A mathematical journey

\(\newcommand{\atantwo}{\text{atan2}} \) \(\newcommand{\R}{\mathbb{R}} \) \(\newcommand{\C}{\mathbb{C}} \) \(\newcommand{\Q}{\mathbb{Q}} \) \(\newcommand{\N}{\mathbb{N}} \) \(\newcommand{\vec}[1]{\boldsymbol{\mathbf{#1}}} \) \(\newcommand{\ver}[1]{\boldsymbol{\mathbf{\hat #1}}} \) \(\newcommand{\tensalg}[1]{\mathcal{T}(#1)} \) Disclaimer: This is a really old post I reposted here because I think it might be interesting. I would definitely approach some things Read more…

How to escape a surface: Part 1

\(\newcommand{\atantwo}{\text{atan2}} \) \(\newcommand{\sgn}{\text{sgn  }} \) \(\newcommand{\R}{\mathbb{R}} \) \(\newcommand{\vec}[1]{\boldsymbol{\mathbf{#1}}} \) \(\newcommand{\ver}[1]{\boldsymbol{\mathbf{\hat #1}}} \) \(\newcommand{\tensalg}[1]{\mathcal{T}(#1)} \) Prerequisites: Trying to understand polar coordinates How to build stuff out of vector spaces Welcome back to the humble world of understanding polar coordinates, for the Read more…

How to build stuff out of vector spaces

\(\newcommand{\atantwo}{\text{atan2}} \) \(\newcommand{\R}{\mathbb{R}} \) \(\newcommand{\vec}[1]{\boldsymbol{\mathbf{#1}}} \) \(\newcommand{\ver}[1]{\boldsymbol{\mathbf{\hat #1}}} \) \(\newcommand{\tensalg}[1]{\mathcal{T}(#1)} \) First post: Trying to understand polar coordinates Welcome to the second installment of this post series! Plot twist: The next posts will have nothing to do with polar coordinates. They Read more…

Trying to understand polar coordinates

\(\newcommand{\atantwo}{\text{atan2}} \) \(\newcommand{\R}{\mathbb{R}} \) \(\newcommand{\vec}[1]{\boldsymbol{\mathbf{#1}}} \) \(\newcommand{\ver}[1]{\boldsymbol{\mathbf{\hat #1}}} \) \(\newcommand{\tensalg}[1]{\mathcal{T}(#1)} \) Everyone seems comfortable with polar coordinates when they see them.  Just another way to describe points on a plane, right? Not for me. For some reason, they made me Read more…