# CS8, 10F, H03, due Tue Lecture 10.05—Miller/Ranum 2.1-2.5 (thru p. 45-61).—Total points: ?

 Name: (4 pts) Umail Address: (4 pts) @umail.ucsb.edu
 Lab Section (2 pts)—circle one: 9am 10am 11am noon unknown crashing
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(For more details, see the syllabus and the homework policy)

Reading: Read Chapter 2, pages 45-61 (Sections 2.1 through 2.5) Then, answer the following questions. Be sure to check both sides.

1. (3 pts) What is the definition of pi?

2. (3 pts) According to what is known to mathematicians today, can the exact value of pi ever be represented with a finite number of digits?

3. (5 pts) This chapter describes three ways of computing approximations of pi—the first of which is described in Section 2.4. Try to understand the basic idea behind this approach to computing the circumference of a circle with a known radius—then, imagine you are trying to explain it to someone in plain english, say, your roomate or your grandmother.

What is the basic idea of this technique? (Don't get lost in the details—just focus on the big picture.)

...continued from other side

1. (4 pts) Section 2.5.2 describes a different approach—one based on a formula that "goes on forever". We approximate pi by summing up just a finite number of terms of this formula—knowing that the terms we "left out" are going to result in some small amount of inaccuracy.

If you add together the first four terms of the Leibniz formula from p. 56, what is the resulting sum?

 Listing 2.2 on page 52 contains a function definition. (3 pts) What is the name of the function being defined? (3 pts) What is the name of the parameter of the function being defined? (3 pts) What is the value that is returned by the function being defined? (4 pts) What is the purpose of typing import math at the top of a Python file, or as the first command in a session in Python? (4 pts) If you have assigned a floating point value to the variable x, what do you type at the Python prompt to display the square root of x? (4 pts) In the code in Listing 2.3 on p. 58 of the textbook, there is a line acc = 0.0 Obviously, this line assigned the variable acc to the value zero (as a floating point number). What I want you to tell me is why? In the context of this program, why are we setting acc to zero? (4 pts) (Continued from the previous problem). We set acc to zero at the start of listing 2.3. At the end of the function, we see the statement return acc. Will the value of acc still be zero at that point? If not, explain what value acc will have. (You'll need to read the text around the listing to learn this.)

End of H03