PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: Very high Entry average rating: Very high
[parent] explementary (Definition)

The explementary arc of an arc $ a$ of a circle is the arc forming together with $ a$ the full circle.

Two angles are called explementary angles of each other, if their sum is the full angle $ 2\pi$, i.e. $ 360^\circ$. In the below picture, the interior angle $ \alpha = 60^\circ$ of an equilateral triangle and its explementary angle $ \beta = 300^\circ$ (which is an exterior angle of the triangle) are seen.


\begin{pspicture}(-1,-3)(2,3) \pspolygon(-1.5,0)(1.5,0)(0,2.6) \psarc(0,2.6){0.2}{-60}{240} \rput[a](0,2.2){$\alpha$} \rput[a](-0.2,2.9){$\beta$} \end{pspicture}



"explementary" is owned by pahio.
(view preamble)

View style:

See Also: complementary angles

Also defines:  explementary angle, explementary arc, full angle

This object's parent.
Log in to rate this entry.
(view current ratings)

Cross-references: triangle, equilateral triangle, sum, angles, circle, arc
There are 3 references to this entry.

This is version 4 of explementary, born on 2007-10-11, modified 2008-02-04.
Object id is 9988, canonical name is Explementary.
Accessed 685 times total.

Classification:
AMS MSC51F20 (Geometry :: Metric geometry :: Congruence and orthogonality)
 51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries)

Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy
Explementary angle by MathNerd on 2007-10-11 17:34:40
Just want to make sure I understand this correctly: let's say alpha is the interior angle of an equilateral triangle in normal (Euclidean) space. The explementary angle of that angle would be 300 degrees, right?
[ reply | up ]

Interact
post | correct | update request | add derivation | add example | add (any)