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.
Author(s): Prof.
Nicholas Patrikalakis and Prof. Takashi Maekawa
This PDF book covers the following topics
related to Geometry : The Five Groups of Axioms, the Compatibility
and Mutual Independence of the Axioms, the Theory of Proportion, the Theory of
Plane Areas, Desargues’s Theorem, Pascal’s Theorem, Geometrical Constructions
Based Upon the Axioms I-V.
Author(s): David Hilbert, Ph. D. Professor of
Mathematics, University of Göttingen
This PDF book covers the following topics
related to Geometry : Introduction, Construction of the Euclidean plane,
Transformations, Tricks of the trade, Concurrence and collinearity, Circular
reasoning, Triangle trivia, Quadrilaterals, Geometric inequalities, Inversive
and hyperbolic geometry, Projective geometry.
This note covers the following
topics: Points, Lines, Constructing equilateral triangle, Copying a line
segment, Constructing a triangle, The Side-Side-Side congruence theorem, Copying
a triangle, Copying an angle, Bisecting an angle, The Side-Angle-Side congruence
theorem, Bisecting a segment, Some impossible constructions, Pythagorean
theorem, Parallel lines, Squares, A proof of irrationality, Fractals.
This is a great mathematics book cover the following topics:
Equilateral Triangle, Perpendicular Bisector, Angle Bisector, Angle Made by
Lines, The Regular Hexagon, Addition and Subtraction of Lengths, Addition and
Subtraction of Angles, Perpendicular Lines, Parallel Lines and Angles,
Constructing Parallel Lines, Squares and Other Parallelograms, Division of a
Line Segment into Several Parts, Thales' Theorem, Making Sense of Area, The Idea
of a Tiling, Euclidean and Related Tilings, Islamic Tilings.
This
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
symplectic geometry.
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 covers the following topics:
Coordinate Systems in the Plane, Plane Symmetries or Isometries, Lines,
Polygons, Circles, Conics, Three-Dimensional Geometry.
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.
Author(s): Prof.
Nicholas Patrikalakis and Prof. Takashi Maekawa