1. Dot product, angle, and cosine similarity
The dot product measures alignment. Cosine similarity divides out length and keeps only direction.
2. Same pattern, different size
Scale Bob's ratings. Distance changes, but cosine similarity stays at 1 when Bob is a positive multiple of Alice.
3. Distance versus cosine
Move point B. Compare the question “How far?” with “How aligned?”
4. Correlation is centered cosine similarity
Change two three-entry score vectors. The app shows raw cosine similarity and centered cosine similarity.
5. Mini document search
A query is compared with five document vectors using cosine similarity.
6. High-dimensional angle simulator
Random vectors in high dimensions tend to be nearly orthogonal. Run the simulation and watch the cosine distribution concentrate near 0.