Mathematics in Colonial America

Date: 11/10/97 at 11:59:15
From: Dylan Hartwell
Subject: Math/History Lesson Plans

Dr. Math,

I am a college student at Miami University in Oxford, Ohio working on 
a Colonial America lesson plan. I am required to do a mathematics 
lesson in this area, but am at a loss at how to incorporate pragmatic 
mathematic lessons into a early America lesson. I realize that this 
may be beyond your realm, but would appreciate any suggestions you
could offer.

Thank you,
Dylan Hartwell

Date: 11/10/97 at 14:10:51
From: Doctor Tom
Subject: Re: Math/History Lesson Plans

Hi Dylan,

Here's an idea.

Take a look at printing. It's interesting from a statistical point
of view, since if you're a printer ordering a bunch of lead type to
set pages of your newspaper, what's the appropriate ratio of the
various letters to order? Clearly you're going to use a lot more e's 
than z's, but how many more? Printers had to know the relative
frequencies of letters for this, and that in order, the most common
letters in English are e,t,a,o,i,n,s,...

Various different cases for holding type were designed, and if you
look at what's called a "California Case," you'll note that there are
different-sized slots for the different letters. The slot for lower-
case e is largest, et cetera.  Also note that the more heavily used 
slots are close together, so a typesetter doesn't have to move his 
hands much. The oddball characters - z, k, q, ... - are in tiny slots 
around the edge.  The letters e, t, h, i, ... are grouped together.  

There's one other interesting thing about the slot sizes - the letter 
"i" although it is common doesn't need as big a slot as you'd think
because the "i" is such a tiny letter. The "w" slot is bigger than
you'd think because although it's an uncommon letter, there's a lot
of lead in each "w".

Another interesting thing about printing type is the spaces. To make
fully justified text, you need to be able to adjust the spaces between
words in a nice way. Typical type spaces came in various thicknesses -
an "em" space is the width of a lower-case "m". An "en" space is one
half the width of an "em" space. Then there are 3-em, 4-em, 5-em, and 
sometimes 6-em spaces that are, respectively, 1/3 em, 1/4 em, 1/5 em, 
and 1/6 em in width. Of course, a printer could use combinations to 
make wider or narrower spaces - a 1/5 em and a 1/6 em is a tiny bit 
less than a 1/3 em. By adding the various combinations of widths (lots 
of fraction addition here), it's interesting to see what the range of 
possible space widths was.

Good luck.

-Doctor Tom,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/