squared | | |
| | | |
| _____ | | |
| \/ [pi] | 1.7724539 | 0.2485750 |
| | | |
| _____ | | |
| \ cubed/ [pi] | 1.4645919 | 0.1657166 |
| | | |
| | | |
| 1 | | |
| -------- | | |
| _____ | 0.5641896 | 1.7514251 |
| \/ [pi] | | |
| | | |
| 2 | | |
| -------- | | |
| _____ | 1.1283792 | 0.0524551 |
| \/ [pi] | | |
| | | |
| 1 | | |
| ---------- | | |
| _____ | 0.2820948 | 1.4503951 |
| 2 \/ [pi] | | |
| | | |
| _____ | | |
| / 6 | | |
| \ cubed/ ---- | 1.2407010 | 0.0936671 |
| V [pi] | | |
| | | |
| ______ | | |
| / 3 | | |
| \ cubed/ ------- | 0.6203505 | 1.7926371 |
| V 4 [pi] | | |
| | | |
| log e [pi] | 1.1447299 | 0.0587030 |
+--------------+-----------+-----------+

Useful fractional approximations are 22/7 and 355/113.

A synopsis of the leading formula connected with the circle will now
be given.

1. _Circle._--Data: radius = a. Circumference = 2[pi]a. Area = [pi]a squared.

2. _Arc_ and _Sector_.--Data: radius = a; [theta] = circular measure
of angle subtended at centre by arc; c = chord of arc; c2 = chord of
semi-arc; c4 = chord of quarter-arc.

Exact formulae are:--Arc = a[theta], where [theta] may be given
directly, or indirectly by the relation c = 2a sin 1/2[theta]. Area of
sector = 1/2a squared[theta] = 1/2 radius x arc.

Approximate formulae are:--Arc = (1/3)(8c2 - c) (Huygen's formula);
arc = (1/45)(c - 40c2 + 256c4).

3. _Segment._--Data: a, [theta], c, c2, as in (2); h = height of
segment, i.e. distance of mid-point of arc from