This course is an introduction to arithmetic geometry, a subject that lies …
This course is an introduction to arithmetic geometry, a subject that lies at the intersection of algebraic geometry and number theory. Its primary motivation is the study of classical Diophantine problems from the modern perspective of algebraic geometry.
Topics in surface modeling: b-splines, non-uniform rational b-splines, physically based deformable surfaces, …
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. Inspection methods. Feature representation and recognition. Shape interrogation for design, analysis, and manufacturing. Involves analytical and programming assignments. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.472J. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.158J.
In the first part of this video, we review the idea of …
In the first part of this video, we review the idea of flat space and the Pythagorean theorem. The second part of the video reviews ideas from trigonometry including the unit circle, sine, cosine, and pi. We conclude with a proof of an angle-sum identity.
This text is intended for a brief introductory course in plane geometry. …
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra.
The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem-proving or formal methods of reasoning. However the topics are ordered so that they may be taught deductively.
The problems are arranged in pairs so that just the odd-numbered or just the even-numbered can be assigned. For assistance, the student may refer to a large number of completely worked-out examples. Most problems are presented in diagram form so that the difficulty of translating words into pictures is avoided. Many problems require the solution of algebraic equations in a geometric context. These are included to reinforce the student's algebraic and numerical skills, A few of the exercises involve the application of geometry to simple practical problems. These serve primarily to convince the student that what he or she is studying is useful. Historical notes are added where appropriate to give the student a greater appreciation of the subject.
This book is suitable for a course of about 45 semester hours. A shorter course may be devised by skipping proofs, avoiding the more complicated problems and omitting less crucial topics.
Geometry of Manifolds analyzes topics such as the differentiable manifolds and vector …
Geometry of Manifolds analyzes topics such as the differentiable manifolds and vector fields and forms. It also makes an introduction to Lie groups, the de Rham theorem, and Riemannian manifolds.
CK-12's Basic Geometry FlexBook is designed to present students with geometric principles …
CK-12's Basic Geometry FlexBook is designed to present students with geometric principles in a simpler, more graphics-oriented course. Students will explore geometry at a slower pace with an emphasis placed on visual aids and approachability.
CK-12 Geometry Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and …
CK-12 Geometry Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and problem solving for teaching CK-12 Geometry Student Edition. The solution and assessment guides are available upon request.
Includes chapters on: Basics of Geometry, Reasoning and Proof, Parallel and Perpendicular …
Includes chapters on: Basics of Geometry, Reasoning and Proof, Parallel and Perpendicular Lines, Triangles and Congruence, Relationships with Triangles, Polygons and Quadrilaterals, Similarity, Right Triangle Trigonometry, Circles, Perimeter and Area, Surface Area and Volume, Rigid Transformations.
In this lesson, students will how to name angles, measure and classify …
In this lesson, students will how to name angles, measure and classify angles, identify congruent angles, and how to find angle measures using Angle Addition Postulate.
An interactive applet and associated web page that calculate the area of …
An interactive applet and associated web page that calculate the area of a triangle using the formula method in coordinate geometry. The applet has a triangle with draggable vertices. As you drag them the triangle's area is recalculated from the vertex coordinates using the formula. The grid and coordinates can be turned on and off. The area calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining area using the formula method, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
This book presents Euclidean Geometry and was designed for a one-semester course …
This book presents Euclidean Geometry and was designed for a one-semester course preparing junior and senior level college students to teach high school Geometry. The book could also serve as a text for a junior level Introduction to Proofs course.
In this course, students take turns in giving lectures. For the most …
In this course, students take turns in giving lectures. For the most part, the lectures are based on Robert Osserman's classic book A Survey of Minimal Surfaces, Dover Phoenix Editions. New York: Dover Publications, May 1, 2002. ISBN: 0486495140.
An interactive applet and associated web page that show how to determine …
An interactive applet and associated web page that show how to determine of one line is perpendicular to another in coordinate geometry. The principle used is that if two lines a re perpendicular to each other the slope of one is the negative reciprocal of the other. The applet shows to lines that the user can move. The slopes are continuously calculated as you drag them, and if the they are parallel they change color. The calculation is shown on screen updated continuously as you drag. The grid, axis pointers and coordinates can be turned on and off. The calculation display can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of perpendicularity, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
This article is about the isoperimetric theorem. It states the theorem, explains …
This article is about the isoperimetric theorem. It states the theorem, explains its history and uses examples and exercises to demonstrate it. The resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.
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