visualising solid shapes.ppt
Post on 10-Apr-2016
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What Are Shapes? Ashapeis ageometrical figurethat 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 flatplane. Three-dimensional objects like cubes will not fit inside of a plane, because they are not flat.
2-dimensional ShapesThese are two-dimensionalshapes or flat planegeometry shapes. Their sidesare made of straight or curved lines. They can have any number ofsides. Plane figures made of lines are calledpolygons. Triangles and squares are examples of polygons
Properties Of 2 Dimensional ShapesTwo-dimensional shapes are planar. They depend on only two coordinates--xandy, for instance--consisting ofxunits andyunits, respectively. 2-D shapes include the square, the triangle, the rhombus, etc.
2-D shapes do not have prominent or rugged parts. For example, square, whereas three-dimensional like a cube, which is like an extended or prominent square.
3-Dimensional ShapesA 3D shape is a solid which encloses a volume and has length, breadth and height
Other 3D shapes
Properties Of 3 Dimensional Shapes3-dimensional shapes have four properties that set them apart from two-dimensional shapes:
faces, vertices, edges and volume.
These properties determine whether the shape is two- or three-dimensional, but also which three-dimensional shape it is.
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.
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.Colors used in Map
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.
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.Scales used in Maps
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.
Face Part of a shape that is flat.(Or curved)E.g. A cube has 6 of these.
EdgeThe line where two faces meet.E.g. A cube has 12 of these.
Vertex (Vertices)The place where three or more edges meet.This pyramid has 4 of these.
A polyhedron is a solid shape bounded by polygons whereas non-polyhedrons 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.
PolyhedronsThese are polyhedrons. These are not polyhedrons. F+V=E+2 is known as Eulers formula and it holds true for any polyhedron. Here F stands for faces, V for vertices and E for the edges of the polyhedron.
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.
PolyhedronsIrregular polyhedron Regular polyhedron
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.PolyhedronsConvex polyhedron
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 and pyramids Prisms Pyramids
PrismsPrisms have two identical, parallel faces joined to one another by rectangles. Examples are;
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
*NOTE: students could copy this down or it can be printed from the associated document*