Update: New Pages and Polar Coordinates

Hello! I have been busy this month with science fair and with making new pages for this blog. I have added a page for the project my partner, Azja Czajkowski, and I brought to the Greater San Diego Science and Engineering Fair. I also added a page for my (actual) experiments. Although there currently is not much on that page, I will be uploading more files there soon. Please check out those pages by following the links above!

I also have something else that was too short to be worthy of its own post.

Polar vs. Cartesian Coordinates

When I was learning Calculus BC, I was confused by polar coordinates. Although I understood how to plot points, trigonometric functions confused me. How could a sine function become a circle? How did shifting the sine function up or down in Cartesian coordinates cause the polar graph to turn into an odd loop shape? This program (link to code) helped me understand how polar coordinates worked. The reason why a loop shape comes out of a vertically shifted sine function is because a normal sine function actually drew the circle twice. Shifting the function up or down would shift where the point was drawn (the radius). I could also understand the parallels between polar and Cartesian coordinates, and it helped me realize how easy polar coordinates were.

Here is a video demonstration of the program (link).polar


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