Vector Similarity Game - Instructions

Welcome to the Vector Similarity Game! This game is designed to help you understand the concept of cosine similarity between vectors.

Understanding Cosine Similarity

Cosine similarity measures the cosine of the angle between two non-zero vectors in a multi-dimensional space. It's a value between -1 and 1, where 1 means the vectors are identical, 0 means they are orthogonal (independent), and -1 means they are completely opposite.

The formula for cosine similarity is:

\( \text{Cosine Similarity} (A, B) = \frac{A \cdot B}{\|A\| \|B\|} \)

where \( A \cdot B \) is the dot product of vectors A and B, and \( \|A\| \) and \( \|B\| \) are the magnitudes (lengths) of vectors A and B.

How to Play

1. Two vectors will be displayed on the screen as dots.
2. Your task is to guess the cosine similarity between these two vectors.
3. Type your guess in the input box. The guess should be a number between -1 and 1.
4. Submit your guess and see how close you were to the actual cosine similarity.
5. The game consists of 5 rounds. Try to get as close as possible in each round!

Scoring

Your score is based on how close your guess is to the actual cosine similarity. The closer you are, the better your score!

Good luck and have fun!

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