Additional Math Pages & Resources

Wednesday, September 21, 2011

What number am I thinking of? Part II

Yesterday I was wondering at our ability to recognize numeral shapes (numbers) in so many different fonts and handwriting styles. Here are 3 fours. I mean three 4s. You can see the variations. Our eyes and brains decide these are all the same shape anyway, ignore the differences, AND determine that they are equivalent to IIII.

I can only imagine the complexity of the tasks that our brains manage when we deal with numbers on a page. It's a wonder that our young students can do this at all - don't be frustrated if your child struggles to process things you take for granted.

I found an information-packed document from FontShop that labels some of the visual aspects of characters. Be sure to check out the education section of their website if you are interested in learning more about fonts.

Here are things your eye notices, but you might never have known about the vertical dimensions of characters (numerals):
  • Ascender is the top of a lowercase character (the topmost point of l)
  • Baseline is where your numerals "sit"
  • Caps Height is the height of the uppercase characters (the height of L)
  • Descender is the bottom of a lowercase character (the bottom point of q)
  • x-Height is the height of lowercase characters, like v
Here are things your eye notices, but you might never have known about the horizontal dimensions of characters (numerals):
  • Compressed, Condensed and Expanded are relative degrees of width of a character
  • Italic characters are shaped more like handwriting, and may be slanted
  • Light, Regular, Bold and Black are relative degrees of weight of a character
  • Oblique characters are slanted, usually with the top to the right of the base; similar to italic
  • Roman is the upright style of characters; NOT slanted
  • Sidebearings (inner and outer) are the white spaces (attached or belonging to the character) on each side of the strokes
  • Weight is the thickness of the lines that make up the characters
  • Width is how wide the characters are. The widest character is an "m"
Not all dimensions concentrate on the strokes that make up the characters themselves. We need white space between the numerals in order to read them quickly and accurately.
  • Kerning is the space between specific pairs of characters; usually adjusted by hand  
  • Tracking is the spacing between characters, words or numerals on a line or in a block of text
  • Leading is the distance between baselines in a block of text
How do you determine the size of a font? This is too complicated to cover in depth, so let's just say:
  • Font size describes the vertical baseline-to-baseline distance for which a font was designed. Fonts are chosen by size, because baseline distance is more relevant for layout design than dimensions of specific characters.
  • Font height is the height in mm of tall letters such as k or H. The font height is often about 72% of the font size, but it can vary.
Amazingly complex, isn't it?  This is why we teach kids mathematics, so they can understand the numbers about numerals!

When you draw characters by hand, you can expand or squeeze them any way you like. But printers, typographers, web designers, etc. have to measure the size of the characters. That should be simple, right? Wrong. These guys use units called picas and points, but alas, not all points and picas are the same:
  • 1 point (Didot) = 0.376 mm = 1/72 of a French royal inch (27.07 mm)
  • 1 point (ATA) = 0.3514598 mm = 0.013837 inch
  • 1 point (TeX) = 0.3514598035 mm = 1/72.27 inch
  • 1 point (Postscript) = 0.3527777778 mm = 1/72 inch
  • 1 point (l’Imprimerie nationale, IN) = 0.4 mm
  • 1 pica (ATA) = 4.2175176 mm = 12 points (ATA)
  • 1 pica (TeX) = 4.217517642 mm = 12 points (TeX)
  • 1 pica (Postscript) = 4.233333333 mm = 12 points (Postscript)
  • 1 cicero = 4.531 mm = 12 points (Didot)