In this activity, students explore how trebuchets were used during the Middle Ages to launch projectiles over or through castle walls as well as how they are used today in events such as Punkin’ Chunkin’. Students work as teams of engineers and research how to design and build their own trebuchets from scratch while following a select number of constraints. They test their trebuchets, evaluate their results through several quantitative analyses, and present their results and design process to the class.

Students work as engineers to design and test trebuchets (in this case LEGO® MINDSTORMS® robots) that can launch objects. During the testing stage, they change one variable at a time to study its effect on the outcome of their designs. Specifically, they determine how far objects travel depending on their weights. As students learn about the different components of robot design and the specific function controls, they determine what design features are important for launching objects.

Examines a number of famous trials in European and American history. Considers the salient issues (political, social, cultural) of several trials, the ways in which each trial was constructed and covered in public discussion at the time, the ways in which legal reasoning and storytelling interacted in each trial and in later retellings of the trial, and the ways in which trials serve as both spectacle and a forum for moral and political reasoning. Students have an opportunity to study one trial in depth and present their findings to the class.

This short video and interactive assessment activity is designed to give fourth graders an overview of the sum of the angles of a triangle.

This short video and interactive assessment activity is designed to teach third graders an overview: sum of the angles of a triangle.

This task gives students a chance to explore several issues relating to rigid motions of the plane and triangle congruence. As an instructional task, it can help students build up their understanding of the relationship between rigid motions and congruence.

The purpose of this task is to emphasize the adjective "geometric" in the "geometric" series, namely, that the algebraic notion of a common ratio between terms corresponds to the geometric notion of a repeated similarity transformation.

Students learn about regular polygons and the common characteristics of regular polygons. They relate their mathematical knowledge of these shapes to the presence of these shapes in the human-made structures around us, especially trusses. Through a guided worksheet and teamwork, students explore the idea of dividing regular polygons into triangles, calculating the sums of angles in polygons using triangles, and identifying angles in shapes using protractors. They derive equations 1) for the sum of interior angles in a regular polygon, and 2) to find the measure of each angle in a regular n-gon. This activity extends students’ knowledge to engineering design and truss construction. This activity is the middle step in a series on polygons and trusses, and prepares students for the Polygon and Popsicle Trusses associated activity.

Students learn about the fundamental strength of different shapes, illustrating why structural engineers continue to use the triangle as the structural shape of choice. Examples from everyday life are introduced to show how this shape is consistently used for structural strength. Along with its associated activity, this lesson empowers students to explore the strength of trusses made with different triangular elements to evaluate the various structural properties.

This task provides a good opportunity for group work and class discussions where students generate and compare equivalent expressions. In class discussion, students should be asked to connect the terms of an expression with quantities shown in the diagram.

This course addresses the design of tribological systems: the interfaces between two or more bodies in relative motion. Fundamental topics include: geometric, chemical, and physical characterization of surfaces; friction and wear mechanisms for metals, polymers, and ceramics, including abrasive wear, delamination theory, tool wear, erosive wear, wear of polymers and composites; and boundary lubrication and solid-film lubrication. The course also considers the relationship between nano-tribology and macro-tribology, rolling contacts, tribological problems in magnetic recording and electrical contacts, and monitoring and diagnosis of friction and wear. Case studies are used to illustrate key points.

Students learn about and use a right triangle to determine the width of a "pretend" river. Working in teams, they estimate of the width of the river, measure it and compare their results with classmates.

Book description: This is a text on elementary trigonometry, designed for students who have completed courses in high-school algebra and geometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but a more geometrical approach is taken than usual. Also, some numerical methods (e.g. the secant method for solving trigonometric equations) are discussed. A brief tutorial on using Gnuplot to graph trigonometric functions is included.

There are 495 exercises in the book, with answers and hints to selected exercises.

This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged.

Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior mathematical work that is necessary for the new section or introduce new concepts and definitions that will be used later in that section. Each section also contains several progress checks that are short exercises or activities designed to help readers determine if they are understanding the material. In addition, the text contains links to several interactive Geogebra applets or worksheets. These applets are usually part of a beginning activity or a progress check and are intended to be used as part of the textbook.

The authors are very interested in constructive criticism of the textbook from the users of the book, especially students, who are using or have used the book. Please send any comments you have to trigtext@gmail.com.

The precursors to what we study today as Trigonometry had their origin in ancient Mesopotamia, Greece and India. These cultures used the concepts of angles and lengths as an aid to understanding the movements of the heavenly bodies in the night sky. Ancient trigonometry typically used angles and triangles that were embedded in circles so that many of the calculations used were based on the lengths of chords within a circle. The relationships between the lengths of the chords and other lines drawn within a circle and the measure of the corresponding central angle represent the foundation of trigonometry - the relationship between angles and distances.

Students investigate the relationships between angles and side lengths in right triangles with the help of materials found in the classroom and a mobile device. Using all or part of a meter stick or dowel and text books or other supplies, students build right triangles and measure the angles using a clinometer application on an Android® (phone or tablet) or iOS® device (iPhone® or iPad®). Then they are challenged to create a triangle with a given side length and one angle. The electronic device is used to measure the accuracy of their constructions.

In this task students must investigate this conjecture to discover that it does not work in all cases: Pick any two integers. Look at the sum of their squares, the difference of their squares, and twice the product of the two integers you chose. Those three numbers are the sides of a right triangle.

This Trinity College Library collection comprises more than 1500 images of people, places and events related to Hartford, CT, and its history. A large portion of the collection resulted from efforts of the former Trinity College Hartford Studies Project to preserve the abandoned photographic archive of a now defunct Hartford newspaper. At that time the photographs were reproduced on slide film, with the slides later digitized by Trinity College Library for this collection. The photographs reside at Hartford Public Library.