 × 111.5 176 cm²
Now, you can leave out a few of those as hopelessly obsolete like the OG iphone, 5, 12 mini, arguably the x, but it's still a pretty wide selection.But for the apps that don't currently support both orientations, it's possible they don't have support for switching aspect ratio on the fly. This design might help with those apps not completely breaking when folding/unfolding.
And the extra irony is I'm currently shipping an app that doesn't deal well with different size phones (just pads the edges), heh, so do as I say, not as I do.
second - main idea is about proportions, if you want to design apps that seamlessly transfer from one screen to another they have to have the same proportions of the sides. This is not a given and depends on the height and width.
If you take iPhone 18 Pro resolution : 2,622 x 1,206 doubling it would make the screen with 2,622 x 2,412 - almost a square screen.
They chose to have the folded phone to have 1.4:1 aspect ratio which is consistent when folded and when unfolded.
Also, when you rotate the device, the ratio changes. This is especially common when unfolding a foldable.
Most have the closed screen plus another view. Or the lock screen which is a full photo open and a small section closed.
Im not saying its not possible but it doesn’t seem like that is their intention.
Their selling point is: Not having to switch from one app to another when Multitasking.