Vector: Mathematical Transformation

Exploring the elegant language of space and time

Inspired by "Vector: A Surprising Story of Space, Time, and Mathematical Transformation" by Robyn Arianrhod

Vector A

A = (3.0, 2.0)
|A| = 3.6

Vector B

B = (1.0, 3.0)
|B| = 3.2

Transformation

Vector Properties

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.

Mathematical Transformation

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.

Space and Time

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.

Dot Product

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.