Tues Sept 26 – Presentations & Math

// Roundup //

According to the Assignments page, by today’s class your Tinkercad Fractal post should be completed, with all formatting and content in line with the assignment guidelines. This week we’ll have final presentations for this project, and work on shoring up the math in the calculational sections.

// Today in class: Presentations //

  • Send anything to the printer that you still need for this project, as long as the print can finish by the end of the class period.
  • Bring final prints to the front of the room (photo time!)
  • One or two brave first volunteers for presentations – we’ll slow down and discuss the math in detail when it happens

// Today in class: Just the Math You Need //

    • What’s below looks nasty but you can just use them as plug-in formulas
    • You can do this
  • Basic logarithms for computing fractal dimension
    • If $A^B = C$ then we say $B = \log_A (C)$
    • You can calculate $\log_A (C)$ with wolframalpha.com
    • Dimension calculations from the 3Blue1Brown video:
      • (scale-down factor)^(dimension) = 1/(number of copies)
      • $S^D = 1/N$
      • $D = \log_S (1/N)$
  • Finite geometric series¬†formula for many of your volume/area/length calculations
    • $a + ar + ar^2 + ar^3 + … + ar^n = a\frac{1-r^{n+1}}{1-r}$
    • Example: $2+2(\frac{1}{9})+2(\frac{1}{9})^2+2(\frac{1}{9})^3+2(\frac{1}{9})^4 = 2\frac{1-(\frac{1}{9})^5}{1-\frac{1}{9}} \approx 2.245$
  • Infinite geometric series¬†formula for many of your volume/area/length calculations
    • $a + ar + ar^2 + ar^3 + … +$ keep going forever… $= a\frac{1}{1-r}$, if $|r|<1$
    • Example: $2+2(\frac{1}{9})+2(\frac{1}{9})^2+2(\frac{1}{9})^3+… = 2\frac{1}{1-\frac{1}{9}} = 2\frac{1}{\frac{8}{9}} = \frac{18}{8} = 2.25$

// For next time //

Your final goal for the Tinkercad Fractal post is to make sure that the math is correct, complete, and, most importantly, CLEAR. ¬†Someone completely new to the project should be able to read your two mathematical sections and follow along with the math, understanding what each term refers to in your fratal and why each step works. Remember this is a math class, so I’m going to be looking at these sections very carefully. This week you will also start looking over the Fourth Dimension book to find a topic that you could illustrate with 3D printing for your next project. See the Assignments page for details.