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Segment : Segment A segment is a part of a lineconsisting of two endpoints, and all points between them Congruent : Congruent Angles or shapes that have the same measure Midpoint : Midpoint The point that divides the line into two congruent lines Perpendicular : Perpendicular Lines that intersect to form right angles Equal : Equal An identical copy Obtuse Angle : Obtuse Angle An Angle whose measure is between 90 and 180 degrees Slide 10: (a) Computer graphics is based on geometry - how images are transformed when viewed in various ways. Graphics used in Mirror’s Edge, the videogame. Geometry being used in : Slide 11: (b) Computer-aided design, computer-aided geometric design. Representing shapes in computers, and using these descriptions to create images, to instruct people or machines to build the shapes, etc. (e.g. the hood of a car, the overlay of parts in a building construction, even parts of computer animation). Geometry being used in : Graphics used for industrial purposes. Slide 12: (c) Robotics. Robotic vision, planning how to grasp a shape with a robot arm, or how to move a large shape without collission. Geometry being used in : A Korean Robot, D2E. Slide 13: (d) Medical imaging - how to reconstruct the shape of a tumor from CAT scans, and other medical measurements. Lots of new geometry and other math was (and still is being) developed for this. Geometry being used in : CAT Scan Chamber. Slide 14: (e) Structural engineering. What shapes are rigid or flexible, how they respond to forces and stresses. Statics (resolution of forces) is essentially geometry. This goes over into all levels of design, form, and function of many things. Geometry being used in : Rigid Buckminster Structure. Slide 15: (f) Protein modeling. Much of the function of a protein is determined by its shape and how the pieces move. Mad Cow Disease is caused by the introduction of a 'shape' into the brain (a shape carried by a protein). Many drugs are designed to change the shape or motions of a protein - something that we are just now working to model, even approximately, in computers, using geometry and related areas (combinatorics, topology). Geometry being used in : Protein Structure. Slide 16: (g) Physics, chemistry, biology, .... . Symmetry is a central concept of many studies in science - and also the central concept of modern studies of geometry. Students struggle in university science if they are not able to detect symmetries of an object (molecule in stereo chemistry, systems of laws in physics, ... ). the study of transformations and related symmetries has been, since 1870s the defining characteristic of geometric studies. Geometry being used in : Symmetry of a Leaf. Slide 17: Geometry is used everywhere. Everywhere in the world there is geometry, mostly made by man. Most man made structures today are in a form of Geometric. How, you ask? Well some examples would the a CD, that is a 3-D circle and the case would be a rectangular prism. Buildings, cars, rockets, planes, maps are all great examples. Here's some examples on how the world uses Geometry in buildings and structure….. Pictures of Geometry used in Real Life Slide 18: 1. This a pictures with some basic geometric structures. This is a modern reconstruction of the English Wigwam. As you can there the door way is a rectangle, and the wooden panels on the side of the house are made up of planes and lines. Except for really planes can go on forever. The panels are also shaped in the shape of squares. The house itself is half a cylinder. Slide 19: 2. Here is another modern reconstruction if of a English Wigwam. This house is much similar to the one before. It used a rectangle as a doorway, which is marked with the right angles. The house was made with sticks which was straight lines at one point. With the sticks in place they form squares when they intercepts. This English Wigwam is also half a cylinder. Slide 20: 3. This is a modern day skyscraper at MIT. The openings and windows are all made up of parallelograms. Much of them are rectangles and squares. This is a parallelogram kind of building. Slide 21: 4. This is the Hancock Tower, in Chicago. With this image, we can show you more 3D shapes. As you can see the tower is formed by a large cube. The windows are parallelogram. The other structure is made up of a cone. There is a point at the top where all the sides meet, and There is a base for it also which makes it a cone. Slide 22: 5. This is another building at MIT. this building is made up of cubes, squares and a sphere. The cube is the main building and the squares are the windows. The doorways are rectangle, like always. On this building There is a structure on the room that is made up of a sphere. Slide 23: 6. This is the Pyramids, in Indianapolis. The pyramids are made up of pyramids, of course, and squares. There are also many 3D geometric shapes in these pyramids. The building itself is made up of a pyramid, the windows a made up of tinted squares, and the borders of the outside walls and windows are made up of 3D geometric shapes. Slide 24: 7. This is a Chevrolet SSR Roadster Pickup. This car is built with geometry. The wheels and lights are circles, the doors are rectangular prisms, the main area for a person to drive and sit in it a half a sphere with the sides chopped off which makes it 1/4 of a sphere. If a person would look very closely the person would see a lot more shapes in the car. Too many to list. Slide 25: Thank You You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.