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
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: 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.
This book explains the following topics:
Classical Geometry, Absolute (Neutral) Geometry, Betweenness and Order,
Congruence, Continuity, Measurement, and Coordinates, Elementary Euclidean
Geometry, Elementary Hyperbolic Geometry, Elementary Projective Geometry.
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 Prasolovís 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 geometry textbook that is being distributed freely on the Internet in separate segments (according to chapter).
I united the Parents Guide, the Geometry Lessons, & the tests, and compiled them into a single pdf file
This lecture note covers the
following topics in surface modeling: b-splines, non-uniform rational b-splines,
physically based deformable surfaces, sweeps and generalized cylinders, offsets,
blending and filleting surfaces, Non-linear solvers and intersection problems,
Solid modeling: constructive solid geometry, boundary representation,
non-manifold and mixed-dimension boundary representation models, octrees,
Robustness of geometric computations, Interval methods, Finite and boundary
element discretization methods for continuum mechanics problems, Scientific
visualization, Variational geometry, Tolerances and Inspection methods.
Nicholas Patrikalakis and Prof. Takashi Maekawa