student
... Now we are going to look at the exterior angles of a polygon and see if we can develop a theorem like we did for interior angles. To draw the exterior angles, you have to keep your orientation consistent. Start at one vertex and move either clockwise or counter-clockwise, extending each side as you ...
... Now we are going to look at the exterior angles of a polygon and see if we can develop a theorem like we did for interior angles. To draw the exterior angles, you have to keep your orientation consistent. Start at one vertex and move either clockwise or counter-clockwise, extending each side as you ...
Block: ______ Geometry Review Unit 1
... ____ 17. Supplementary angles are two angles whose measures have sum ____. Complementary angles are two angles whose measures have sum ____. ...
... ____ 17. Supplementary angles are two angles whose measures have sum ____. Complementary angles are two angles whose measures have sum ____. ...
circular functions
... Circular functions are equivalent to trigonometric functions in radians. This equivalency provides an opportunity to expand the concept of trigonometric functions. Trigonometric functions were first defined using the angles of a right triangle and later expanded to include all angles. The concept of ...
... Circular functions are equivalent to trigonometric functions in radians. This equivalency provides an opportunity to expand the concept of trigonometric functions. Trigonometric functions were first defined using the angles of a right triangle and later expanded to include all angles. The concept of ...
Geometry 5 Foundation 506.39KB 2017-03-28
... Two quarter circles are cut out from the card as shown. The radius of each circle is 3 cm. By considering the area of the square, and the area of each quarter circle, work out the percentage of the square that is cut out. ...
... Two quarter circles are cut out from the card as shown. The radius of each circle is 3 cm. By considering the area of the square, and the area of each quarter circle, work out the percentage of the square that is cut out. ...
Steinitz's theorem
In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the (simple) 3-vertex-connected planar graphs (with at least four vertices). That is, every convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are also known as polyhedral graphs. Steinitz's theorem is named after Ernst Steinitz, who submitted its first proof for publication in 1916. Branko Grünbaum has called this theorem “the most important and deepest known result on 3-polytopes.”The name ""Steinitz's theorem"" has also been applied to other results of Steinitz: the Steinitz exchange lemma implying that each basis of a vector space has the same number of vectors, the theorem that if the convex hull of a point set contains a unit sphere, then the convex hull of a finite subset of the point contains a smaller concentric sphere, and Steinitz's vectorial generalization of the Riemann series theorem on the rearrangements of conditionally convergent series.↑ ↑ 2.0 2.1 ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑