Plains are large, flat areas with little difference in elevation. Coastal plains are located relatively close to the coastline of the ocean. The highlighted area indicates coastal plains along the Atlantic and Gulf coast.

From time to time, throughout North American history, a large portion of the continent has been covered with massive sheets of ice called glaciers. The ice sheet pictured here covered all of Canada and extended as far south as Iowa and Illinois.

Most of the water from the Interior Plains drains into the Mississippi River watershed. The Mississippi River travels south to the Gulf of Mexico, where it deposits sediments in the Mississippi River delta.

The Appalachian mountains stretch from Alabama, along the eastern United States, to Newfoundland, Canada. The Rocky Mountains stretch from New Mexico to Alberta and British Columbia.

See how the geology of the North Dakota badlands has changed over time in this video segment from NatureScene, featuring the landscape at Theodore Roosevelt National Park.

Introduction to discrete and computational geometry. Topics covered: planar graphs, geometric graphs, the theory of crossings, extremal graph theory, arrangements of curves and points in the plane (mainly pseudolines and pseudocircles), problems involving distances, Gallai-Sylvester-type problems, Davenport-Schinzel sequences. Emphasis on teaching methods in combinatorial geometry. Many results presented are recent, and include open problems.

This course is an intensive introduction to architectural design tools and process, and is taught through a series of short exercises. The conceptual basis of each exercise is in the interrogation of the geometric principles that lie at the core of each skill. Skills covered in this course range from techniques of hand drafting, to generation of 3D computer models, physical model-building, sketching, and diagramming. Weekly lectures and pin-ups address the conventions associated with modes of architectural representation and their capacity to convey ideas. This course is tailored and offered only to first-year M.Arch students.

How does a lens form an image? See how light rays are refracted by a lens. Watch how the image changes when you adjust the focal length of the lens, move the object, move the lens, or move the screen.

This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal.

Open Middle provides math problems that have a closed beginning, a closed end, and an open middle. This means that there are multiple ways to approach and ultimately solve the problems. Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.

In this lesson designed for kindergarteners, students explore geometric shapes and how their bodies move through motion activity.

In this course, you will study the relationships between lines and angles. You will learn to calculate how much space an object covers, determine how much space is inside of a three-dimensional object, and other relationships between shapes, objects, and the mathematics that govern them.

This site teaches the Geometry of Circles to High Schoolers through a series of 1084 questions and interactive activities aligned to 9 Common Core mathematics skills.

Thirteen straightedge and compass constructions are described and illustrated. The original version, in Word format, can be downloaded and distributed.

This site teaches High Schoolers how to express geometric properties with equations through a series of 1721 questions and interactive activities aligned to 12 Common Core mathematics skills.

This site teaches High Schoolers Geometric Measurement and Dimension through a series of 82 questions and interactive activities aligned to 4 Common Core mathematics skills.

This geometry lesson shows that that an inscribed angle is half of a central angle that subtends the same arc. [Geometry playlist: Lesson 24 of 31]

This site teaches High Schoolers how to Interpret Categorical and Quantitative Data through a series of 45 questions and interactive activities aligned to 2 Common Core mathematics skills.

Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work.

A rigorous introduction designed for mathematicians into perturbative quantum field theory, using the language of functional integrals. Basics of classical field theory. Free quantum theories. Feynman diagrams. Renormalization theory. Local operators. Operator product expansion. Renormalization group equation. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and string theory.