Gabriel's horn

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/gabriel-s-horn

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 discoverer and date?Evangelista Torricelli, mid-17th century
2. What is the key mathematical property?Infinite surface area and finite volume
3. How can a shape that goes on forever have only a finite volume?When the curve y = 1/x is turned around the x‑axis, it gets thinner as it goes farther out. Adding up all the tiny slices of space gives a total volume of π, a single number.
4. Why do mathematicians call it a paradox?It is called a paradox because something that goes on forever seems like it should be endless, yet math shows it has a limited size.

Solid of Revolution: A three-dimensional shape created by rotating a 2D curve around an axis.
Integral Calculus: A branch of calculus used to find areas, volumes, and sums of continuous functions.
Convergence: When an infinite series or process approaches a specific, finite value.