Earlier in my life, I spent a lot of time studying for mathematics competitions. In my sophomore year of high school, I switched to studying physics, and that's what I've been doing since. I have participated in various physics competitions, and I plan to major in physics as an undergraduate!
Here are some problems that I've researched for fun. You might find some of the math to be not as interesting, but I have a lot of interesting pictures and plots that you might find interesting as a casual reader. But if you're really interested by it, don't be daunted by the math! Most of it is at a basic calculus level.
- The bucket question (Circular caustics)
What's that shape that light forms on the bottom of any reflective cylinder? Some various approaches to this problem, using computer and analytical methods.
Fun with sand (Angle of Repose)
What is the slope of the sand that collects in the bottom of the hourglass? How does the shape of the sand grains affect the slope? Microscopes, Fourier analysis....
These are some intriguing questions I've written about. Some of them are questions I've come up on my own - others are just fascinating things that I've come across in my reading.
- Real sunsets (atmospheric refraction)
How much later does the sun set due to the refraction of light in the atmosphere?
And a generalization of the sun's positional error to times other than sunset
An interesting phenomenon that you may have observed in the past. (Not to be confused with "rainbow" color patterns formed by oil films on pavement.)
Meadows in the Sierra Nevada [in progress]
How do are alpine meadows in the Sierra formed? How do they disappear? What are the effects of human activity?
Density Wave Theory [in progress]
How do galaxy arms form? If things closer to the center rotate faster, why don't the spirals "wind up"?
Antlion Death Traps [in progress]
This is something I found in my research for my "Fun with sand" project above, and I found it immensely fascinating.
These are fun physics-related projects that I've done over the years that don't necessarily examine a particular question.
Corona discharge [on hold]
Trying to photograph the faint blueish violet corona discharge of transmission towers. (Corona discharge is the ionization of air in regions with high electric field.)
Trying to make a small budget spectrometer. Originally tried to use darkroom photo paper as a sensor - did not work that well.
Some faffing around with MATLAB, creating a n-body simulation. Comparing various integration methods.