- The boundary line of a circle.
- The boundary line of a figure, area, or object.
- (Abbr. c or circ.) The length of such a boundary.
[Middle English, from Old French circonference, from Latin circumferentia, from circumferēns, circumferent-, present participle of circumferre, to carry around : circum-, circum- + ferre, to carry.]
circumferential cir·cum'fer·en'tial (-fə-rĕn'shəl) adj.SYNONYMS circumference, circuit, compass, perimeter, periphery. These nouns refer to a line around a closed figure or area: the circumference of the earth; followed the circuit around the park; stayed within the compass of the schoolyard; the perimeter of a rectangle; a fence around the periphery of the property.
is the ellipse's 
![\begin{align}\mbox{E2}\left[0,90^\circ\right]&= \mbox{Integral}'s\mbox{ divided difference};\\ Pr&=a\times\mbox{E2}\left[0,90^\circ\right] \quad(\mbox{perimetric radius});\\
c&=2\pi\times Pr.\end{align}\,\!](http://wpcontent.answers.com/math/9/3/9/939fc8fb907ae4e20a48f3fee43e4767.png)
![\mbox{E2}\left[0,90^\circ\right]](http://wpcontent.answers.com/math/e/1/f/e1fe981c9404c5671af2545dd0739605.png)
based series expansion is used to find the actual value:![\begin{align}\mbox{E2}\left[0,90^\circ\right]
&=\cos^2\!\left(\frac{o\!\varepsilon}{2}\right)\frac{1}{UT}\sum_{TN=1}^{UT=\infty}{.5\choose{}TN}^2\tan^{4TN}\!\left(\frac{o\!\varepsilon}{2}\right),\\
&=\cos^2\!\left(\frac{o\!\varepsilon}{2}\right)\Bigg(1+\frac{1}{4}\tan^4\!\left(\frac{o\!\varepsilon}{2}\right)
+\frac{1}{64}\tan^8\!\left(\frac{o\!\varepsilon}{2}\right)\\ &\qquad\qquad\qquad\;\,+\frac{1}{256}\tan^{12}\!\left(\frac{o\!\varepsilon}{2}\right)
+\frac{25}{16384}\tan^{16}\!\left(\frac{o\!\varepsilon}{2}\right)
+...\Bigg);\end{align}\,\!](http://wpcontent.answers.com/math/8/d/0/8d0b8bb78055480559ec5f767b9b8a3a.png)
