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Abbott Lawrence Academy 2016-2017 Curriculum Map: Year at a
Abbott Lawrence Academy 2016-2017 Curriculum Map: Year at a

... Project: Factoring a Sequence of Polynomials: students will demonstrate the relationship between cyclotomic polynomials and integers by building tables in the factors of xn-1. ...
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- Kennedy HS

... Bring compass, straightedge, and graph paper tomorrow. When 2 figures are congruent, they have the same size AND same shape. This means that the corresponding sides and the corresponding angles are congruent in congruent polygons. When 2 polygons are not congruent, they can be different sizes or dif ...
Extremal properties of ray-nonsingular matrices
Extremal properties of ray-nonsingular matrices

TRIANGULATING POLYGONS WITHOUT LARGE ANGLES 1
TRIANGULATING POLYGONS WITHOUT LARGE ANGLES 1

... forces us to seek only an approximate solution. Steiner points also add another parameter to the quality of the output: the number of triangles in the triangulation, which we call the size of the triangulation. Size directly a ects computation times in nite element methods, or expense in measuring ...
Number Algebra Shape, space and measures Handling data G write
Number Algebra Shape, space and measures Handling data G write

... show how 2 congruent scalene triangles put together can make an isos. triangle use a map and scale to measure and find distance plot a point given bearing (obtuse) and distance work out area of 4.6 by 5.2 rectangle and perimeter ...
RELATIONS BETWEEN CUMULANTS IN NONCOMMUTATIVE PROBABILITY
RELATIONS BETWEEN CUMULANTS IN NONCOMMUTATIVE PROBABILITY

... Fourier analysis is the tool of choice for most problems in classical probability, cumulants are an indispensable ingredient for many investigations in noncommutative probability. An intriguing aspect of noncommutative probability is the existence of several kinds of independence [Voi85, SW97, Mur01 ...
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... The amplitude of y = a sin x (or y = a cos x) is half the distance between the maximum and minimum values of the function. amplitude = |a| If |a| > 1, the amplitude stretches the graph vertically. If 0 < |a| > 1, the amplitude shrinks the graph vertically. If a < 0, the graph is reflected in the x- ...
Course: Algebra 1 Unit #5: Quadratic Functions
Course: Algebra 1 Unit #5: Quadratic Functions

... 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the functionh(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the funct ...
spectra of large random trees
spectra of large random trees

... The recent availability of large amounts of data has led to an explosion in the number of models used to model real-world networks, and dynamically grown models such as various preferential attachment schemes have attracted significant interest from the computer science and mathematical physics commu ...
Andrej Risteski - The Program in Applied and Computational
Andrej Risteski - The Program in Applied and Computational

Centroidal Voronoi Diagram
Centroidal Voronoi Diagram

Reasoning and Proof in a Spatial Geometry
Reasoning and Proof in a Spatial Geometry

... Question 2. Produce them with specific materials. Question 3. Prove that the previously established list is valid and complete. 2.2. Mathematical analysis of the problem First, let’s look at the definition. There are several possibilities, which from the start raises the question of their equivalenc ...
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7-3-formulas-involving-polygons-ppt

Mitri Kitti Axioms for Centrality Scoring with Principal Eigenvectors
Mitri Kitti Axioms for Centrality Scoring with Principal Eigenvectors

... corresponding graph in which there is an edge between nodes i and j if aij > 0. Without loss of generality we may assume that the weight of the edge is aij . Let G(A) denote the directed graph corresponding to A. It will be assumed that A is irreducible; nodes that cannot be connected to each other ...
ppt - Chair of Computational Biology
ppt - Chair of Computational Biology

... corresponding row of the initial matrix by -1. If the exchange flux is unconstrained  move the entire row to a temporary matrix T(E). This completes the first tableau T(0). T(0) and T(E) for the example reaction system are shown on the previous slide. Each element of these matrices will be designat ...
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On the approximability of the maximum feasible subsystem

... 1.2 Our results In this paper, we consider only max- 6. Due to lack of space, we only present sketches for imum feasible subsystems where the constraint matrix most of the proofs. The final version of the paper will is a 0/1 matrix with non-negative solutions. Under this contain complete proofs. res ...
Polygons_worksheet3 - Penns Valley Math Resources
Polygons_worksheet3 - Penns Valley Math Resources

... EXERCISE 3: What is the sum of the interior angles of a 13-gon? EXERCISE 4: Can the sum of the interior angles of a polygon be 450º? EXERCISE 5: What is the measure of the interior angle of a regular ...
McDougal Geometry chapter 4 notes
McDougal Geometry chapter 4 notes

... TK#33: Corollary to Base Angles Thm: If a triangle is equilateral, then it is equiangular. TK#34: Corollary to Converse of Base Angles Thm: If a triangle is equiangular, then it is equilateral. Prove the Base Angles Thm. (Use the back of this page.) Guided practice 1-5. (Use the back of this page.) ...
Coordinate geometry: working with slopes
Coordinate geometry: working with slopes

... c. What is special about triangle ABC? Justify your answer using slopes. 2. You can calculate the midpoint of a line segment by thinking of the two endpoints as a data set and finding their average. The midpoint’s x-coordinate is the average of the x-coordinates of the endpoints, and the midpoint’s ...
Ways to find slope
Ways to find slope

... d. How many right angles does this quadrilateral have? Tell how you know. 5. Consider quadrilateral WXYZ with vertices W(–2, 3), X(–1, 8), Y(9, 6), and Z(8, 1). a. Is this quadrilateral a parallelogram? Justify your answer using slopes. b. Is this quadrilateral a trapezoid? Justify your answer using ...
tetrahedron - PlanetMath.org
tetrahedron - PlanetMath.org

Answer - Imagine School at Lakewood Ranch
Answer - Imagine School at Lakewood Ranch

... Find the degrees for each part. Round to the nearest whole degree. ...
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computational

... Distance function not differentiable on the medial axis Still can define a generalized concept of gradient ...
SAT Subject Tests - collegereadiness
SAT Subject Tests - collegereadiness

... these four intervals, there is a value k in that interval such that f (k) = 2. This shows that there are at least four such values of k, and the fact that x 4 − 3x 3 − 9x 2 + 4 is a polynomial of degree 4 means that there can be at most four such values of k. Therefore, there are four values of ...
Nonoverlap of the Star Unfolding
Nonoverlap of the Star Unfolding

... To create such an overlap, we must start with a vertex in the polyhedron with negative curvature, then cut in such a way that one image of the vertex will retain at least 2π of the surface material. Convex polyhedra clearly avoid 1-local overlaps, since they contain no vertices with negative curvatu ...
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Signed graph

In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign.Formally, a signed graph Σ is a pair (G, σ) that consists of a graph G = (V, E) and a sign mapping or signature σ from E to the sign group {+,−}. The graph may have loops and multiple edges as well as half-edges (with only one endpoint) and loose edges (with no endpoints). Half and loose edges do not receive signs. (In the terminology of the article on graphs, it is a multigraph, but we say graph because in signed graph theory it is usually unnatural to restrict to simple graphs.)The sign of a circle (this is the edge set of a simple cycle) is defined to be the product of the signs of its edges; in other words, a circle is positive if it contains an even number of negative edges and negative if it contains an odd number of negative edges. The fundamental fact about a signed graph is the set of positive circles, denoted by B(Σ). A signed graph, or a subgraph or edge set, is called balanced if every circle in it is positive (and it contains no half-edges). Two fundamental questions about a signed graph are: Is it balanced? What is the largest size of a balanced edge set in it? The first question is not difficult; the second is computationally intractable (technically, it is NP-hard).Signed graphs were first introduced by Harary to handle a problem in social psychology (Cartwright and Harary, 1956). They have been rediscovered many times because they come up naturally in many unrelated areas. For instance, they enable one to describe and analyze the geometry of subsets of the classical root systems. They appear in topological graph theory and group theory. They are a natural context for questions about odd and even cycles in graphs. They appear in computing the ground state energy in the non-ferromagnetic Ising model; for this one needs to find a largest balanced edge set in Σ. They have been applied to data classification in correlation clustering.
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