# Day 156: Fractals and the Mandelbrot Set

*AP Physics C:* We watched the NOVA special *Fractals: Hunting the Hidden Dimension*. There were a lot a parallels between what the mathematicians where saying and the themes in *Arcadia*. Mandelbrot is a main focus of the special, along with applications of fractals — from CGI special effects to antennas to fashion. Minds were blown.

As a bonus, we looked at select scenes from Stoppard’s *Rosencrantz and Guildenstern are Dead*. Again, Stoppard shows a knack for mixing science and humor:

*College-Prep Physics*: Students began work on WebAssign problems about waves.

*Conceptual Physics:* Students wrapped-up work on the bike light presentations.

# Day 155: Temperature vs. Wavelength

*College-Prep Physics:* I had a clear 250-W bulb plugged into an variac and slowly increased the voltage from 0 to 120 V. We saw the color of the glowing filament change from red to orange to yellow to white. The temperature and the brightness of the filament increased as well. Now that we have a way of measuring the color of light (by its wavelength), we can look for a mathematical relationship between the temperature of the glowing filament and the peak wavelength of the light emitted. We used a blackbody applet to collect data: http://bit.ly/blackbodysim.

*AP Physics C: *Students wrapped up their investigation of Val’s grouse, concluding with the creation of a bifurcation diagram. Here’s a bifurcation program I made in GlowScript.

*Conceptual Physics:* Students continued work on their bike light presentations. Some groups used http://circuitlab.com to make professional-looking circuit diagrams for their presentations.

# Day 154: Chaos and Valentine’s Grouse

*AP Physics C:* We finished reading *Arcadia* and began exploring the (sometimes chaotic, sometimes predictable) behavior of a simple logistic equation for modeling animal populations. The handout is here: Valentine’s Grouse: An Exploration of Chaos in Populations. And you can explore it yourself using my version of the population program in GlowScript.

*College-Prep Physics:* Wrapped up the wave/buggy lab from yesterday. We determined the model for our data to be *wavelength = speed / frequency.*

*Conceptual Physics:* Students finished building/testing their bike circuits and began drawing and annotating their final circuit diagrams.

# Day 152: Interference of Light

*College-Prep Physics:* Tied our observations of yesterday’s slinky wave interference to water wave interference and then to light interference. Showed this totally awesome Veritasium video about Young’s original double slit experiment (done with sunlight).

*AP Physics C:* Continued reading Stoppard’s *Arcadia*. In the video, Stoppard reads 2 of my favorite scenes from the play.

*Conceptual Physics*: Students finished building and testing their modified bike light circuits.

# Day 151: Build Phase (Modified Bike Light Circuit)

*Conceptual Physics:* Groups started building their modified bike light circuits based on their designs from yesterday. (Nobody said it had to look pretty!)

*College-Prep Physics:* Reflected upon the video we saw yesterday showing wave interference in the pond (areas of rippling water and still water).

- What do you observe?
- Come up with 3 possible explanations for what we observe.
- Shared explanations.
- Show students long slinky and send pulses along it.
- Use the slinky to design an experiment to test the “canceling out” explanation.

*AP Physics C:* Began reading Tom Stoppard’s *Arcadia, *an* *amazing play about love, physics, and mathematics.