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Visualising solid shapes

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Visualising solid shapes

  1. 1. What Are Shapes? A shape is a geometrical figure that can be described with mathematics. One way to classify shapes is to describe a bigger shape that the shape fits inside of. For example, two-dimensional shapes like circles will fit inside of a flat plane. Three-dimensional objects like cubes will not fit inside of a plane, because they are not flat.
  2. 2. 2-dimensional Shapes These are twodimensional shapes or flat plane geometry shapes. Their sides are made of straight or curved lines. They can have any number of sides. Plane figures made of lines are called polygons. Triangles and squares are examples of polygons
  3. 3. Properties Of 2 Dimensional Shapes Two-dimensional shapes are planar. Graphically speaking, they depend on only two coordinates--x and y, for instance-consisting of x units and y units, respectively. In the case of a coordinate system of more than two dimensions, then a 2-D shape would still depend on two coordinate directions. For example, in a spatial xyz coordinate system (which is threedimensional) a two-dimensional shape would be expressed with points such as (x,y,0), (x,0,z), or (0,y,z). Therefore, it would depend on either x and y, x and z, or y and z. 2-D shapes include the square, the triangle, the rhombus, etc. To understand it more easily, you can say that 2-D shapes do not have prominent or rugged parts. For example, speaking two-dimensionally you would have a square, whereas threedimensionally you would have a cube, which is like an extended or prominent square.
  4. 4. 3-Dimensional Shapes A 3D shape is a solid which encloses a volume and has length, breadth and height
  5. 5. Other 3D shapes
  6. 6. Properties Of 3 Dimensional Shapes Three-dimensional shapes have four properties that set them apart from two-dimensional shapes: faces, vertices, edges and volume. These properties not only allow you to determine whether the shape is twoor three-dimensional, but also which three-dimensional shape it is.
  7. 7. What is a Map? A map is a graphic representation of a portion of the earth's surface drawn to scale, as seen from above. It uses colors, symbols, scales and labels to represent features found on the ground.
  8. 8. Colors used in Map a. Black. Indicates cultural (man-made) features such as buildings and roads, surveyed spot elevations, and all labels. b. Red-Brown. The colors red and brown are combined to identify cultural features, all relief features, non-surveyed spot elevations, and elevation, such as contour lines on red-light readable maps. c. Blue. Identifies hydrography or water features such as lakes, swamps, rivers, and drainage. d. Green. Identifies vegetation with military significance, such as woods, orchards, and vineyards. e. Brown. Identifies all relief features and elevation, such as contours on older edition maps, and cultivated land on red-light readable maps. f. Red. Classifies cultural features, such as populated areas, main roads, fire station,and boundaries, on older maps. g. Other. Occasionally other colors may be used to show special information. These are indicated in the marginal information as a rule.
  9. 9. Scales used in Maps A map is a scaled graphic representation of a portion of the earth's surface. The scale of the map permits the user to convert distance on the map to distance on the ground or vice versa. The ability to determine distance on a map, as well as on the earth's surface, is an important factor in planning and executing military missions.
  10. 10. Scales used in Maps -Distances Shown on the map are proportional to the actual distance on the ground. -While drawing a map, we should take care about: How much of actual distance is denoted by 1mm or 1cm in the map - It can be : 1cm = 1 Kilometers or 10 Km or 100Km etc. - This scale can vary from map to map but not with in the map.
  11. 11. Points to remember  A map depicts the location of a particular object/place in relation to other objects/places.  Symbols and colors are used to depict the different objects/places.  There is no reference or perspective in map, i.e., objects that are closer to the observer are shown to be of the same size as those that are farther away.  Maps use a scale which is fixed for a particular map. It reduces the real distances proportionately to distances on paper.
  12. 12. Platonic Solid Picture Number Number Number Shape of of Faces Number Unfolded of of Faces Faces at Each of Edges Polyhedron (Net) Vertices Vertex Tetrahedron 4 Equilateral Triangle (3-sided) Cube 6 Square (4-sided) 3 8 12 8 Equilateral Triangle (3-sided) 4 6 12 12 Regular Pentagon (5-sided) 3 20 30 20 Equilateral Triangle (3-sided) 5 12 30 Octahedron Dodecahedron Icosahedron 3 4 6
  13. 13. Face • Part of a shape that is flat.(Or curved) • E.g. A cube has 6 of these.
  14. 14. Edge • The line where two faces meet. • E.g. A cube has 12 of these.
  15. 15. Vertex (Vertices) • The place where three or more edges meet. • This pyramid has 4 of these.
  16. 16. Polyhedrons A polyhedron is a solid shape bounded by polygons whereas nonpolyhedrons do not have polygon shaped faces. Cubes, cuboids, prisms, and pyramids are few examples of polyhedrons. Spheres, cones and cylinders are a few examples of non-polyhedrons. These are polyhedrons . These are not polyhedrons . The polygonal regions forming the polyhedron are known as its faces, two intersecting faces meet at a line segment called an edge and three edges meet at a point called the vertex. F+V=E+2 is known as Euler’s formula and it holds true for any polyhedron. Here F stands for faces, V for vertices and E for the edges of the polyhedron.
  17. 17. Polyhedrons A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex. An irregular polyhedron is made of polygons whose sides and angles are not of equal measure. Regular polyhedron Irregular polyhedron
  18. 18. Polyhedrons In a convex polyhedron , the line segment joining any two points on the surface of the polyhedron lies entirely inside or on the polyhedron. A polyhedron some of whose plane sections are concave polygons is known as a concave polyhedron . Concave polygons have at least one interior angle greater than 180° and has some of its sides bent inward. Convex polyhedron
  19. 19. Prisms and pyramids A prism is a polyhedron with parallel congruent polygon bases and sides made of parallelograms. A pyramid is a polyhedron whose base is a polygon of any number of sides and whose lateral faces are triangles with a common vertex. Prisms and pyramids are named after the shape of their base. Maps represent the location of a place or object in relation to other places or objects. Prisms Pyramids
  20. 20. Prisms • Prisms have two identical, parallel faces joined to one another by rectangles. Examples are;
  21. 21. Pyramids • Pyramids have one face with at least 3 edges, the faces meeting these edges are ALL triangles. NOTE: Pyramids get their name from the shape of their base. • There are many more pyramids than these ones shown

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