Below you will find my posts on math and programming sorted in reverse chronological order. Generally, I will write about key insights that allowed me to obtain a better understanding of a particular topic, in the hopes that this information is useful to someone. I will also write about topics that I find interesting, but typically only if I have some additional insight that a quick web search or elementary textbook will not reveal. Finally, I enjoy writing posts that introduce someone without the requisite background to key mathematical concepts. I believe that everyone should be allowed a glimpse into the beauty of mathematics - if they have the desire - even though they may not possess the time or inclination to take the mathematical journey themselves.
The Singular Value Decomposition (SVD) is an incredibly useful tool with a staggering number of applications in seemingly unrelated fields. In this post I want to write about how the SVD is utilized to determine the orientation of a body segment from the skin markers attached to it. It's an interesting application of the SVD because it has straightforward geometrical interpretation.
In this post I want to explore a simple insight about rotating between two orientations. Rotations are notoriously confusing and unintuitive, as evidenced by the fact that Wikipedia lists six different formalisms for representing rotations. Rotations are important to understand, however, because they play an integral role in physics, robotics, biomechanics, 3D animations, and a multitude of other disciplines.