Geometry is the branch of mathematics which investigates the relations, properties, and measurement of solids, surfaces, lines, and angles. It is the science of the relations of space. Sourse: Webster's Dictionary

In this lesson, students will investigate error. As shown in earlier activities from navigation lessons 1 through 3, without an understanding of how errors can affect your position, you cannot navigate well. Introducing accuracy and precision will develop these concepts further. Also, students will learn how computers can help in navigation. Often, the calculations needed to navigate accurately are time consuming and complex. By using the power of computers to do calculations and repetitive tasks, one can quickly see how changing parameters likes angles and distances and introducing errors will affect their overall result.

In this lesson, students learn how to determine location by triangulation. We describe the process of triangulation and practice finding your location on a worksheet, in the classroom, and outdoors.

In this activity about light and refraction, learners discover how a lens creates an image that hangs in midair. A large Fresnel lens creates upside-down images of distant objects and right-side-up images of nearby objects. Learners can locate the upside-down images by using a piece of white paper as a screen. The right-side-up images are harder to find. Activity includes detailed explanations and diagrams to explain how the images are created.

In this activity, learners explore liquid crystals, light and temperature. Using a postcard made of temperature-sensitive liquid crystal material, learners monitor temperature changes. By observing these changes, learners show that dark materials absorb and reemit the energy contained in light more readily than light-colored materials. Learners can also distinguish energy absorbed and reemited by radiation, convection, and conduction by comparing the behavior of black, white, and silver objects. This resource guide includes detailed explanation of the phenomenon and background information about liquid crystals.

GEM4 VisionGEM4 has brought together researchers and professionals in major institutions across the globe with distinctly different, but complementary, expertise and facilities to address significant problems at the intersections of select topics of engineering, life sciences, technology, medicine and public health.GEM4 creates new models for interactions across scientific disciplinary boundaries whereby problems spanning the range of fundamental science to clinical studies and public health can be addressed on a global scale through strategic international partnerships.Through initial focus areas in cell and molecular biomechanics, and environmental health, in the context of select human diseases, GEM4 creates a global forum for the definition and exploration of grand challenges and scientific studies, for the cross-fertilization of ideas among engineers, life scientists and medical professionals, and for the development of novel educational tools.GEM4 ActivitiesGEM4 enables the brokering of engineers, life scientists and medical professionals with shared facilities and joint students and post-doctoral fellows to tackle major problems in the context of human health and diseases that call for state-of-the-art experimental and computational tools in cell and molecular mechanics, biology and medicine. Broad examples of problems addressed include:infectious diseases such as malaria,cancer,cardiovascular diseases,biomechanical origins of inflammation.In each of these areas, the initial emphasis has included (but will not be limited to) molecular, subcellular and cellular mechanics applied to biomedicine, where a single investigator or institution is not likely to have the full spectrum of expertise, infrastructure or resources available to cover fundamental molecular science all the way to clinical studies and societal implications. Currently, twelve institutions in North America, Europe and Asia participate in this effort as Core institutions, focusing on mechanistic studies, as well as novel methods for diagnostics, vaccines or drug development and delivery.Funds have been raised to provide a structure for coordinated studies from major organizations under the umbrella of GEM4. These funds are being used for:organization of major symposia/conferences specifically targeted at the theme areas of the initiative,training grants for student fellowships for the partner institutions,summer schools to develop teaching materials,the exchange of students and researchers,operations of a central secretariat for handling the administrative and infrastructure details for such interactions,maintenance of a web site for dissemination of information.

Students will answer the Challenge Question and use the acquired learning from Lesson 1, "Fix the Hip Challenge" and Lesson 2, "Skeletal System Overview"to construct an informative brochure addressing osteoporosis and the role biomedical engineering plays in diagnosing and preventing this disease.

Students explore the effects of regional geology on bridge foundation, including the variety of soil conditions found beneath foundations. They learn about shallow and deep foundations, as well as the concepts of bearing pressure and settlement.

In this case study activity, students will investigate arctic geology and hydrology as well as tundra ecology and consider options for sewage treatment. Public safety, environmental impact, and issues of construction and engineering will be explored. This Starting Point example page builds on the Lifelines Online case study and includes learning goals, context for use, teaching notes and tips, teaching materials, assessment ideas, references and topics covered.

This lesson introduces the MRI Safety Grand Challenge question. Students are asked to write journal responses to the question and brainstorm what information they will need to answer the question. The ideas are shared with the class and recorded. Students then watch a video interview with a real life researcher to gain a professional perspective on MRI safety and brainstorm any additional ideas. The associated activity provides students the opportunity to visualize magnetic fields.

Students are introduced to the Robotics Peripheral Vision Grand Challenge question. They are asked to write journal responses to the question and brainstorm what information they require to answer the question. Their ideas are shared with the class and recorded. Then, students share their ideas with each other and brainstorm any additional ideas. Next, students draw a basis for the average peripheral vision of humans and then compare that range to the range of two different focal lengths in a camera. Through the associated activity provides, students see the differences between human and computer vision.

Students use graph theory to create social graphs for their own social networks and apply what learn to create a graph representing the social dynamics found in a dramatic text. Students then derive meaning based on what they know about the text from the graphs they created. Students learn graph theory vocabulary, as well as engineering applications of graph theory.

Students learn about an important characteristic of lines: their slopes. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero or undefined. Students get an explanation of when and how these different types of slope occur. Finally, they learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another.

Students analyze their social networks using graph theory. They gather data on their own social relationships, either from Facebook interactions or the interactions they have throughout the course of a day, recording it in Microsoft Excel and using Cytoscape (a free, downloadable application) to generate social network graphs that visually illustrate the key persons (nodes) and connections between them (edges). The nodes in the Cytoscape graphs are color-coded and sized according to the importance of the node (in this activity, nodes are people in students' social networks). After the analysis, the graphs are further examined to see what can be learned from the visual representation. Students gain practice with graph theory vocabulary, including node, edge, betweeness centrality and degree on interaction, and learn about a range of engineering applications of graph theory.

This intereactive Flash applet helps children learn grouping, tally marks, place value, addition, and subtraction. Students help the alien spaceship move cows into corrals by counting by 5s and 10s. They also can apply those grouping skills to practice adding and subtracting two-digit numbers with regrouping. Audio cues and prompts reinforce the user's actions and facilitate counting and the development of math language.

In this lesson, the students will investigate what types of plants and insects they could eat to survive in the Amazon. They will research various plants and/or insects and identify characteristics that make them edible or useful for the trip. The students will create posters and present their findings to the class.

The marine environment is unique and requires technologies that can use sound to gather information since there is little light underwater. The sea-floor is characterized using underwater sound and acoustical systems. Current technological innovations are allowing scientists to further understand and apply information about animal locations and habitat. Remote sensing and exploration with underwater vehicles allows scientists to map and understand the sea floor, and in some cases, the water column. In this lesson, the students will be shown benthic habitat images produced by GIS. These imaged will lead to a class discussion on why habitat mapping is useful and how current technology works to make bathymetry mapping possible. The teacher will then ask inquiry-based questions to have students brainstorm about the importance of bathymetry mapping.

In this activity about chemistry and electricity, learners form a battery by placing their hands onto plates of different metals. Learners detect the current by reading a DC microammeter attached to the metal plates. Learners experiment with different metals to find out what combination produces the most current as well as testing what happens when they press harder on the plates or wet their hands. Learners also investigate what happens when they wire the plates to a voltmeter.

Students explore the concept of similar right triangles and how they apply to trigonometric ratios. Use this lesson as a refresher of what trig ratios are and how they work. In addition to trigonometry, students explore a clinometer app on an Android® or iOS® device and how it can be used to test the mathematics underpinning trigonometry. This prepares student for the associated activity, during which groups each put a clinometer through its paces to better understand trigonometry.

Students experience haptic (the sense of touch) feedback by using LEGO® MINDSTORMS® NXT robots and touch sensors to emulate touch feedback recognition. With four touch sensors connected to LEGO NXTs, they design sensor attachments that feel physically distinguishable from each another. Then students answer questions and communicate their answers to the NXT by pressing the touch sensor that is associated with the right multiple-choice answer letter. Haptics becomes essential when students must use the NXT sensors to answer the next set of questions without the aid of their vision. This challenges them to rely solely on the tactile feeling of each unique touch sensor attachment that they created in order to choose the correct peripheral slot. Students also learn about real-world applications of haptics technology.