{"id":26,"date":"2021-08-13T13:21:36","date_gmt":"2021-08-13T17:21:36","guid":{"rendered":"https:\/\/opentextbc.ca\/patterndevelopment\/part\/geometric-construction\/"},"modified":"2021-08-13T13:21:36","modified_gmt":"2021-08-13T17:21:36","slug":"geometric-construction","status":"publish","type":"part","link":"https:\/\/opentextbc.ca\/patterndevelopment\/part\/geometric-construction\/","title":{"raw":"Geometric Construction","rendered":"Geometric Construction"},"content":{"raw":"\n

Introduction<\/h1>\nAs a sheet metal worker, we work with different lines, angles and shapes. We work with geometry. Be it in the field or in a shop, geometry is a tool we use in many different ways. From creating 2D patterns of 3D objects, to making sure roof panels are installed square, to locating duct runs and penetrations, geometry is used everyday by a sheet metal worker. This is the foundation for which all layout is done. Craftspeople who excel at this stage are able to quickly transform any complex ideas into reality.\n
\n

Learning Objectives<\/p>\n\n<\/header>\n

\n
    \n \t
  1. Understand the process of geometric construction and its uses<\/li>\n \t
  2. Learn geometric terms<\/li>\n<\/ol>\n<\/div>\n<\/div>\n
    \n

    Geometric Terms<\/p>\n\n<\/header>\n

    \n
      \n \t
    • Acute Angle\/Triangle<\/strong> \u2013 <\/strong>an angle\/triangle with an angle smaller than 90\u00b0<\/li>\n \t
    • Bisect<\/strong> \u2013 <\/strong>to divide in half<\/li>\n \t
    • Horizontal<\/strong> \u2013 <\/strong>a line\/plane level with the horizon. Flat, level<\/li>\n \t
    • Obtuse Angle\/Triangle<\/strong> \u2013 <\/strong>an angle\/triangle with an angle larger than 90\u00b0<\/li>\n \t
    • Parallel<\/strong> \u2013 <\/strong>a line\/plane that is equal distance from another<\/li>\n \t
    • Parts of a Circle\"A<\/strong>\n
        \n \t
      1. Radius <\/strong>\u2013 the distance from centre to any point of the circumference<\/strong> or half the diameter<\/strong><\/li>\n \t
      2. Diameter <\/strong>\u2013 the distance across a circle at centre, twice the radius<\/strong><\/li>\n \t
      3. Circumference <\/strong>\u2013 the distance around a circle, perimeter<\/strong> of a circle<\/li>\n \t
      4. Arc <\/strong>\u2013 a portion of a circumference<\/strong><\/li>\n \t
      5. Chord <\/strong>\u2013 a straight line from 2 points on a circumference<\/strong><\/li>\n \t
      6. Segment \u2013<\/strong> the area of a circle bound by an arc<\/strong> and a chord<\/strong><\/li>\n \t
      7. Sector <\/strong>\u2013 the area of a circle bound by 2 radii<\/strong> and an arc<\/strong><\/li>\n \t
      8. Quadrant <\/strong>\u2013 a sector<\/strong> which equals one quarter of the area of a circle<\/li>\n \t
      9. Tangent<\/strong> \u2013 a line which touches only 1 point of a circumference<\/strong><\/li>\n \t
      10. Point of Tangency <\/strong>\u2013 90\u00b0 to the centre of the circle<\/li>\n<\/ol>\n<\/li>\n \t
      11. Perpendicular <\/strong>\u2013 a line\/plane which is 90\u00b0 to another<\/li>\n \t
      12. Right Angle\/Triangle <\/strong>\u2013 an angle\/triangle which has a 90\u00b0 angle<\/li>\n \t
      13. Vertical <\/strong>\u2013 a line\/plane straight up and down, vertically level (plumb)<\/li>\n \t
      14. Vertex <\/strong>\u2013 the point at which an angle is formed<\/li>\n<\/ul>\n<\/div>\n<\/div>\n
        \n\nCircle Facts:\n
          \n \t
        • There are 360\u00b0 in a circle.<\/li>\n \t
        • Circumference (or perimeter) = Pi \u00d7 diameter or 2 \u00d7 Pi \u00d7 radius.<\/li>\n \t
        • Area = Pi \u00d7 radius2<\/sup>.<\/li>\n<\/ul>\n<\/div>\n

          Points, Lines, Angles and Shapes<\/h1>\nIn geometry we deal with many different shapes. All shapes are made up of various points, lines and angles.\n

          Lines<\/h2>\nWe can define a point (A) as a single location on a shape or line.\n\nA line (A-B) is made up of 2 points. There are different types of lines:\n
            \n \t
          • horizontal<\/strong> (level with the horizon),<\/li>\n \t
          • vertical<\/strong> (up and down, also known as plumb),<\/li>\n \t
          • tilted (neither vertical nor horizontal), and<\/li>\n \t
          • arcs (a line from a radius point).<\/li>\n<\/ul>\nWe also have lines which are parallel<\/strong> or equal distance apart and lines which are perpendicular<\/strong> or at right angles to one another.\n

            Angles<\/h2>\nAn angle is formed at a point at where 2 lines meet (vertex<\/strong>). We deal with three different types of angles:\n
              \n \t
            • Right angles<\/strong> are at 90\u00b0 and are very important in layout,<\/li>\n \t
            • Obtuse angles<\/strong>, which are greater than 90\u00b0, and<\/li>\n \t
            • acute angles<\/strong>, which are smaller than 90\u00b0.<\/li>\n<\/ul>\n

              Shapes<\/h2>\nWith a combination of points, lines, and angles, we start to create shapes. Triangles (A-B-C), squares or rectangles (A-B-C-D),<\/span> and circles are some of the most common shapes seen in the sheet metal industry. It is a combination of points, lines, and angles that make up different shapes \u2014or in our case, our patterns.<\/span>\n","rendered":"

              Introduction<\/h1>\n

              As a sheet metal worker, we work with different lines, angles and shapes. We work with geometry. Be it in the field or in a shop, geometry is a tool we use in many different ways. From creating 2D patterns of 3D objects, to making sure roof panels are installed square, to locating duct runs and penetrations, geometry is used everyday by a sheet metal worker. This is the foundation for which all layout is done. Craftspeople who excel at this stage are able to quickly transform any complex ideas into reality.<\/p>\n

              \n
              \n

              Learning Objectives<\/p>\n<\/header>\n

              \n
                \n
              1. Understand the process of geometric construction and its uses<\/li>\n
              2. Learn geometric terms<\/li>\n<\/ol>\n<\/div>\n<\/div>\n
                \n
                \n

                Geometric Terms<\/p>\n<\/header>\n

                \n
                  \n
                • Acute Angle\/Triangle<\/strong> \u2013 <\/strong>an angle\/triangle with an angle smaller than 90\u00b0<\/li>\n
                • Bisect<\/strong> \u2013 <\/strong>to divide in half<\/li>\n
                • Horizontal<\/strong> \u2013 <\/strong>a line\/plane level with the horizon. Flat, level<\/li>\n
                • Obtuse Angle\/Triangle<\/strong> \u2013 <\/strong>an angle\/triangle with an angle larger than 90\u00b0<\/li>\n
                • Parallel<\/strong> \u2013 <\/strong>a line\/plane that is equal distance from another<\/li>\n
                • Parts of a Circle\"A<\/strong>\n
                    \n
                  1. Radius <\/strong>\u2013 the distance from centre to any point of the circumference<\/strong> or half the diameter<\/strong><\/li>\n
                  2. Diameter <\/strong>\u2013 the distance across a circle at centre, twice the radius<\/strong><\/li>\n
                  3. Circumference <\/strong>\u2013 the distance around a circle, perimeter<\/strong> of a circle<\/li>\n
                  4. Arc <\/strong>\u2013 a portion of a circumference<\/strong><\/li>\n
                  5. Chord <\/strong>\u2013 a straight line from 2 points on a circumference<\/strong><\/li>\n
                  6. Segment \u2013<\/strong> the area of a circle bound by an arc<\/strong> and a chord<\/strong><\/li>\n
                  7. Sector <\/strong>\u2013 the area of a circle bound by 2 radii<\/strong> and an arc<\/strong><\/li>\n
                  8. Quadrant <\/strong>\u2013 a sector<\/strong> which equals one quarter of the area of a circle<\/li>\n
                  9. Tangent<\/strong> \u2013 a line which touches only 1 point of a circumference<\/strong><\/li>\n
                  10. Point of Tangency <\/strong>\u2013 90\u00b0 to the centre of the circle<\/li>\n<\/ol>\n<\/li>\n
                  11. Perpendicular <\/strong>\u2013 a line\/plane which is 90\u00b0 to another<\/li>\n
                  12. Right Angle\/Triangle <\/strong>\u2013 an angle\/triangle which has a 90\u00b0 angle<\/li>\n
                  13. Vertical <\/strong>\u2013 a line\/plane straight up and down, vertically level (plumb)<\/li>\n
                  14. Vertex <\/strong>\u2013 the point at which an angle is formed<\/li>\n<\/ul>\n<\/div>\n<\/div>\n
                    \n

                    Circle Facts:<\/p>\n

                      \n
                    • There are 360\u00b0 in a circle.<\/li>\n
                    • Circumference (or perimeter) = Pi \u00d7 diameter or 2 \u00d7 Pi \u00d7 radius.<\/li>\n
                    • Area = Pi \u00d7 radius2<\/sup>.<\/li>\n<\/ul>\n<\/div>\n

                      Points, Lines, Angles and Shapes<\/h1>\n

                      In geometry we deal with many different shapes. All shapes are made up of various points, lines and angles.<\/p>\n

                      Lines<\/h2>\n

                      We can define a point (A) as a single location on a shape or line.<\/p>\n

                      A line (A-B) is made up of 2 points. There are different types of lines:<\/p>\n

                        \n
                      • horizontal<\/strong> (level with the horizon),<\/li>\n
                      • vertical<\/strong> (up and down, also known as plumb),<\/li>\n
                      • tilted (neither vertical nor horizontal), and<\/li>\n
                      • arcs (a line from a radius point).<\/li>\n<\/ul>\n

                        We also have lines which are parallel<\/strong> or equal distance apart and lines which are perpendicular<\/strong> or at right angles to one another.<\/p>\n

                        Angles<\/h2>\n

                        An angle is formed at a point at where 2 lines meet (vertex<\/strong>). We deal with three different types of angles:<\/p>\n

                          \n
                        • Right angles<\/strong> are at 90\u00b0 and are very important in layout,<\/li>\n
                        • Obtuse angles<\/strong>, which are greater than 90\u00b0, and<\/li>\n
                        • acute angles<\/strong>, which are smaller than 90\u00b0.<\/li>\n<\/ul>\n

                          Shapes<\/h2>\n

                          With a combination of points, lines, and angles, we start to create shapes. Triangles (A-B-C), squares or rectangles (A-B-C-D),<\/span> and circles are some of the most common shapes seen in the sheet metal industry. It is a combination of points, lines, and angles that make up different shapes \u2014or in our case, our patterns.<\/span><\/p>\n","protected":false},"parent":0,"menu_order":1,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-26","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/pressbooks\/v2\/parts\/26","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":0,"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/pressbooks\/v2\/parts\/26\/revisions"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/wp\/v2\/media?parent=26"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/wp\/v2\/contributor?post=26"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/wp\/v2\/license?post=26"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}