By Diane N. Palmer
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Extra info for A Teacher's Guide to The Struggle against Slavery: A History in Documents (Pages from History)
Take a square and make creases by folding it in half vertically and folding one diagonal, as shown. Then make a crease that connects the midpoint of the top edge and the bottom right-hand corner. P Question 1: Find the coordinates of the point P, where the diagonal creases meet. ) Question 2: Why is this interesting? What could this be used for? Question 3: How could you generalize this method, say, to make perfect 5ths or nths (for n odd)? HANDOUT Folding Perfect Thirds It is easy to fold the side of a square into halves, or fourths, or eighths, etc.
001 . )2 . 075 left over. This is bigger than 1/16, so the fourth digit is a 1. 0125 left. This is smaller than 1/32 and 1/64. But wait, 1/80 = (1/5)(1/16) and we got 1/80 after removing the 1/16 term from it. This means that if we factor out a 1/16 from our 1/80 remainder, we get 1/5 and we’re back to where we started! 0011)2 . In Question 2, we know that in Fujimoto’s method to make 1/5ths, we had to fold the right side twice and then the left side twice. So we folded the sequence Right, Right, Left, Left.
The second line does the same for the second pinch, and so on. As you can see, the right side starts at 6 and comes back to 6 after only 3 lines. So it doesn’t make all 1/7ths pinch marks. 7ths 7ths left right 1 6 4 3 2 5 1 6 Assignment: Make similar tables for 1/5ths, 1/9ths, 1/11ths, and 1/19ths: 5ths 5ths left right 1 4 9ths 9ths left right 1 8 11ths 11ths left right 1 10 19ths 19ths left right 1 18 Question 7: Think about what these tables are telling you in the number system Z n (the integers mod n) under multiplication, where n is the number of divisions.
A Teacher's Guide to The Struggle against Slavery: A History in Documents (Pages from History) by Diane N. Palmer