Koch Snowflake






UFO Animation

To perform the UFO animation, you must first put in the picture of the UFO. This will be done by clearing the previous drawings and tuning off the axes, then entering x and y coordinates to make the desired shape.



Next, we need to move it up and to the right. This is done by adding to the y and x values respectively. We can loop this so it repeats, and will rise move in small increments without having to repeat ourselves.



Now, to change the size, we just multiply the x and y values by some number greater than 1 multiple times, and we can return it to its original size doing the same process with division. This works because the UFO is centered on the origin. If it were not, then multiplication would also move it right or left, rather than just increasing the size.



Finally, to move the UFO up and to the left, simply add to the x and y values.



Riemann Sums revisited



Discussion Questions

UFO- The transformations of the UFO graph are very simple, and using a calculator makes them even easier. Rather than having to find each iteration of the UFO as it travels, you can have the calculator redraw it at each step, handling the calculations much faster. This program is helpful for someone to picture what a transformation is in terms of x and y change, and how being in different quadrants of a graph could change what a multiplicative transformation means visually.