ression, being of the nature of an incommensurable
number. Very early in the history of geometry it was known that the
circumference and area of a circle of radius r could be expressed in the
forms 2[pi]r and [pi]r squared. The exact geometrical evaluation of the second
quantity, viz. [pi]r squared, which, in reality, is equivalent to determining a
square equal in area to a circle, engaged the attention of
mathematicians for many centuries. The history of these attempts,
together with modern contributions to our knowledge of the value and
nature of the number [pi], is given below (_Squaring of the Circle_).

The following table gives the values of this constant and several
expiessions involving it:--

+--------------+-----------+-----------+
| | Number. | Logarithm.|
+--------------+-----------+-----------+
| [pi] | 3.1415927 | 0.4971499 |
| 2 [pi] | 6.2831858 | 0.7981799 |
| 4 [pi] |12.5663706 | 1.0992099 |
| (1/2) [pi] | 1.5707963 | 0.1961199 |
| (1/3) [pi] | 1.0471976 | 0.0200286 |
| (1/4) [pi] | 0.7853982 | 1.8950899 |
| (1/6) [pi] | 0.5235988 | 1.7189986 |
| (1/8) [pi] | 0.3926991 | 1.5940599 |
| (1/12) [pi] | 0.2617994 | 1.4179686 |
| (4/3) [pi] | 4.1887902 | 0.6220886 |
| | | |
| [pi] | | |
| ------ | 0.0174533 | 2.2418774 |
| 180 | | |
| | | |
| 1 | | |
| ------ | 0.3183099 | 1.5028501 |
| [pi] | | |
| | | |
| 4 | | |
| ------ | 1.2732395 | 0.1049101 |
| [pi] | | |
| | | |
| 1 | | |
| ------ | 0.0795775 | 2.9097901 |
| 4 [pi] | | |
| | | |
| 180 | | |
| ------ |57.2957795 | 1.7581226 |
| [pi] | | |
| | | |
| [pi] squared | 9.8696044 | 0.9942997 |
| | | |
| 1 | | |
| -------- | 0.0168869 | 2.2275490 |
| 6 [pi]