Mathematic Symbols Part 3:
Radical Calculus

The last post, Part 2, includes comparative symbols, degree, percent, and fraction slash: > < ≤ ≥ ° % and ⁄. This time, in Part 3, I’m covering the radical, integral, partial derivative, and infinity signs (√ ∫ ∂ ∞).

Radical

The radical ( √ ) is basically a check mark. It has a funny little bit hanging off the top (left) end of the downstroke. The beginning of the radical starts below the x-height. The glyph sometimes sits on the baseline, and sometimes dips below.

The radical always rises higher than ascender height. This is in order to overshadow the figures that follow it. When it needs to be clear that the radical applies to a whole series of figures, a vinculum is attached to it (not part of this font).

The angle of the upstroke doesn’t seem to have much relation to the slash. It’s often close, but not the same. The weight, however, is the same as the slash.

Integral

The integral ( ∫ ) is related to the long s. The terminals can be ball terminals or abrupt terminals. In order to match this typeface, the terminals on the ∫ in Protest are abrupt.

The integral is 1 em high, the same as the em dash is long. The top is well above the ascender height (for the same reason as the radical), and the bottom dips below the baseline, but not down to the descender line.

Integral isn’t necessarily straight up and down. The spines of some lean back slightly (like the spine of an s) and some lean forward slightly. Whether and how much it leans depends on the typeface and what looks good. Protest’s integral leans forward just slightly, about 1.5°.

The weight of the integral is about the same as the slash, and just a little thicker in the middle in instances when there is some stroke contrast. This is the case in Protest, and it has a bit of weight to harmonize with the other glyphs in terms of typographic color.

Paritial Derivative

The partial derivative (∂), or partial dee, is a stylized d. It has nothing to do with the Greek lowercase delta. It is a little closer to an italic d. It is similar to a backward 6, but is not formed the same way. Basically, it’s kind of weird, and one has to look at standard examples to figure out form.

Form varies fairly widely from typeface to typeface. In some the stroke weight is thicker on just the left side of the bowl. In others it’s thicker both there and along the right side.

So basically, there’s an assumption on the one hand that the form is drawn in a single looping stroke starting at the join and ending at the upper terminal. Then on the other hand that the form is drawn with two strokes, one from the join moving counterclockwise to the bottom of the bowl, and the other from the upper terminal down to the bottom of the bowl. Protest uses the latter assumption.

Infinity

Infinity (∞) is not a sideways 8. The top of the 8 is smaller than the bottom, whereas the sides of the ∞ should be equal, though they aren’t in many cases.

Some argue that the stroke sloping downward from left to right through the middle should be the downstroke (the thicker stroke), and in many instances this is not the case. However, whether the left–to–right or right–to–left sloping stroke is the downstroke all depends on which direction the glyph is drawn.

The infinity symbol is smaller than the 8, as well as a lighter stroke, so that the overall color of the glyph harmonizes with the rest of the typeface. It should be about as wide as a lowercase m, and the intersection in the middle is about as wide as the lowercase downstroke.

It should be vertically spaced at visual center to the figures, or at least above the level of the minus. Protest has its ∞ a bit lower than center, but still higher than the minus.

Up Next

The final post in this series will cover the sum, product, and change signs, as well as pi.

• Mathematic Symbols
  1. + − ± × ÷ = ≠ ≈
  2. > < ≤ ≥ % ° ⁄
  3. √ ∫ ∂ ∞
  4. ∑ ∏ Δ π
• Diacritics