Circle

A m area, ╥ {pi) = 3.1416.

╥/4= .7854 p = perimeter or circumference.

p = ╥d = 3.1416 d.

p = 3 1/7 d (approximately).

p = 2╥r = 6.2832r.

d = P/╥ = p/3.1416 d = 7/22 p (approximately). d = l.l28√A r=p/2╥ = p/6.2832 r = .5642√A

A =╥d2 = .7854d2.

A = ╥r2 = 3.1416 r2.

Circle 159

Side of square of area equal to circle = .8862 d. Diameter of circle of area equal to a given square = 1.128 X side.

Circle 160

Ring

Area = .7854(D2 -d2).

Sector

If radius r and rise h are known, chord c

Sector 161

If chord c and rise h are known,

radius r =(c2 + 4h2)/8h

Approximately, r = c2/8h.

Subchord e =

Sector 162Sector 163

If h is not more than .4 c, length of arc l= (8e-c)/3, nearly. If l and r are known,

Angle E* = 57.296(l/r),

= 57.3(l/r), nearly.

Area = 1/2 lr.

If r and angle E* are known.

length l=Er/57.296=Er/57.3, nearly.

= .0175 Er. Area = .0087r2E.

Segment

Area of segment = area of sector - area of triangle.

Height of triangle = r - h. If I, r, c, and h are known,

Area = 1/2 lr - 1/2 c(r- h). If c, h, r, and E are known, find I as shown under Sector; the area may then be found by the preceding formula.

Segment 164

Ellipse

Ellipse 165

Area = .7854 Dd.

Ellipse 166

*If the angle E contains minutes and seconds, these must be expressed in decimals of a degree. Divide the minut-60, and the seconds (if any) by 3,600, and add the sum of the decimals to the degrees; thus. 30°45'36"= 30° + 45/60 + 36/3600 =30.76°. If E is given in degrees and decimals, it may be reduced to minutes and seconds thus, .76°= .76° X 60' = 45.6'; .6' X 60" = 36"; hence, 30.76° = 30° 45' 36".

† The perimeter of an ellipse cannot be exactly determined, and this formula is merely an approximation giving fairly close results.

Helix

d = diameter of helix;

I = length of 1 turn of helix; t = pitch, or rise in 1 turn; n = number of turns;

╥2= 9.8696.

I = Helix 167 t =

Total length = nl = Helix 169

Helix 170