created 01/01/03

Exercise 1

Rewrite the TriangleTester program described in the chapter so that the user is asked for N and that the value entered is tested to make sure it is positive.

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Exercise 2

Rewrite TriangleTester so that Triangle() is a static method of that class. Eliminate the TriangleCalc class. (Include user input from exercise 1, if you want.)

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Exercise 3

Write a program that implements this definition of square numbers:

square(1) = 1
square(N) = square(N-1) + 2N -1

Make a complete program similar to TriangleTester.java given in the chapter.

Aside: where did this crazy definition of square come from?

Easy: this is just algebra:

(N-1)² = N² - 2N + 1

rearrange to get:

N² = (N-1)² + 2N - 1

Another way to think of this is a square number give the total number of pins in a square arrangement of pins with N pins on a side. Draw a square with four dots (pins) on a side. Then expand the square so that it has five dots on a side. Using your picture, explain why the recursive definition of square numbers is correct.

Square numbers are also mentioned in the quiz for this chapter.

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Exercise 4

Write a program that implements this definition of log for positive integers N:

log(1) = 1
log(N) = 1 + log(N/2)

Use only integer math for this.

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