Surface (mathematics)

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/surface-mathematics

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. What is a surface in math?A surface is a shape that locally looks like a flat piece of paper, having two dimensions.
2. Why do surfaces have curvature?Curvature shows how a surface bends, and mathematicians like Gauss studied it to understand shapes like spheres.

Manifold: A topological space that locally resembles Euclidean space of a given dimension.
Homeomorphism: A continuous transformation between two spaces that has a continuous inverse, preserving topological properties.
Genus: A topological invariant representing the maximum number of non-intersecting simple closed curves that can be drawn on a surface without separating it.
Tangent Space: The set of all possible velocity vectors of curves passing through a point on a surface.