## Jeremy Côté

Bits, ink, particles, and words.

# The Distance Formula (Equation Explainer)

The distance formula is one of the most frequently used relations in physics, allowing us to decompose a variety of vectors into different components. It’s something that every physics student uses, and so it becomes second-nature for most of us. However, I’ve come across the sad fact that many secondary schools don’t seem to teach how the distance formula comes about and its connections with earlier work. As such, the link between algebra and geometry is lost and the distance formula gets lost in calculating differences between \$x\$ and \$y\$. Here, the goal is for us to look at the distance formula and see how it relates to other concepts that are of much use.

# Examples Before Abstraction

When learning a new topic, there’s always a certain tension between two approaches: going straight to abstraction, or starting off easier with examples. I see this more and more as I learn about more complex and detailed physics and mathematics, and it has always made me wonder which way I should go about trying to learn. Just like anyone else, I want to get to a place where I feel fully comfortable with the concept in abstraction, but I don’t want to subject myself to a painful learning process by hitting myself against the brick wall of abstraction.