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/
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