Thurs Nov 9 – Surface Area

First: Print some grids

  • Create, export, slice, and print grids for Level 2 and Level 3 using the file gridlines.scad in the 3SPACE SHARE folder

Second: Quizzes

  • Print check:  Each person should have at least one print of their Fractal Carpet at the start of class
  • Geometric series:  Second quiz on adding up a geometric series

Third: Calculate surface area

  • Each of your prints is 100mm across, but we’re going to pretend that it is “4 units” on each side
  • Given the above, look at one of the Fractal Carpets you printed, and calculate its surface area
  • Express this surface area as the total area of the square, minus what is taken away. Depending on what level your fractal print is, you may have to take away 1, 2, or 3 sizes of things.
  • Think about the other two levels of your Fractal Carpet (which you may not have printed yet). What is the surface area of each one? Again express your answer as the total area of the square, minus anything that is taken away.
  • If you made level 10 of your Fractal Carpet, what would its area be? Express your answer the same way as your previous answers, as a total area minus what is taken away in each stage.
  • If we have time, some students can come to the front to show their calculations.
  • If we have time, we’ll walk through the OpenSCAD code line by line and talk about what it does.
  • Start thinking about this: What is the surface area of your complete, infinite-level Fractal Carpet, and why? Can you figure this out using a geometric series?

For next time

  • Print the other two levels of your Fractal Carpet, if you haven’t already (at the 100mm size)
  • Start an individual blog post about your Fractal Carpet. See the Assignments page for requirements.