In preparation for college apps, I went through all of my independent projects up until this point and put together the most compelling projects I had worked on.

Mathematics subjects

Investigation of inverse functions

I compared the relationship between exponential and logarithmic functions with trigonometric and inverse trigonometric functions.

Investigation of the definite integral of sin(x)

With a unit circle interpretation of trigonometric functions, the definite integral of sin(x) from 0 to pi/2 seems to sweep out the area of a pi/2 sector of a circle. However, this integral evaluates to 1.

Attempting to measure the period of the length of fibonacci numbers

Calculating the area under a curve using triangles

Examination of optimal circle packing

Defining three-dimensional objects using transformations of two-dimensional objects

Equation showing the curvature of sin(x)

Experimentation with prime numbers

Explanation of cos x^2

Exploration of exponents and natural logs

Exploration of the rate at which a function diverges/converges

Finding a constant relating the length of fibonacci numbers

Investigation of the birthday paradox and the newly coined “permutation space”

Integral of sin(x)

Permutation of ratios

Relationship between i and phi

Understanding the exponent e^x

Unit Circle - Secant, Cosecant, Cotangent (for a colleague)

Physics subjects

Graph of 3D electric force field

Explanation of displacement (for a colleague)

Force on a particle between two particles

Social subjects

The Art of Nonconformity

Social justice and capitalism

Humanities

Circle of Knowledge

Candid Poems & Some Neurotheology

Psychology, encoding, and Dvorak

Trying to prove God is not real