The History of Trigonometry - Macalester College

[Pages:43]TheHistoryof Trigonometry

David Bressoud Macalester College, St. Paul, MN

NorthHennepinCommunityCollege BrooklynPark,MN March30,2011

Theseslidesareavailableat macalester.edu/~bressoud/talks

"The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them. In this regard, the history of science must be our guide."

Henri Poincar?

1854?1912

OldBabylonianEmpire,2000?1600BCE

PrincetonUniversityPress, 2008

Plimpton322(ColumbiaUniversity),tableof Pythagoreantriples,circa1700BCE,about9by13cm

Mathematical Association of America, 2004

B

C

A

SimplePythagoreantriples:

32 + 42 = 52 52 + 122 = 132 82 + 152 = 172

B

C

A

A 119 3367 4601 12709 65 319 2291 799 481 4961 45 1679 161 1771 28

B 120 3456 4800 13500 72 360 2700 960 600 6480 60 2400 240 2700 45

C 169 4825 6649 18541 97 481 3541 1249 769 8161 75 2929 289 3229 53

The difference between the square of side X+Y and the square of side X?Y is four rectangles of size XY.

( X + Y )2 - ( X - Y )2

= 4 XY

If XY = ?, then (X + Y)2 and

(X ? Y)2 differ by 1.

X ? Y X+ Y

X = 6 5, Y = 5 24

Y

6? 5 =1

5 24 4

6 - 5 = 119 , 5 24 120

X

6 + 5 = 169

5 24 120

169 120

2

-

119 120

2

=

1

1692 = 1192 + 1202

B

C

A

A 119 3367 4601 12709 65 319 2291 799 481 4961 45 1679 161 1771 28

B 120 3456 4800 13500 72 360 2700 960 600 6480 60 2400 240 2700 45

C 169 6/5,5/24 4825 32/27,27/128 6649 75/64,16/75 18541 125/108,27/125 97 9/8,2/9 481 10/9,9/40 3541 27/25,25/108 1249 16/15,15/64 769 25/24,6/25 8161 81/80,20/81 75 1,1/4 2929 24/25,25/96 289 15/16,4/15 3229 25/27,27/100 53 9/10,5/18

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