You have to understand 1:√2. It’s not merely folding in half. The test is the folded half has to be the same ratio as the parent. It’s same ratio all the way down.

“The mathematical brilliance of A*”

https://youtu.be/oQfzSt5bLVs

It isn't just twice the size.

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.

first - it's not hard to make. Outside screen size doesn't have to be half of the open screen.

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.

The difference is that it has the same aspect ratio folded and unfolded. If you look at other folding phones the inside screen is twice the area, but the shape of the phone is different. 1 : sqrt(2) is the only ratio where you can fold one side in half and the ratio stays 1:sqrt(2). Any other ratio of sides and the inside and outside have different ratios. Therefore, things have to move around, or scale.

Yes, but 1:√2 keeps the ratio even when you rotate the screen vertically. A folded 1:1 screen becomes 2:1 when "unfolded" and the area doubles, so you can go from showing one 1:1 window to two 1:1 windows side by side. But when rotated to a vertical orientation, you can't just scale that 1:1 window to double its size. With 1:√2 you can.