Isn’t diagonality relative? Think about italics: they weren’t invented to be used alongside romans to create a hierarchy.

When I think about diagonals I often think back to a professor who would often catch lazy students using diagonals to try and whip up a dynamic composition. When confronted with the question “Why do the diagonals make this composition dynamic?” the students never had an answer.

But at the same time I guess one can always find diagonals from a strictly mathematical perspective: in a shape with an odd number of sides all sides are at diagonals to all others, none are parallel (At least I think it works that way, I’d have to write a program to test it). So within the mathematical structure of reality there are always some kinds of diagonals.

I’m not exactly sure what you mean with this question.

I think I may be trying to answer a different one here, but as I understand it, the brain distinguishes a diagonal line faster than a vertical or horizontal one. The theory, as I recall being that something that is on a diagonal is either moving or unstable and therefore a possible threat, or perhaps dinner.

In designing signage, it’s something that’s very consciously used to grab attention... as in, “this is a concrete wall. Don’t drive into it.”

-=®=-

> in a shape with an odd number of sides all sides are at diagonals to all others, none are parallel (At least I think it works that way, I’d have to write a program to test it). So within the mathematical structure of reality there are always some kinds of diagonals.

Well, a stair(case) is a DIAGONAL flight of PARALLEL stairs.

Think DIAGONALLY with Flowers

in a shape with an odd number of sides all sides are at diagonals to all others, none are parallel (At least I think it works that way, I’d have to write a program to test it).

Home plate asks you to reconsider! ;-)

Sorry Craig, I wasn’t being specific enough. I was thinking of those regular shapes in which all sides and angles have the same measure. I don’t know enough about geometry to know what they’re called.

An interesting question. I think the concept of the diagonal would be meaningless without our instinctive bodily awareness of the vertical and the horizontal as defined by gravity. This is very basic. Aziz’s stairs is an excellent example: They lead up (or down) and also cross a ’horizon’-tal distance. In geometry the diagonals join the corners of a square or a cube, or of the capital letter N; or can be found in the Arabic medial kaf. The formula for a diagonal is y=ax with ’a’ some constant defining the slope. If a=1 the line is at a 45 degree angle. In the case of the lower edge of the eyebrow in hrant’s thumbnail it is 9 pixels high and 27 across so a=0.3333 :)

These answers seem perfectly good but what I though of when i read the question I thought: ” what roman glyphs are fundamentally diagonal”. eg maybe the “x”. In an italic one part may be at 90 degrees but part of it must be diagonal.

If we eliminate the italic then I would say the x, X v V y, Y, M, X, w, W, k , K, N, Q, R, Z, 2, 4, 7.

But maybe curves count in which case the question is closer to “which glyphs don’t require diagonals?”.

Hrant, spill those beans. What are on about?

I would say ramps are fundamentally diagonal. And aqueducts. And rivers?

It could be argued that in the Latin alphabet, the V is fundamentally diagonal.
All other letters can be adequately rendered with perpendiculars, but a diagonal in V is needed to distinguish it from U.
However, there are other means of disambiguating U and V:

Although this is barely functional, it does show that the diagonal is not funadamentally necessary to a script/glyph system.

Diagonals might imply movement because, as Russell said, they imply instability. Think of walking — or running — as the body leaning/falling forward and the legs hurrying to catch up with it. (At least that’s how a Segway representative once explained it to my High School.)

> What fonts are fundamentally diagonal?
Or What fundamental fonts are diagonal?

http://www.typophile.com/node/44140

What things are fundamentally diagonal?
All things that are neither vertical nor horizontal.

In nature diagonal doesn’t really exist. Plants grow towards the sun - upwards. We either stand or we lie down. Diagonal would be an unstable situation (falling) in between (unless we are leaning against a wall).

In nature diagonal doesn’t really exist. Exceptions abound. What about trees that lean from the wind blowing all the time?

This is an abstract answer: eye level.

... trees that lean from the wind blowing all the time - or plants growing on a window shelf leaning towards the sun.
Yes, but that’s kinda forced diagonality, isn’t it?

Forced diagonality is diagonal nonetheless, ne in flickr parlance, the property of “diagonalness”. Mountains are “natural” and quite diagonal in form & appearance. Would you say the erosive forces and tectonic plate movements that create mountains create them in a “forced” way? That’s just nature doing its thing. If seeds fall in a place where the seedlings / sapling plants are in shadow but there’s light nearby I guess those saplings grow up diagonally to begin with. Isn’t that just nature doing it’s thing?

This is an abstract question, one I’m
not sure I really understand myself:

Here is an abstract answer, one I’m not really sure I understand myself:

Well pictures move from left to right
I stand where I can see
But ignorance is golden in the end
And now it’s quite intangible
This life in front of me
But ignorance is golden in the end, my friend
—words by Sarah McLeod

When I draw diagonal lines in fonts I think of them as getting from one side of a picture to the other side. Not so much A, v, w, y, z, which largely consist of diagonal bodies. If drawing a lower case double story a for example, or the spine of s, parts of the stroke are diagonal. A font is a big pile of pictures, and with some of these pictures diagonals offer a way of getting from one side of the picture to the other.

Well pictures move from left to right
I stand where I can see

In the end I really don’t know. The question is very abstract and so must be the answer.

But ignorance is golden in the end

j a m e s

In Sibyl and other cursive pen-like blackletter styles
diagonalness exists everywhere, most visible in the
numerals. I studied pen-drawn examples very closely when
drawing these, and the thing I remember most about doing
them was the diagonalness they required.

The bodies of these Tuscan figures are made out verticals
and horizontals, but diagonals are clearly very useful for
getting from one side of each glyph to the other.

j a m e s

Agree with James P. It’s all relative. Diagonal-ity/-ness needs accepted perpendicular axes which may be real or imaginary otherwise how can you tell what is diagonal? You’re definitely looking for one or a pair of perpendicular axes as a reference.

Alternatively, diagonal literally means ’across angles’ or similar. Thus a diagonal could be horizontal or vertical depending on how the shape whose angles one is crossing is placed on the page, or in its own space relative to the ground (which is ’flat’ if it is perpendicular to the gravitational pull, so gravity comes into it too... maybe?) Suppose you draw a regular pentagon sitting on one of its sides. The line that you draw between the two points below the apex would be both ’horizontal’ and yet ’diagonal’ too.

My head hurts.

>In nature diagonal doesn’t really exist.

Quite the contrary, really. Right angles are nearly impossible to find, but diagonals are everywhere. A bee hive has perfectly regular (meaning all sides are the same length) hexagons, so the hive is constructed of nothing but diagonals. Snow flakes, crystals, the arrangement of seeds in a sunflower (a spiral constructed of series of diagonals)...

Even were this not the case, I’m not sure I’d buy the idea that a font is somehow more “natural” if it only has vertical and horizontal strokes. I’m not sure that was indeed the implication, but the point of this thread is a bit elusive.

.. the arrangement of seeds in a sunflower (a spiral constructed of series of diagonals)...
.. and the arrangement of rods in Bicycle-Wheels ⊕x⊕
.. and the arrangement of letters in Ladders + Flowers:
http://www.wordandnumberpuzzles.com/flowers/WFlowers.htm
http://mymidwestmagazine.com/2008/01/01/crosswordbrainteasers-6/
http://www.pennydellpuzzles.com/Upload/PuzzleFiles/Sample/flw_p0508_samp...

OK, we’re back.
Thanks for the insights guys.

> the brain distinguishes a diagonal line
> faster than a vertical or horizontal one

Very interesting (although not shocking).
Do you have a reference for this?

> In the case of the lower edge of the eyebrow in hrant’s
> thumbnail it is 9 pixels high and 27 across so a=0.3333

I just KNEW there was something special about my eyebrows!
For one thing, unlike many Armenians I happen to have two of them.

Craig, I like rivers.

Jan, I have to agree with those who say that Nature is more about diagonals and not orthogonals. But it might be just a way of looking at things.

James, I like those “Proprietary type” numerals.
Just the bottom of the “7” needs less flaring.

> the hive is constructed of nothing but diagonals.

Well, a regular hexagon is also three sets of parallels... :-/

> I’m not sure I’d buy the idea that a font is somehow more
> “natural” if it only has vertical and horizontal strokes.

Indeed, I would say that entirely rectilinear fonts are unnatural. As Evert said (quoting a teacher of his, AFAIR): A straight line is a dead line. On the other hand, straight lines can say something nice: honesty. I tried to gently emphasize straight lines in Patria (like having a short straight segment at the tip of the nose of the “e”) and I think without that it would be less focused and more boring.

Aziz, those petal puzzles are great.

hhp