The kind of geometry that we will be using in this manual is called plane geometry. Plane geometry deals with points, lines, polygons (A shape with more than two sides, i.e. square, triangle, hexagon, etc.) and circles on a flat surface (plane). Sheet metal flat patterns are done in plane geometry. Solid geometry deals with points, lines, and planes in space, (3 dimensional). When our flat part gets bent up then it becomes solid geometry. Normally our blueprints are describing a part that is going to be solid geometry, but since they are drawn on flat pieces of paper they have to define the part using plane geometry. PLANE: In geometry a plane is an even or flat surface. It has width and length but no thickness. You could think of one surface of a flange on a sheet metal part as a plane. Where two planes intersect is a line. In sheet metal we can see this where two flanges meet. PLANE GEOMETRY:Study of points, lines, line segments, circles, arcs on a flat surface(plane). SOLID GEOMETRY:Study of points, lines, and planes in space. You may be asking "Why bother with all these definitions?" Well I'll tell you why. For one reason developing sheet metal into a flat pattern has everything to do with math. When I was in high school I can remember trying to learn trigonometry, but a lot of it just didn't make sense to me. Until I wound up in the sheet metal trade and started to find out that without knowing trig there were some jobs I just couldn't figure out. Someone showed me how to use trig tables in a book to figure out a job one day and I said "OH! That was what they were trying to teach me in High School". I guess I couldn't really understand trigonometry until I had something to relate it to. This is called practical application. I found out that the more math I knew the easier and faster my job became. So just keep plugging away at this manual and I will try to use sheet metal parts in the examples and maybe it will all come together for you. http://www.dvcplanners.com
PLANES, PLANE AND SOLID GEOMETRY