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double pi = 3.14159265358979323846; tout << "pi = ' << pi -CC endl; cout.precision(l6); tout << 'pi = ' c-c pi << endl; tout C-K 'pi = " << pi << endl; cout.precision(20); tout CC "pi = ' << pi C=C endl;

360 1. Each central angle c measures n . (n 2)180 2. Each interior angle i measures . n 360 3. Each exterior angle e measures n .

(Continues on next page)

Pi =- 3*14259

Thus for the regular pentagon ABCDE of Fig. 10-2, m/AOB and m/ABS 360 n 360 5 72 m/ABC m/ABC m/ABS (n 180 2) 180 n (5 2) 180 5 108

pi. 22 3,141592453589793 pi = 3.1415~~Z6535897~3 pi = 3.242592653589793116 -

Fig. 10-2

. . ._.'.. : ."' .%_ . r, '::_. . . .*,. _' . :.:.. ._ '.' ', . '.:: .: '_ .:

10.1 Finding measures of lines and angles in a regular polygon (a) Find the length of a side s of a regular pentagon if the perimeter p is 35. (b) Find the length of the apothem a of a regular pentagon if the radius of the inscribed circle is 21. (c) In a regular polygon of five sides, find the measures of the central angle c, the exterior angle e, and the interior angle i. (d) If an interior angle of a regular polygon measures 108 , find the measures of the exterior angle and the central angle and the number of sides.

The default value for the _prec data member is 6. This means that floats will be displayed using 6 dig- its, as the first output of pi shows. Changing that to 16 causes tout to print 16 digits. That is the maximum number of digits that type double can store (on a 32-bit machine), so increasing it to 20 only results in garbage digits after the 16th. Note that, unlike the -f i 11 and w i d t h parameters, the precision parameter does not revert back to its default value after the next output. 12.3 ios FORMAT FLAGS

The width, precision, and fill parameters for a stream object are implemented with separate data members because each parameter can have more than two values. For example, any letter of the alphabet could be the fill character. But streams have many other attributes which are Boolean; i.e., their value is either true or false. These are the parameters that are listed in the first enum definition above, and are summarized in Table 12.1 below. All 15 of these flags are packed into the single data member - flags. The next example illustrates one way to change a stream s format flags.

Fig. 10-3

main0 -t int n = 234; long oldf = cout.flags( ios::hex I ios::uppercase >; tout << n << endl; cout.flags( ios::hex I ios: :showbase >; tout << n CC endl; cout.flags(oldf); tout << n << endl; >

CHAP. 8]

(b) Since an apothem r is a radius of the inscribed circle, it has length 21. (c) n (d) m/i 5. Then m/c 360 n 360 5 72 ; m/e 360 n 72 ; m/i 360 n ,n 180 m/e 108 .

. . .,

5. (See Fig. 10-3.)

_: " ., ,.'.., : . ., .:,(._i. :,. , . . .. iZ -.-:

Proving a regular-polygon problem stated in words Prove that a vertex angle of a regular pentagon is trisected by diagonals drawn from that vertex.

The first call to tout . flags ( ) sets the hex and uppercase flags, while saving all the previous settings in oldf. Notice that the hexadecimal form for the integer 234 is ea, which is printed EA because the uppercase flag is set. (See Appendix H for more information on hexadecimal numerals.) The second call to tout. flags () sets the hex and showbase flags, causing all other flags to be cleared, so that the second output prints the hexadecimal letters for n in lowercase and with the leading OX to show that the numeral is hexadecimal. The third call to tout . flags ( ) restores the original .( default) settings. Table 12.1 Format Flags