| Title | Description |
| Angles and Roots | A collection of applets that focus on angles of circles, opposite angles in cyclic quadrilaterals, and natural roots. |
| Math Insight | A collection of applets that target higher level math courses such as Linear Algebra, and Calculus I II and III. Each applet is arranged in alphabetical order. |
| IntMath | A collection of applets that range between Algebra, Calculus, Probability, and Art. Each applet is separated by its category. |
| Directory | A collection of applets that are separated into categories of Geometry, Algebra, Functions, Fractions, and Other. |
| Math Warehouse | A collection of applets that are applicable to Geometry, Algebra, and Trigonometry. These applets are sorted by alphabetical order within topics. |
Here is a link to my original geogebra applet, titled
Fibonacci Circles.
Motivation: My motivation for this assignment was to find a different representation to show the Fibonacci Sequence and golden ratio without using the squares which results in the golden spiral.
To get something new and different, I tried recreating the golden spiral with different shapes.
I started out with regular polygons: triangles, pentagons, and hexagons.
With triangles, I found that the beginning was not able to resemble the Fibonacci sequence because I needed three triangles all of length 1 instead of only two.
Eventually, it formed a spiral but upon closer examination, it was a different shape of spiral that didn't build from the golden ratio.
The pentagons and hexagons were also a bust because no matter the arrangement, a uniform spiral did not appear.
Therefore, I decided to try out circles because I remembered reading about golden angles.
I wasn't sure how to build the circles from the previous circles and form a spiral, but by playing around with it I started to notice a pattern with the radius of the circle and where I would build the next circle.
Instead of creating a spiral, I found that I could create a linear growth of circles.
Then I started to wonder how I could find the scale factor for these circles and demonstrate where they would land in regard to the first circle centered at the origin.
This is how I started got to thinking about a line that goes through the tops of the circles.
Eventually I found that the equation for the line that predicts the highest point of the circles to correspond to the golden ratio.
The golden ratio is 1.618, and in my paper, I discuss how 1.618-1=0.618 is the same thing as 1/1.618=0.618.
Therefore, the slope of the line is one less than the golden ratio, or the inverse of the golden ratio.
New Feature: I used the best fit line, which I found the call to best fit line, and then you type all of the points that you want to include.
I wanted to see if the two lines would be the same, however, since the first three circles have points at much different heights, it altered the slope and the intercept quite a bit.
I learned that you can fit other things such as points that resemble an exponential curve or a growth curve.
You can also fit points and a function.
There are a lot of possibilities when wanting to fit different things.