Homotopy

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/homotopy

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. How big is Homotopy?Topological Data Analysis (TDA) for feature extraction from complex datasets
2. What is the mathematical discipline?Topology, specifically Algebraic Topology
3. What is homotopy in simple words?Homotopy is like stretching a rubber band without breaking it; it shows when two shapes can be changed into each other smoothly.
4. How does homotopy help compare shapes?It lets us group shapes that can be stretched or squished into each other, even if they look different at first.

Topological Space: A set equipped with a topology, defining notions of open sets, continuity, and convergence.
Continuous Map: A function between topological spaces that preserves the structure of open sets.
Homotopy Class: An equivalence class of continuous maps under the relation of homotopy.
Fundamental Group (π1): The group of homotopy classes of loops based at a point in a topological space.