PA Reporting Category: M04.C-G Geometry PA Core Standards: CC
... 3. Least Complex Level: Content target: Identify when a flat surface (2-D) is separated into equal parts. Example: Use a simple shape that is easy to identify for sameness when divided. Use only one type of shape per set of examples and no other changes in attributes across shape (color, size, ...
... 3. Least Complex Level: Content target: Identify when a flat surface (2-D) is separated into equal parts. Example: Use a simple shape that is easy to identify for sameness when divided. Use only one type of shape per set of examples and no other changes in attributes across shape (color, size, ...
M04CG1.1.3a Recognize a line of symmetry in a two
... 3. Least Complex Level: • Content target: Identify when a flat surface (2-D) is separated into equal parts. • Example: Use a simple shape that is easy to identify for sameness when divided. Use only one type of shape per set of examples and no other changes in attributes across shape (color, size, ...
... 3. Least Complex Level: • Content target: Identify when a flat surface (2-D) is separated into equal parts. • Example: Use a simple shape that is easy to identify for sameness when divided. Use only one type of shape per set of examples and no other changes in attributes across shape (color, size, ...
49. INTRODUCTION TO ANALYTIC GEOMETRY
... Analytic Geometry Analytic geometry, usually called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra ...
... Analytic Geometry Analytic geometry, usually called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra ...
Oct 1982 WHAT DO MATHEMATICIANS DO? by George W. Mackey
... around at random so have the mathematicians built a marvelously articulated body of abstract concepts by following their individual instincts with an eye to what their colleagues are doing. An interesting example occured during the first two decades of the twentieth century. While the physicists wer ...
... around at random so have the mathematicians built a marvelously articulated body of abstract concepts by following their individual instincts with an eye to what their colleagues are doing. An interesting example occured during the first two decades of the twentieth century. While the physicists wer ...
640109
... Prerequisite: [Math 026 or Math 107 or placement into Math 111] and [Permission of Department] Co-req.: none Special Notation: Primarily for those intending to teach in grades K-8 Course description: Math content course on geometry and measurement stressing depth of understanding needed for effectiv ...
... Prerequisite: [Math 026 or Math 107 or placement into Math 111] and [Permission of Department] Co-req.: none Special Notation: Primarily for those intending to teach in grades K-8 Course description: Math content course on geometry and measurement stressing depth of understanding needed for effectiv ...
String theory provides a theoretical framework to accurately describe
... late ’90s, and its basic premise is that there is an exact equivalence between a theory which includes gravity in D+1 dimensions – and a theory without gravity in D dimensions,” he explains. “At first sight the statement that those two theories are exactly the same is completely bizarre: how can a t ...
... late ’90s, and its basic premise is that there is an exact equivalence between a theory which includes gravity in D+1 dimensions – and a theory without gravity in D dimensions,” he explains. “At first sight the statement that those two theories are exactly the same is completely bizarre: how can a t ...
Support Worksheet – Topic 2, Worksheet 1
... A particle moves on a straight line with constant acceleration. The initial velocity of the body is 4.0 m s1 and becomes 6.0 m s1 4.0 s later. Determine the distance travelled by the particle in this time. ...
... A particle moves on a straight line with constant acceleration. The initial velocity of the body is 4.0 m s1 and becomes 6.0 m s1 4.0 s later. Determine the distance travelled by the particle in this time. ...
Show all work on a separate sheet of work paper
... TRUE or FALSE Some, but not all, squares are parallelograms. ...
... TRUE or FALSE Some, but not all, squares are parallelograms. ...
Math 1218 - College of DuPage
... Section 10.7 (Other sections optional) The Active Coursed File states “NonEuclidean Geometry”. Please see Active Course File for topics to cover. ...
... Section 10.7 (Other sections optional) The Active Coursed File states “NonEuclidean Geometry”. Please see Active Course File for topics to cover. ...
Geometry Session 6: Classifying Triangles Activity Sheet
... We saw in Session 5 that symmetry can be used for classifying designs. We will try this for triangles. The activity sheet for sorting triangles has several triangles to classify, but instead of ...
... We saw in Session 5 that symmetry can be used for classifying designs. We will try this for triangles. The activity sheet for sorting triangles has several triangles to classify, but instead of ...
Simply Symmetric
... If we now further view and classify a rectangle as a special parallelogram, there is obviously no need to prove that it has opposite sides equal and parallel, because it then inherits those properties from the parallelogram. However, if need be, one can also easily derive these properties of a recta ...
... If we now further view and classify a rectangle as a special parallelogram, there is obviously no need to prove that it has opposite sides equal and parallel, because it then inherits those properties from the parallelogram. However, if need be, one can also easily derive these properties of a recta ...
String Theory
... • The extra dimensions are hidden a la Kaluza, Klein theory (1921) • Supersymmetry is there but broken (somehow) • The fact that these aren’t observed at current scales is in no sense a theoretical problem, the natural scale for such things would be the string scale ie. around the plank scale. • If ...
... • The extra dimensions are hidden a la Kaluza, Klein theory (1921) • Supersymmetry is there but broken (somehow) • The fact that these aren’t observed at current scales is in no sense a theoretical problem, the natural scale for such things would be the string scale ie. around the plank scale. • If ...
Program for ``Topology and Applications``
... Lie (pseudo)groups of symmetries will be discussed. It will be shown that under some conditions the Lie–Tresse theorem is valid and the quotients itself could be realized as new differential equations (dif ietes). Applications to classical problems in theory of algebraic invariants, relativity theor ...
... Lie (pseudo)groups of symmetries will be discussed. It will be shown that under some conditions the Lie–Tresse theorem is valid and the quotients itself could be realized as new differential equations (dif ietes). Applications to classical problems in theory of algebraic invariants, relativity theor ...
Composition of Transformation
... 1. The composition of two reflections across two intersecting lines is equivalent to a ___________________. The _____________________ is the intersection of the lines. The angle of rotation is ________________ the measure of the angle formed by the lines. 2. A _____________________ of two isometries ...
... 1. The composition of two reflections across two intersecting lines is equivalent to a ___________________. The _____________________ is the intersection of the lines. The angle of rotation is ________________ the measure of the angle formed by the lines. 2. A _____________________ of two isometries ...
Domain: Geometry Grade: 4 Core Content Cluster Title: Draw and
... the figure in half and draw a line on the fold. Then ask students to identify if both parts match. Define where the line of symmetry is on the figure. Define what makes the figure symmetrical. Try the same thing with a two-dimensional figure that is not symmetrical. Assessment Tasks Used Skill-based ...
... the figure in half and draw a line on the fold. Then ask students to identify if both parts match. Define where the line of symmetry is on the figure. Define what makes the figure symmetrical. Try the same thing with a two-dimensional figure that is not symmetrical. Assessment Tasks Used Skill-based ...
Quantum Field Theory I: Basics in Mathematics and Physics
... and divergent integrals, • divergent integrals and distributions (Hadamard’s finite part of divergent integrals), • the passage from a finite number of degrees of freedom to an infinite number of degrees of freedom and the method of counterterms in complex analysis (the Weierstrass theorem and the Mitt ...
... and divergent integrals, • divergent integrals and distributions (Hadamard’s finite part of divergent integrals), • the passage from a finite number of degrees of freedom to an infinite number of degrees of freedom and the method of counterterms in complex analysis (the Weierstrass theorem and the Mitt ...
Unwrapped Standards: G.CO.3 - Given a rectangle
... Common Core Standards - Resource Page The resources below have been created to assist teachers' understanding and to aid instruction of this standard. Standard: G.CO.3 - Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and Domain reflections that carry it onto ...
... Common Core Standards - Resource Page The resources below have been created to assist teachers' understanding and to aid instruction of this standard. Standard: G.CO.3 - Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and Domain reflections that carry it onto ...
Mirror symmetry (string theory)
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.Mirror symmetry was originally discovered by physicists. Mathematicians became interested in this relationship around 1990 when Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that it could be used as a tool in enumerative geometry, a branch of mathematics concerned with counting the number of solutions to geometric questions. Candelas and his collaborators showed that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a longstanding problem. Although the original approach to mirror symmetry was based on physical ideas that were not understood in a mathematically precise way, some of its mathematical predictions have since been proven rigorously.Today mirror symmetry is a major research topic in pure mathematics, and mathematicians are working to develop a mathematical understanding of the relationship based on physicists' intuition. Mirror symmetry is also a fundamental tool for doing calculations in string theory, and it has been used to understand aspects of quantum field theory, the formalism that physicists use to describe elementary particles. Major approaches to mirror symmetry include the homological mirror symmetry program of Maxim Kontsevich and the SYZ conjecture of Andrew Strominger, Shing-Tung Yau, and Eric Zaslow.