How Math Explains the World.pdf

analysts, defined by f(x) 0 if x is rational and f(x) 1 if x is irrational, can be

calculated for every valuable of the variable. This function is highly artificial, as

it never shows up in any process related to the real world.

3. A. B. Chace, L. S. Bull, H. P. Manning, and R. C. Archibald, The Rhind Mathe-
   matical Papyrus (Oberlin, Ohio: Mathematical Association of America, 1927–29).
   A good description of this method, known as the method of false position, can
   b e f o u n d a t h t t p : / / w w w - g r o u p s. d c s. s t - a n d. a c. u k / ~ h i s t o r y / H i s t T o p i c s / E g y p t i a n _
   papyri .html.


4. An example of solving an equation by completing the square is

x^2 
 4 x
 5  0

x^2 
 4 x 5

x^2 
 4 x 4  5 4 (the “completing-the-square” step)

(x
2)^2  9

x
 2  3 or 
 3

x 5 or x
 1

5. W. Dunham, Journey Through Genius (New York: John Wiley & Sons, 1990).


6. A s q u o t e d a t h t t p : / / w w w - h i s t o r y. m c s. s t - a n d r e w s. a c. u k / B i o g r a p h i e s / C a r d a n. h t m l.


7. G. Cardano, Ars Magna (Basel, 1545).


8. Ibid.


9. A s q u o t e d a t h t t p : / / w w w - g r o u p s. d c s. s t - a n d. a c. u k / ~ h i s t o r y / B i o g r a p h i e s / R u f f i n i
   .html.


10. Carl B. Boyer, A History of Mathematics (New York: John Wiley & Sons, 1991),
    p. 523.


11. Quoted in F. Cajori, The Teaching and History of Mathematics in the United States
    (Whitefish, MT: Kessinger Publishing, 2007).


12. The geometric series with ratio r is the infinite sum 1 rr^2 r^3 ... ; hyper-
    geometric series generalize this series. A more extensive discussion of this topic
    can be found at http:// en .wikipedia .org/ wiki/ Hypergeometric _functions, but
    unless you plan on a career that requires a substantial knowledge of advanced
    mathematics, you can skip this discussion.

100 How Math Explains the World