Which alphabet letters are convex polygons?

Answer 1

A convex polygon is defined as a polygon whose interior is a convex set.

The definition of a convex set is that for any two points x, y from the set the line connecting them must not leave the set (the polygon, in our case).

For instance the letter I (capital i) is a simple rectangle in many fonts, which is convex (pick any two points in a rectangle and connect them, you will never leave the rectangle).

The character T (capital t) is composed of two rectangles in many fonts, which is not convex at all (just pick a point at the top left and one at the bottom center, the line connecting them will leave the shape).

Now you should be able to see that almost no characters are convex, the following can be eliminated right away:

• all fonts with serifs: the little details attached to the line endings cause problems
• all characters that consist of multiple shapes (i, j, !, %, etc.), you can always pick point x in the first shape, point y in the second shape and the connecting line will offend the convexity criterion
• all characters with holes in them (a, b, d, o, etc.), simply chose a point "left and right" of the hole.

And here is a list of commonly used characters and symbols that are convex at least in some fonts:

• I (capital i)
• l (lowercase L)
• - (minus)
• _ (underscore)
• . (dot)
• /, \ (slash, backslash)
• `, ´, ' (gravis, acute, tick)
• , (comma)

Answer 2

Is L concave or convex