is an introductory note in generalized geometry, with a special emphasis on
Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as
generalized complex geometry, as introduced by Hitchin. Dirac geometry is based
on the idea of unifying the geometry of a Poisson structure with that of a
closed 2-form, whereas generalized complex geometry unifies complex and
This note is intended for students who have
a background in multivariable calculus and some experience in proof-based
mathematics. Topics covered includes: Euclidean geometry, Polygons,
Triangulations and Tilings, The Chord Theorem, Tangrams and Scissors Congruence,
Spherical Geometry, Hyperbolic geometry, Euclids axioms and the parallel
postulate, Incidence geometry and Hyperbolic isometries.
This is the companion article to Teaching Geometry according to the Common
Core Standards. Topics covered includes: Basic rigid motions and
congruence, Dilation and similarity, The angle-angle criterion for similarity,
The Pythagorean Theorem, The angle sum of a triangle, Volume formulas, basic
rigid motions and assumptions, Congruence criteria for triangles, Typical
theorems, Constructions with ruler and compass.
This note explains the following topics:
History of Greek Mathematics, Triangles, Quadrilateral, Concurrence,
Collinearity, Circles, Coordinates, Inversive Geometry, Models of Hyperbolic
Geometry, Basic Results of Hyperbolic Geometry.
This note explains the following topics: Vectors, Cartesian
Coordinates, The Scalar Product, Intersections of Planes and Systems of Linear
Equations, Gaubian Elimination and Echelon Form, Vector Product, Matrices,
Determinants, Linear Transformations, Eigenvectors and Eigenvalues.
The book is addressed to high
school students, teachers of mathematics, mathematical clubs, and college
students.The collection consists of two parts. It is based on three Russian
editions of Prasolov’s books on plane geometry. Topics covered includes: Similar
Triangles, Inscribed Angles, Circles, Area, Polygons, Loci, Constructions,
Geometric Inequalities, Inequalities Between The Elements Of A Triangle,
Calculations And Metric Relations, Vectors, The Symmetry Through A Line,
Homothety and Rotational Homothety, Convex and Nonconvex Polygons, Divisibility,
This is a reading guide
to the field of geometric structures on 3–manifolds. The approach is to
introduce the reader to the main definitions and concepts, to state the
principal theorems and discuss their importance and inter-connections, and to
refer the reader to the existing literature for proofs and details.
book covers the following topics: Algebraic Nahm transform for parabolic Higgs
bundles on P1, Computing HF by factoring mapping classes, topology of ending
lamination space, Asymptotic behaviour and the Nahm transform of doubly periodic
instantons with square integrable curvature, FI-modules over Noetherian rings,
Hyperbolicity in Teichmuller space, A knot characterization and 1–connected
nonnegatively curved 4–manifolds with circle symmetry.
Tis book covers the following
topics related to the Geometry of the Sphere: Basic information about spheres, Area on the sphere, The area of a spherical
triangle, Girard's Theorem, Consequences of Girard's Theorem and a Proof of
This book is primarily an introduction to geometric concepts and tools
needed for solving problems of a geometric nature with a computer. Topics
covered includes: Logic and Computation, Geometric Modeling, Geometric Methods
and Applications, Discrete Mathematics, Topology and Surfaces.