On Mon, Jun 18, 2018 at 9:54 AM, Kevin Cole < kevin.c...@novawebdevelopment.org> wrote:
> Sticking my nose in where it don't belong. ;-) But that's never stopped me > before. ;-) > > Hi Kevin. I for one welcome your comments as I do think teachers need to prepare students for more than one way of doing coordinate systems. As you well know, and point out, in maths we almost always make the positives go to the right and the negatives to the left (number line). Then we add a 2nd number line going up and down, with positives increasing in magnitude going up and negatives getting bigger going down. This arrangement of two numbered lines considered "most normal" i.e. this schema is rather ubiquitous and must be considered something of a home base in classroom projects. Where to put the origin (0,0) is another question and is usually (A) at the lower left of the plot (if we don't need all four quadrants) or (B) in the middle (if we do need all quadrants), like when doing a unit circle. However if you walk around to the back and look from the other side... my right is your left and so on -- these are terms relative to a point of view, not to the object in front of us, which is where the confusion often begins. Who's left? Stage left means what again? It's the actor's left, not the audience's left. Theater practice is another place to absorb geometry. The screen is a kind of stage after all, with sprites = puppets. I always tell my Scratch students that programming is a kind of theater (stuff follows a script, objects i.e. actors, agents, sprites, do stuff i.e. act). https://www.sewwhatinc.com/blog/wp-content/uploads/2010/02/stage_diagram1.jpg Computer graphics (Blender et al) reintroduces the camera or viewpoint, which is often missing from elementary maths textbooks. Math texts don't believe in talking about an observer for some reason, or multiple observers. I expect the influence of computer science to be a positive influence in helping address that blind spot over time. MIT Scratch, by far the most popular way to introduce programming in my neck of the woods (Silicon Forest), puts (0,0) in the middle, Y up, X right. Also, should we make the Z axis go into the page or stay on the page perpendicular to X? Again, viewpoint matters. Where is the viewer in this picture, and in what direction is the viewer looking? Important questions! Getting off the XY plane to XYZ is always the next step in maths, including in computer graphics. We may introduce latitude and longitude at this point, along with spherical coordinates, in addition to XYZ. I've used POV-Ray in some of my classes, and certainly for my own Python projects. http://4dsolutions.net/ocn/pymath.html In POV-Ray the positive Z-axis points into the screen and Y goes towards the top of the screen, matching most textbooks that stick to X and Y. When I teach Codesters (Python) in the classroom, I always warn them that when they get to Codepen.io later (where we use HTML, SVG etc), the coordinate system will flip and they'll hear a lot more about H and W (height and width). We'll also talk a lot more about pixels (cells) and the level of resolution (frequency) which, in a DGGS (geospatial data system) might be hexagonal and pentagonal. http://i.stack.imgur.com/UtStp.jpg https://www.eat-the-planet.com/wp-content/uploads/2017/07/tile_resources2_comp.png Kirby
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