Desmos Polar Graphs

In this project, I explored polar graphs by using Desmos to create fun, visually-appealing graphs.

This was the first piece of art I created.  Rose graphs can be created using the r=asinbtheta.  I utilized this equation along with the slider function on Desmos to create this pretty flower design.  The best part?  It's completely math-powered!  Here is the function I used:

Moving the "a" slider left and right adjusts the size of the graph.  Both positive and negative numbers yield the same results - if I had used 3.3 for "a" rather than -3.3, the graph would have been the same size.

Moving the "b" slider left and right adjusts the number of petals and the design of the rose.  

For example, here is the graph where b=1.1:

Here, b=2.5:

And here, b=3:

Each graph is drastically different depending on the value of "b."

Rose graphs were just one of the types of graphs we explored using Desmos.  We also learned about limacon graphs and "Spiral of Archimedes" graphs.  Limacon graphs use the equation r=a+bsin theta and create two interlocking circles.  The "Spiral of Archimedes" can be created using the equation r=theta.

I then used all of the polar graphs we learned and combined them into one crazy graph!

I used the following equations to create this graph.

College Loans

I will likely utilize a government subsidized loan.  With a subsidized loan, you aren't required to begin making payments until you graduate.

If I took out a $5,000 loan for each of my first four years of college, I would have a total loan amount of $20,000.  Therefore, P=20,000.  The interest rate on a subsidized loan is 3.86%, so r=0.0386.  I will pay back the loan over 20 years, so t=20.
A=P(1+r)^t
A=20,000(1.0386)^20   = $42,657.59 total/240 months = $177.74 per month = $41.02 per week = $5.84 per day

Other loan options include government non-subsidized loans, credit union loans, or bank loans.  Non-subsidized loans have an interest rate of 3.86%, like subsidized loans, but payments begin before graduating.  The interest rate on credit union loans begins at 2.76% for a variable rate private student loan and 6.74% for a fixed rate private student loan.  A typical bank loan would have an interest rate of 5.49%.

Geogebra Art

I created this piece of art using geogebra.  I used many different functions to achieve the finished result.  The families of functions I used included sin, cos, tan, sec, and cot.  The functions I used were as follows:

Using positives, negatives, and fractions I was able to create a unique piece of art featuring many different types of functions and graphs.  The addition of colors pushed it past the point of gaudy and into the realm of extraordinary!