Sierpinski N-Gons - Grand Valley State University
... The Deterministic Algorithm Applied to Regular n-gons: In the above discussion there seems to be no reason why we should restrict ourselves to looking at only three points. Why not generalize to n points? Let v1 , v2 ," , vn be n distinct points in the plane such that the line segments joining vi to ...
... The Deterministic Algorithm Applied to Regular n-gons: In the above discussion there seems to be no reason why we should restrict ourselves to looking at only three points. Why not generalize to n points? Let v1 , v2 ," , vn be n distinct points in the plane such that the line segments joining vi to ...
An Algorithm to Generate Repeating Hyperbolic Patterns
... fundamental polygon, and with some minimally labeled 2 and 3, and some polygons adjacent to A. exposed and maximally exposed polygons marked with m and M respectively. To describe the replication algorithm, we define the exposure of a polygon by its relation to the next layer. In Figure 7, we say th ...
... fundamental polygon, and with some minimally labeled 2 and 3, and some polygons adjacent to A. exposed and maximally exposed polygons marked with m and M respectively. To describe the replication algorithm, we define the exposure of a polygon by its relation to the next layer. In Figure 7, we say th ...
cannot use - WordPress.com
... -Rigid Motions produce congruent figures -Translation, Rotation, Reflections are all rigid motions -Rigid Motions preserve size, shape and angle measure, they only change the position of a figure ...
... -Rigid Motions produce congruent figures -Translation, Rotation, Reflections are all rigid motions -Rigid Motions preserve size, shape and angle measure, they only change the position of a figure ...
Perpendicular Bisectors Of A Triangle
... Now we are ready to begin the lesson. We will start with an acute triangle. Look at your screen to determine if you already have an acute triangle. Remember that you have the measures of all three angles to examine. If you do not have an acute triangle, you will change it into an acute triangle by g ...
... Now we are ready to begin the lesson. We will start with an acute triangle. Look at your screen to determine if you already have an acute triangle. Remember that you have the measures of all three angles to examine. If you do not have an acute triangle, you will change it into an acute triangle by g ...
Chapter 5 Notes
... statements, each of which follows logically from previous statements, the hypotheses, postulates, definitions, or other proven theorems. The final statement should be the conclusion of the theorem. Method of Indirect Proof: We assume the hypotheses are true as before, but in addition we assume that ...
... statements, each of which follows logically from previous statements, the hypotheses, postulates, definitions, or other proven theorems. The final statement should be the conclusion of the theorem. Method of Indirect Proof: We assume the hypotheses are true as before, but in addition we assume that ...
Triangle Congruence Re
... o Triangle Sum Theorem: the sum of the interior angles of a triangle is 180 o Exterior Angle Theorem: the exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles o Third Angles Theorem: if 2 angles of one triangle are congruent to 2 angles of another triangle, then th ...
... o Triangle Sum Theorem: the sum of the interior angles of a triangle is 180 o Exterior Angle Theorem: the exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles o Third Angles Theorem: if 2 angles of one triangle are congruent to 2 angles of another triangle, then th ...
Contest Geometry
... In the special case where one of the angles in a triangle is a right angle, you can use the Pythagorean theorem to relate the lengths of the three sides. If angle C in the generic triangle is D E F , then the Pythagorean theorem states that G HJILK HMON H . Note that by dropping an appropriate alti ...
... In the special case where one of the angles in a triangle is a right angle, you can use the Pythagorean theorem to relate the lengths of the three sides. If angle C in the generic triangle is D E F , then the Pythagorean theorem states that G HJILK HMON H . Note that by dropping an appropriate alti ...
Congruence Postulate - If three sides of one triangle are congruent
... Side-Side-Side (SSS) Congruence Postulate - If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. Side-Angle-Side (SAS) Congruence Postulate - If two sides and the included angle of one triangle are congruent to two sides and the incl ...
... Side-Side-Side (SSS) Congruence Postulate - If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. Side-Angle-Side (SAS) Congruence Postulate - If two sides and the included angle of one triangle are congruent to two sides and the incl ...
problems
... It must be remembered that above theorem is the best possible result. We have already seen an example of a triangle in H in which the sum of the measures of the angles is actually strictly The basic approach of Saccheri (and those who followed him) was to try to prove something less than 180. In you ...
... It must be remembered that above theorem is the best possible result. We have already seen an example of a triangle in H in which the sum of the measures of the angles is actually strictly The basic approach of Saccheri (and those who followed him) was to try to prove something less than 180. In you ...
4.1 Symmetry Geometry and measures
... Use a ruler and a protractor to make an accurate drawing of each of the following triangles. Measure and label the other angles on your drawing. a ...
... Use a ruler and a protractor to make an accurate drawing of each of the following triangles. Measure and label the other angles on your drawing. a ...
Stability of Quasicrystal Frameworks in 2D and 3D
... that every rhombus may be reached from any other by a contiguous succession of rhombi. Two rhombi are contiguous if they share a common side. Two diamonds touching at a vertex will not be considered as connected. By simply connected we shall mean that the carpet has no holes. That is, if two differe ...
... that every rhombus may be reached from any other by a contiguous succession of rhombi. Two rhombi are contiguous if they share a common side. Two diamonds touching at a vertex will not be considered as connected. By simply connected we shall mean that the carpet has no holes. That is, if two differe ...
ch 5 - ariella and nikki - 2012
... Theorem 5-7: If the diagonals of a quadrilateral bisects each other, then the quadrilateral is a parallelogram. ...
... Theorem 5-7: If the diagonals of a quadrilateral bisects each other, then the quadrilateral is a parallelogram. ...
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 ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑