Exploring the elegant language of space and time
Inspired by "Vector: A Surprising Story of Space, Time, and Mathematical Transformation" by Robyn Arianrhod
Vectors have both magnitude (length) and direction. They represent quantities like velocity, force, and electromagnetic fields. The beauty of vectors lies in their ability to describe how things move and interact in space.
Vectors can be rotated, scaled, and combined through mathematical operations. These transformations preserve the essential relationships between quantities, allowing us to understand physics across different reference frames.
Vector calculus provides the language for describing how fields change over space and time. This mathematical framework enabled Maxwell's electromagnetic theory and Einstein's relativity.
A · B = 9.0
The dot product measures how much two vectors point in the same direction. It's fundamental to calculating work, energy, and projections.