Assignment 41
"The mathematician is fascinated with the marvelous beauty of the forms he constructs, and in their beauty he finds everlasting truth."  (J. B. Shaw, Mathematical Maxims and Minims, 1988)
Girolamo Cardano (15011576): Born in Italy, Cardano was an unprincipled mathematical genius whose greatest work, Ars Magna , is one of the most important treatises ever written on algebra. During his turbulent life he was imprisoned for heresy because he published a horoscope of Christ's life. A frequent gambler, he was eventually to become known as a founder of probability theory. He became involved in a famous dispute with another Italian mathematician, Niccolo Tartaglia of Brescia (14991577) over the discovery of solution methods for cubic equations. Both men contributed much to the development of mathematics.

What does Herkimer call a crazy man who inflates balloons?
Answer: A balloonatic.
Herky's friends:
PETER DOUT...this guy usually gets tired very quickly.
NICK O'TEEN ...a nice guy with a bad habit. 
ASSIGNMENT #41
Reading: Section 6.9, pages 380383.
Written: No problems from book.

Mathematical word analysis: MILLION: Related to the Latin mille, meaning thousand. It literally means "great thousand." Italian mathematician Luca Paciola (14451515) was the first to use the word million in published writings. 
A cubic polynomial has the form y = f(x) = ax^{3} + bx^{2} + cx + d.
Note that values of a, b, c, and d are needed to identify a specific polynomial. Basically, four noncollinear points determine a cubic polynomial. Consider the points (1,0), (0,3), (1,0), and (3,0). If you put the xvalues in list L1, and the yvalues in list L2, and then do a cubic regression computation, you will find a = 1, b = 3, c = 1, and d = 3, with R^{2} = 1. The cubic function that contains the four given points is y = x^{3}  3x^{2}  x + 3.
Problem: Fit a polynomial model to the data displayed in the table.
x 
1 
2 
3 
4 
5 
6 
y 
4 
1 
10 
26 
54 
76 
Solution (with communication):
If you use cubic regression, you will find that the cubic polynomial function
y = 0.324x^{3} + 6.278x^{2}  13.970x + 4.667
fits the data set quite well, with R^{2} = 0.99639
For this data set, a quadratic polynomial function
y = 2.875x^{2}  3.696x  3.5
is also a good fit, with R^{2} = 0.99505.

