Typography & The Fibonacci Sequence Leonardo Fibonacci, or, most commonly, simply Fibonacci, an Italian mathematician, considered by some the most talented western mathematician of the Middle Ages.

I received a question from one of my typography students today asking about the mathematics of the Fibonacci Sequence and it is applied in the use of setting type.

Hello Mike, I am busy studying for the exam and have a question about the math connected to the Fibonacci Sequence. I understand the sequence of numbers but my notes say that there is a way to determine the header size for 11 point copy and I don’t understand how that works. Please help.
(I wanted to post my explanation here as a little example of typographic snack for friends and clients. So, this is how I responded below.)

If I needed a header size to accommodate my 11pt body copy and wanted to use the Fibonacci model, I would do the math as such;

Fibonacci Sequence = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…

First, take two of the numbers in the sequence, here I am using 8 and 13, and insert x to determine the header size;

8/13 x 11/x = 17.875 or 18

I simply took two of the corresponding sequence numbers and used them to find my header size. So another look at the math would be;

13 x 11 ÷ 8x = 17.875 = x (header size)
(143 ÷ 8 = 17.875)

So my body copy, if at 11pt, would have an accommodating header size of 18pt. Or, two different numbers in the sequence will also yield the same answer;

55 x 11 ÷ 34x = 17.8 = x (header size)
(605 ÷ 34 = 17.8 or 18)

You can also apply the math to determine your leading for the 11pt body copy. But remember, type is always a relative measurement which is why your eye needs to be trained to know what looks appropriate for the size and leading proportions. I wouldn’t want you to use the exact measurement of 17.875 or 17.8 lead to an 11pt type size. I want you to see what 11/15, 11/18, 11/21 and 11/24 looks like before you choose the right combination for your layout.

Also, your type size would have to do with the width of your measure (column width) as well. If you’re eyeing up an 11pt type size, you must have your measure in the vicinity of 22 picas in width (2 to 2.5 times the width of the type size in picas, is the rule-of-thumb). You will still, in the end, determine the type proportions based on sight but the start of your journey in arriving at a type size over lead ratio should start with the math.

One Comment to Typography & The Fibonacci Sequence

• anonymous Mar 20, 2013 at 3:57 pm

How do you do when you have to define not 1, but 4 level of headings for a 11 pt font size?