Catenary

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/catenary

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 the mathematical definition?The graph of the hyperbolic cosine function: y = a cosh(x/a)
2. What is the physical principle?Represents the shape of minimum potential energy for a hanging flexible cable
3. Why does a hanging chain make a U shape instead of a straight line?Because the chain’s own weight pulls every part down, and the tension grows the farther you go from the lowest point. This balance of forces creates the U‑shaped catenary.
4. How is a catenary different from a parabola?A parabola is a different curve that looks similar, but the catenary is defined by the hyperbolic cosine function, not by a quadratic equation. The two shapes are mathematically distinct.

Hyperbolic Cosine (cosh): A hyperbolic function, defined as (e^x + e^-x)/2, forming the catenary curve.
Minimal Surface: A surface that locally minimizes its surface area, like a soap film.
Compressive Force: A force that tends to shorten or squeeze an object.