The Story of Eratosthenes: How Geometry Measured the Earth

Real-world math can feel hard to illustrate in everyday life, but powerful stories from history show just how much simple geometric thinking can help us understand the world. One of the most extraordinary examples is the discovery made by Eratosthenes—an ancient Greek scholar who measured the size of the entire Earth using nothing more than sunlight, shadows, and basic geometry. His clever method reveals how mathematical thinking can spark curiosity and inspire children to see math as a tool for solving big, exciting problems.

A Sunlit Observation

Eratosthenes (pronounced Err-uh-TOS-thuh-neez) was born around 276 BC and later became the chief librarian at the world-famous Library of Alexandria. A true polymath, he studied mathematics, astronomy, geography, poetry, and philosophy.

One day, he read a fascinating report from Syene (modern-day Aswan, Egypt). On the summer solstice—the longest day of the year—the sun’s rays shone directly into a deep well at noon, creating no shadow at all. To most people, this was just an interesting phenomenon. But to Eratosthenes, it was a clue.

A Clever Calculation

Eratosthenes compared Syene’s observation with what he saw in Alexandria, a city directly north. On the same day and time, a vertical stick in Alexandria did cast a shadow.

Instead of dismissing the difference, he used it to uncover the Earth’s shape and size.

Measuring the Shadow

He placed a simple gnomon (a vertical stick) into the ground in Alexandria.
At noon on the solstice, the shadow formed an angle of about 7.2°.

Because he already believed the Earth was spherical, Eratosthenes realized that the difference in shadow angles reflected the curvature of the Earth. Sunlight travels in parallel rays, so any angle difference must come from the Earth’s curved surface—a direct application of basic geometry.

Finding the Distance

To solve the problem fully, he needed to know the distance between Syene and Alexandria.
He relied on bematists, professional distance-walkers, who measured it to be 5,000 stadia—an ancient Greek unit of length.

Calculating the Earth’s Circumference

With both measurements in hand—an angle and a distance—Eratosthenes set up a simple proportion.

Using Geometry to Scale Up

A full circle is 360°.
His shadow measurement was 7.2°.

Therefore:

7.2° is 1/50 of a circle
(360 ÷ 7.2 = 50)

So, the distance from Syene to Alexandria represented 1/50 of Earth’s total circumference.

He multiplied:

5,000 stadia × 50 = 250,000 stadia

A Remarkably Accurate Result

Scholars debate the exact length of a “stadia,” but most estimates place his final result between:

24,000 and 29,000 miles

The modern value is 24,901 miles—meaning Eratosthenes’ estimate was astonishingly close, especially for a calculation made more than 2,200 years ago using only simple tools and clear reasoning.

Why This Story Matters for Children Today

Eratosthenes’ discovery is more than a historical curiosity. It shows children that:

• Math explains real phenomena, not just worksheets
• Geometry builds critical thinking, observation, and reasoning
• Big problems can be solved using simple ideas applied creatively
• Curiosity fuels innovation

Real-world math stories like this help kids see math as exciting and meaningful—something that connects directly to how the world works.

Support Your Child’s Math Thinking

At Think Academy, we help students build the same reasoning skills that Eratosthenes used—observation, logic, and geometric understanding.

If you want to know whether your child is on track for strong math growth:

Try the Think Academy Math Evaluation

It identifies your child’s current level and provides a personalized learning path tailored to school success and long-term math advancement, from foundational skills to honors and competition-level pathways.

About Think Academy

Think Academy, part of TAL Education Group, helps K–12 students succeed in school today by building strong math foundations and critical thinking skills. At the same time, we focus on the bigger picture—developing learning ability, curiosity, and healthy study habits that inspire a lifelong love of learning. With expert teachers, proven methods, and innovative AI tools, we support every child’s journey from classroom confidence to long-term growth.

To access Think Academy’s free math worksheets for students in PreK through Grade 12, download them here.

Want more insights into math learning and parenting? Fill out the form on this page and subscribe to our newsletter for weekly tips and the latest resources.