Elco13

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Posts

  • : New website design
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    Projects

  • : Multivariable Calculus Extension Questions
    • I had the opportunity in my Multivariable Calculus class this past school year to explore a wide variety of extension questions. I was able to further pursue, alongside another classmate of mine, one of our own theorems which we had conjectured in class, and we ended up being able to prove this theorem together (it relates to what makes certain vector fields have path independence and thus be conservative). While it's obviously not a new or special result, it was really fun to try and explore further into content in the class while we learned it.
  • : Cryptography Tests
    • These are some programs I wrote while interested in cryptography during my Computational Problem Solving class (wherein we made a rudimentary implementation of the RSA algorithm). I pursued a couple projects beyond the basic requirements for the class which are linked above.
  • : 16k Digits of Pi
    • For Pi Day, I tried writing a program (using only my own math knowledge in my head at the time) to estimate as many digits of π as I could. The result is the codebase linked above, which contains my own program written in C that uses the GNU MP Bignum Libary to accurately compute 16k digits of π.
  • : Pendulum(s)
    • After initially implementing a simulated simple pendulum using my knowledge from AP Physics 1 (alongside a little calculus), I wanted to try and implement a double pendulum. This led me to researching the principle of least action and the Euler-Lagrange equations for a double pendulum. Using those equations, I was then able to simulate a double pendulum quite successfully (although there are still some issues I'd like to square out).
  • : 3D Renderer in Desmos
    • After a particularly interesting Linear Algebra class, I was able to create animated orthographic projections of 3D objects from their vertices (using a cube and an icosahedron).
  • : Paint
    • This simple MS Paint-like application was made in 8th grade (it was my creative project for my high school application). It uses jQuery and works on both mobile and desktop devices. I had a really good time learning how to write multi-file frontend JavaScript applications and the end result is a pretty useful application for basic drawing. Both before this project and after, I've built a lot of HTML5 Canvas applications, so look out for more of those to be posted soon.
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    About

    Hi, I'm Cruz. Welcome to my website. I like mathematics, running, programming, physics, and really anything that interests me. Above all else, I am a proud Catholic. I hope you enjoy my website, and I hope you have a great day!

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