Definition:Circumscribe/Circle around Polygon
< Definition:Circumscribe(Redirected from Definition:Polygon Circumscribed by Circle)
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Definition
A circle is circumscribed around a polygon when its circumference passes through each of the vertices of that polygon:
In the words of Euclid:
- A circle is said to be circumscribed about a figure when the circumference of the circle passes through each angle of the figure about which it is circumscribed.
(The Elements: Book $\text{IV}$: Definition $6$)
Not all polygons can be circumscribed.
Here is an example of one that cannot:
Also known as
As well as circumscribed around, the following can also be seen:
The more archaic circumscribed without can also occasionally be encountered.
Also see
Note that such a polygon can also be described as being inscribed in the circle.
In the words of Euclid:
- A rectilineal figure is said to be inscribed in a circle when each angle of the inscribed figure lies on the circumference of the circle.
(The Elements: Book $\text{IV}$: Definition $3$)
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): circumscribed
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): circumscribed