# golden rectangles, functional aesthetics, & the future of the iPad

## Rho rho rho your boat

When I was young I loved the film Donald in mathmagic land.

In March, I heard a mathematician give a delightful exposition about why π isn't that great.

In April I read the elements of typographic style.

Today I heard the prompt begin to describe a report on the possibility of a two app split screen mode. They cited 9to5 Mac for their report. And said windows 8 had a split screen mode.

## gently down the stream

I have not used or seen a windows 8 screen.

I have not read the 9 to 5 mac post.

I have paused the prompt @ 46:05.

Much like John Siracusa used to explain, he wouldn't listen to shows so that he could come to the idea fresh, without having to deal with the worry of having any opportunity to plagiarize others (or in another sense to upset your own thinking by the rapids that result from the arrival of another thought stream).

## merrily merrily merrily meerily

I have been enjoying thinking about the importance of geometric structure in the history of thought. Euclidean geometry held away for so very long. And certainly if we are interacting with a flat surface it will imitate Euclidean geometry. Thus, we may have something to learn from the ancient Greeks about flat design.

I remember from Donald that there was a general obsession with ratios. In particular, whole number ratios when it came to music, and one particular ratio, the golden ratio, when it came to analyzing physical objects. It appeared in the buildings' proportions.

The fascination continued to Da Vinci whose vitruvian man supposedly embodied this ratio. It appears again in the Nautilus’s golden spiral

ok technically that isn't true on 2 grounds; 1) a Nautilus is well described by a logarithmic spiral 2) there is no such thing as the Nautilus, it's an idea not a thing. I'll point you toward

John dupréfor the counterpoint and I will elaborate on some other day.

But this is aside from the point.

## life is but a dream

My point is that the golden ratio involves a self-similarity that goes deep. If I remember correctly, you can take a chunk of the golden rectangle out by following the following recipe:

- shares 1 complete side with the smaller side of the rectangle
- the two smaller rectangle's sides that meet the aforementioned side(perpendicularly) will share some space with the large rectangle's longer sides.
- the length of these sides would be equal to some ratio (
*ϱ*) times the length of the short side of the big rectangle(which, remember, is the same size as the length of the smaller rectangle)

- the length of these sides would be equal to some ratio (
- the larger rectangle's ratio is also

I leave this as evidence of my line of thinking. I now will rework it: cut out a square with sides equal to the short edge of the rectangle from the golden rectangle and you still have a golden rectangle.

Damn, that self similar thing I thought world work. I thought you could cut out a scaled down version of the same shape but turned sideways and what remained would be an object that obeys the golden ratio, but that doesn't make sense. Since the long side would be subtracted from exactly what is needed to make the other one a golden ratio. But if we're to subtract from the long side, the only way to keep the golden ratio is for it to become the short side. But then you have two short sides connected end to end that are equal, since they share the same long edge. Which means that the two new shapes are the same. Like a book's pages are laid out.

But that's actually what I wanted to avoid. As Siracusa elsewhere has made more than abundantly clear, there are cases where you do want true secondary controls. That is, you want to not have two equally prominent sets of controls

ordisplays — that's the beauty of a true interface like an iPad versus an outerface like a Cinema Display

Rather, what you want is one primary (large) and one secondary interface, and you want to embed them in a rectangle that will take the max of their edges to know how small they will need to be. Since the larger rectangle is fixed, the best way to lay out the two secondary rectangles is to use as much space as is possible, so it makes sense for the small side on one to be congruent with and equivalent to the long side on the other one.

One solution is to given primary a square and secondary what remains, now unfixing the big rectangle's long side, we can search for what works best such that what remains always has an area less than the square and retains the fixed side that must run congruent and identical to the square. Now the question is what ratio do you want the remaining portion to have between it's sides?

My suggestion is that you make it the same ratio as the iPad and put portrait mode in there that spot.

I was hoping for a scaled down version of it would fit but then I realized that that produced a contradiction given what I had been trying to say about maximizing the area of the iPad while putting two things that share a side that have the same ratio as the full iPad, but scaled down so that one would be portrait the other landscape. But that doesn't work. Still the square would be a fun shape to design for).

Or, you make it the iPhone's or iPod's ratios and include the display from the respective device.

I think developers could do a lot with a new form factor. I think designers would do cool thinks with the square.

I should also mention the silver ratio

which I have mentally encoded as the mod 2 version of the golden ratio. I think because you take a square out of it once and then you take a square out of that one, and then you get back something with a silver ratio. Or something.

But there's also a bronze which was mod 3? But I don't know if 4 would work…

does that suggest a connection to the prime numbers? And Fermat/Wiles? Or is it more analogous to galois and 4 will exist but nothing greater than 5.

But, to be honest I just don't remember too much about the silver ratio in particular. I read about it in the elements.

No not euclid's.

Not that his wouldn't also be useful for designers to read… I just haven't read it, so I don't know.

In any case hopefully these mathematically inclined wanderings through land of the possible ways that the dual screen could be implemented. We had some false routes, but hopefully we even learned something from the act of retracing our steps and seeing where we made a wrong turn and righting what can be wrought from what remains after attempting to ford the river of thought, thinking it merely a thought stream.

If educational games in school taught me anything it would have to be this: never ford the river.

Cheers, :€