I was a bit surprised to read that Wikipedia describes matra
as a horizontal line. This probably refers to the headstroke itself, and the only term I've seen for that is shirorekha
. If you do a web search for "Devanagari matra", you'll quickly get a provision of links that point to the usual meaning, the various signs for vowels, nasality, and extra consonants. In the French Wikipedia article on Devanagari there is a nice illustration of all these signs, where they are clearly described as matras
A good place to illustrate the standard stroke orders is here:http://commons.wikimedia.org/wiki/Categ ... roke_order
If all the gifs don't display a moving image of the letters being drawn, then you'll have to click on each individually. You can see how in all the letters with a headstroke, the head stroke is drawn last. I think they are taught this way because at this stage people are concentrating on individual letters and not on writing words as a whole. But as you can see in the ITF images, nobody
writes the headstroke separately over each individual letter.
As for the non-cursive appearance of Devanagari, the Devanagari we know has always been a formal script variety. Over five centuries ago, people already used informal handwriting varieties where they formed the letters much more loosely, writing the headstroke first, shortening it to a short dash at the top left of the letter and later on even dropping it, joining strokes loosely by "stretching" parts of the body of the letter together or up to the headstroke or by drawing transitional strokes instead of lifting the reed/pen, and making a smooth curve joining the body of the letter to the top of the stem on the right, instead of a sharp, clear join near the middle of the stem.
These cursive, informal ways of writing Devanagari gradually evolved into distinct regional and mercantile scripts across northern India, like Baniauti, Sarrafi, Mahajani, Kayathi and so on, some of which developed into distinct regional scripts like Kaithi, Modi, Sylhet Nagori and Gujarati (reincorporating formal elements from Devanagari along the way.) Meanwhile Devanagari remained the formal, traditionalist writing style that had taken its basic shape about millennium ago. It was the script associated with Hindu religious texts and partly because of this fact, a politico-religious movement in the 19th century campaigned, in most cases successfully, to replace regional scripts with Devanagari as a symbol of "Hindu-ness" and a single Hindu Indian identity. Gujarati is about the only descendant of informal cursive Devanagari that survived this script replacement policy.
So that's basically why Devanagari has no real cursive style: the cursive styles that developed naturally over the centuries were essentially wiped out and replaced by a stilted, formal style. It's as if ordinary cursive Latin script styles were replaced by a book style where everyone was taught to form their letters exactly as they appear in typographic printing, including the unusual printed shapes for g and a, and to make sure to write all the serifs "correctly".