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preface to fifteenth edition

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2.110 SECTION 2<br />

Regular Polygon of n Sides (Fig. 2.1)<br />

1 180<br />

2<br />

A na ctn where a is lengthof side<br />

4 n<br />

a 180<br />

R csc where R is radius of circumscribed circle<br />

2 n<br />

a 180<br />

r ctn where r is radius of inscribed circle<br />

2 n<br />

360 2<br />

radians<br />

n n<br />

<br />

<br />

n 2 n 2<br />

· 180 radians where and are the angles indicated in<br />

n n Fig. 2.1<br />

<br />

a 2r tan 2R sin<br />

2 2<br />

FIGURE 2.1<br />

Circle (Fig. 2.2).<br />

Let<br />

C circumference<br />

R radius<br />

D diameter<br />

A area<br />

S lengthof arc subtended by <br />

l chord subtended by arc S<br />

h rise<br />

central angle in radians<br />

C 2R D 3.14159 ...<br />

1<br />

1<br />

S R ⁄2D D cos<br />

d<br />

R<br />

<br />

l 2 R2 d2<br />

p 2R sin 2d tan<br />

2 2<br />

<br />

1 2 2<br />

d ⁄2 4R l R cos 1<br />

p<br />

⁄2l ctn<br />

2 2<br />

h R d<br />

FIGURE 2.2<br />

S 2S d l l<br />

1 1 1<br />

2 cos 2 tan 2 sin<br />

R D R 2d D<br />

A (circle) R2 1⁄4D2<br />

A (sec<strong>to</strong>r) 1⁄2Rs 1⁄2R 2<br />

A (segment) A (sec<strong>to</strong>r) A (triangle) 1⁄2R 2<br />

( sin )<br />

R h<br />

R cos (R h) p2Rh h<br />

R<br />

2 1 2

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